Estimation Of Long-Term Sediment Loads In The Fitzroy Catchment, Queensland, Australia

Size: px
Start display at page:

Download "Estimation Of Long-Term Sediment Loads In The Fitzroy Catchment, Queensland, Australia"

Transcription

1 Estmaton Of Long-Term Sedment Loads In The Ftzroy Catchment, Queensland, Australa Joo, M., 2 B. Yu, B. Fente and 3 C. Caroll Natural Resources and Mnes, 80 Meers Rd Indoorooplly Qld 4068 Emal: Maranna.Joo@nrm.qld.gov.au 2 Faculty of Envronmental Scences, Grffth Unversty, Nathan Qld 4. 3 Natural Resources and Mnes, Bolsover St, Level 2, Rockhampton Qld Keywords: Sedment ratng curves; sedment, Ftzroy catchment EXTENDED ABSTRACT Wth a catchment area of nearly 40,000 km 2, the Ftzroy dscharges a sgnfcant amount of sedment to the Great Barrer Reef lagoon. Sedment dscharge s related to water turbdty whch has a drect mpact on coastal ecosystems. Prevous estmates of the long-term average sedment of the Ftzroy vary greatly Mt ( Mt = 9 kg). These estmates, however, were mostly based on an extrapolaton of sedment s other catchments n Queensland. In addton, sedment s major trbutares of the Ftzroy have not been assessed for nternal consstency n the estmated sedment s. Measured total suspended solds (TSS) concentratons sx stes n the Ftzroy were used to develop sedment ratng curves. Sedment ratng curves were corrected usng smearng estmates to remove an nherent bas as a result of log-transformaton. These ratng curves combned wth streamflow data were used to estmate long-term mean sedment of the Ftzroy and ts man trbutares for a common 30-year perod Sedment ratng curves for the sx stes show consderable smlarty, and varaton n sedment dscharge at gven flow rates s consderably larger than between-ste varatons n the expected sedment dscharge at the flow rate. The mean sedment was estmated to be 3.09 Mt for the Ftzroy at the Gap for the 30-year perod (see Table below). Most of the sedment of the Ftzroy comes the Nogoa and Comet subcatchments. The combned s of the four major trbutares are consstent wth the total estmated for the Ftzroy at the Gap. Load estmated for the MacKenze ste appeared to be low. At gven level of runoff, sedment concentraton on average was hghest for the Nogoa and Comet subcatchments, and the lowest for the Isaac. An ntensfed perod of water qualty montorng snce 993 concded wth a perod of relatvely low streamflow. for the perod was about half, on average, of the 30-year perod nvestgated. Gaugng Staton Ste locaton, mean flow, and sedment s n the Ftzroy for the perod of Rver Locaton Catchment area (km 2 ) dscharge (GL) sedment Upper 95% predcton nterval of Lower 95% predcton nterval of 3029A Nogoa Duck Ponds 27, A Comet 7.2 km 6, A Isaac Yatton 9,79 2, A MacKenze Coolmarnga 76,645 3, A Dawson Beckers 40, A Ftzroy The Gap 35,757 5,

2 . INTRODUCTION The Ftzroy s the largest coastal catchment n Queensland. Wth a catchment area of nearly 40,000 km 2, the Ftzroy dscharges a sgnfcant amount of sedment to the Great Barrer Reef lagoon. Sedment dscharge s related to water turbdty, whch has a drect mpact on coastal ecosystems. It s therefore mportant to accurately determne the amount of sedment the Ftzroy carres to the coastal areas. The Ftzroy basn s a prorty catchment n the Natonal Acton Plan for Salnty and Water Qualty (NAPSWQ), and has been dentfed as a hgh mpact catchment n the Great Barrer Reef Marne Protecton Plan. Prevous estmates of the long-term average sedment of the Ftzroy vary greatly. Belpero (979) estmated a mean of 2.5 Mt ( Mt = 9 kg) for the Fztroy by assumng the sedment ratng curve (an emprcal relatonshp between water dscharge and sedment dscharge) derved for the Burdekn rver.. Moss et al (992) assumed a constant flow-weghted sedment concentraton of 250 mgl - for catchments south of the Burdekn. Ths would lead to a mean of.3 Mt usng the streamflow data for the Ftzroy at the Gap (see Table 2). Nel and Yu (996) modelled sedment ratng curves for sx catchments n Queensland, and developed relatonshps between runoff (mm) and mean sedment per unt area per unt runoff (t km - mm - ). Usng ths method, Nel and Yu (996) estmated a mean sedment of 2.4 Mt for the Ftzroy under natural condtons and up to.3 Mt when the catchment s fully dsturbed as a result of agrcultural producton and urbansaton. Prevous nvestgatons are mostly based on extrapolaton of results other catchments n Queensland. Estmates of sedment s of the Ftzroy have been derved measured total suspended solds (TSS) concentratons for the catchment. In addton, sedment s major trbutares of the Ftzroy have not been assessed for nternal consstency n the estmated sedment s. Spatal dstrbuton of sedment and sedment budget on a long-term bass are mportant for valdatng spatal sedment yeld models such as SedNet (Fente et al. 2005). Ideally, streamflow and TSS concentraton are contnuously montored so that the total sedment s can be determned by ntegratng nstantaneous s for the requred perod at a partcular ste. In the absence of extensve and contnuous long-term montorng of TSS concentratons, sedment s commonly estmated usng sedment ratng curves. Wth sedment ratng curves, long-term flow records can be used to estmate nstantaneous s so that the total or average s can be estmated for the requred perod. The lmtatons of usng ratng curves are many and generally known. These nclude a lack of sedment samples durng hgh flows, samplng for certan flow ranges, dsparate sedment dscharge durng rsng and fallng stages of the hydrograph, varatons n TSS concentraton as a result of dfferent sedment generaton mechansms and dfferent locatons of the centre of storm events. Large varatons around the ratng curves lead to uncertantes about the functonal form of the ratng curves and parameter values assocated wth the ratng curves. Despte these lmtatons, wth rregularly collected TSS concentraton data, ths method remans the best avalable, and most accepted one to use to estmate long-term sedment s. The objectves of ths paper are to develop dscharge-sedment relatonshps for sx stes n the Ftzroy catchment, to estmate long-term sedment s for a common 30-year perod, and to assess the qualty of the estmated sedment s. 2. DATA AND METHOD The man trbutares n the Ftzroy catchment are the Nogoa, Comet, Isaac, and Dawson rvers. The MacKenze collects flows the Nogoa, Comet, and Isaac. It then jons wth the Dawson the south to become the Ftzroy (Fg. ). The long-term mean streamflow of the Ftzroy s 5227 GL at the Gap (Table 2) or 39 mm. The Isaac generates most water per catchment area wth 27mm yr -, whle the Dawson has the lowest runoff of 2 mm yr - among the four major trbutares. The Queensland Department of Natural Resources and Mnes collects water qualty data, ncludng TSS concentraton, under ts Surface Water Ambent Network program, snce the 970s and more ntensvely snce 990s. Ths program provdes a large amount of TSS concentraton data to allow an estmaton of long-term sedment s throughout the Ftzroy catchment. For ths study, all avalable TSS concentraton and flow data were extracted the Department s HYDSYS surface water database for the perod between 974 and 2003 when the data were most complete. 62

3 Nogoa 2. Comet 3. Isaac 4. MacKenze 5. Dawson 6. Ftzroy began n 993 under the Department s Surface Water Ambent Network program. Both low (<80 percentle) and hgh flows (>80 percentle) were well sampled at all stes, however the upper 2 percentle of flows were well sampled only at the Nogoa and Ftzroy stes, moderately sampled n the MacKenze and poorly sampled n the Comet, Isaac, and Dawson stes. In terms of maxmum dscharge sampled relatve to the maxmum dscharge on record, the rato was 65% for the Ftzroy ste, 45% for the Comet and Dawson stes, 35% for the Nogoa, 8% for the MacKenze, and was only 5% for the Isaac. Fgure. Subcatchments and TSS samplng stes n the Ftzroy catchment. Long term flow data were avalable 974 at all stes except the Nogoa where flow montorng commenced only n 993. The streamflow at ths ste pror to 993 was estmated by takng the dfferences between flows of the Comet Rver at 7.2 km (30504A) and that of the MacKenze Rver at Carnangarra (area = 45,370 km 2 ) whch s just downstream the Nogoa-Comet juncton. The estmated and measured flows were compared for the perod when streamflow was measured at all three stes (Fg. 2). The scatter for hgh flows s small, although at low flows there s a large amount of scatter around the : lne. When the sedment was estmated usng observed and the estmated flow for the Nogoa, the dfference s no more than 6% n estmated sedment s for the perod 993 and Streamflow data for the Nogoa were extended to 974 to create a complete data set for the 30-year perod October 973 to September 2003 for all sx stes n the catchment. Total suspended sedment concentratons were measured occasonally the 970s at all stes except for the Nogoa where ntensve samplng m odelled (m 3/s) measured (m3/s) Fgure 2 Modelled versus measured flow, Nogoa Rver at Duck Ponds for the perod between 993 and Table. Comparson of measured and estmated mean flow and sedment s for the Nogoa ste ( ). Mea d Est d Estmaton Error (%) (GL) 2,53 2, Load Table 2. Ste locaton, mean flow, and sedment s for the perod of Gaugng Staton Rver Locaton Catchment area (km 2 ) dscharge (GL) sedment Upper 95% predcton nterval of Lower 95% predcton nterval of 3029A Nogoa Duck Ponds 27, A Comet 7.2 km 6, A Isaac Yatton 9,79 2, A MacKenze Coolmarnga 76,645 3, A Dawson Beckers 40, A Ftzroy The Gap 35,757 5,

4 Data on TSS concentratons were collected at rregular tme ntervals, often three to four tmes a year. All the TSS data were used to develop ratng curves for the ste. Measured nstantaneous sedment dscharge was calculated usng TSS concentratons and correspondng flow measurements n the form of: Q s = x * Q * C () where Q s s the nstantaneous suspended sedment s (t/d), Q the flow rate (m 3 /s), C s the TSS concentraton (mg/l), and x s a unt converson factor (0.0864). Measured nstantaneous suspended sedment dscharge was plotted aganst the flow rate for each ste and ratng curves were developed n the form of: b Q s = a Q C f (2) where a and b are regresson constants usng logtransformed flow and sedment data, and C f s a correcton factor to remove an nherent bas ntroduced as a result of log-transformaton (Ferguson 986). Smearng estmate was used to calculate ths correcton factor (Duan 983): C f = n = ε n (3) where ε s the error term, or the resdual, for each measurement: Q s ( a b log Q ) ε = log + (4) and n the sample sze. Standard error of estmates, SE, was calculated as: 2 (log log ) Q Q SE = t s + + (5 n SQQ where t s the Student s t 2 dstrbuton, s = s where s 2 s the varance, n s the sample sze, and S QQ n = ( ) 2 logq = logq. These sedment ratng curves were then used to convert contnuous dscharge measurements nto nstantaneous sedment dscharge estmates. 0.5 More detaled flow data were used n ths study, whle prevous estmates of sedment s were based on monthly and daly flows (Belpero 983; Nel and Yu 996). The tme nterval over whch the flow rate s assumed to be constant vares as sgnfcant change n water stage occurs. For the Ftzroy at the Gap, for nstance, about 50% of flow was recorded at tme ntervals less than sx hours, and 85% of the flow recorded at tme ntervals < 2 hours. Estmated sedment dscharge was ntegrated to determne long-term sedment for the 30 year perod between 974 and RESULTS AND DISCUSSION Ratng curves developed for the sx stes are presented n Fg. 3. The grey plots under each graph show all data all stes to ndcate the dstrbuton of TSS concentratons relatve to other stes n the Ftzroy catchment. Sample sze, estmated parameter values for ratng curves are presented n Table 3. Table 3 also ncludes a sedment ratng curve developed usng all avalable TSS concentraton data all sx stes. Table 3 Sample sze (n), estmated model parameters for ratngs (a and b), and standard errors (ε), for the sx stes n the Ftzroy catchments where sedment dcharge (Q s ) s n td - and dscharge (Q) s n m 3 s -. Rvers na a b ε r 2 Nogoa Comet Isaac MacKenze Dawson Ftzroy Combned data set Fg. 3 shows that of the four major trbutares of the Ftzroy, the Nogoa and Comet have hgher sedment dscharge at a gven flow rate, especally durng hgh flows. Durng low flows, the sedment dscharge s generally lower for the Nogoa than that for the Comet. The Isaac has the lowest TSS and sedment dscharge values of all stes, although TSS measurements at hgh flows are very lmted at the ste. The MacKenze receves water and sedment the Nogoa, Comet, and Isaac subcatchments and the TSS concentratons here appear to be dluted by streamflow the Isaac subcatchment. In the Dawson Rver, the TSS concentratons le n the md-ranges although measurements of TSS 64

5 TSS concentraton vs. dscharge TSS vs. dscharge Nogoa TSS (t/d) Comet 00 0 TSS (t/d) Isaac 00 0 TSS (td/) MacKenze TSS (td/) Dawson TSS (t/d) Ftzroy TSS (t/d) TSS all subcatchment TSS ndvdual subcatchments 80th percentle of flow for ndvdual subcatchments maxmum recorded flow for ndvdual subcatchments Fgure 3. Sedment flow relatonshps n the Ftzroy catchment concentraton at hgh flows are not well represented. The Ftzroy ste receves water MacKenze and the Dawson.. Fg. 3 shows that the Ftzroy and MacKenze stes have smlar sedment ratng curves, and TSS concentratons reman relatvely low at the two stes. It s nterestng to note that the varablty n the sedment-dscharge relatonshp at any one ste s greater than the varaton among dfference stes. Varatons n the expected sedment dscharge among the sx stes are consderably smaller than the varatons n measured TSS concentratons at a gven ste. From Table 3, t can be seen the standard error for the ratng curve usng combned 65

6 dataset s of a smlar magntude when compared to the standard error for ndvdual stes. It s nterestng to note that the varablty n the sedment-dscharge relatonshp at any one ste s greater than the varaton among dfference stes. Varatons n the expected sedment dscharge among the sx stes are consderably smaller than the varatons n measured TSS concentratons at a gven ste. From Table 3, t can be seen the standard error for the ratng curve usng combned data set s of a smlar magntude when compared to the standard error for ndvdual stes. Usng all the avalable concentraton data, the flow-weghted TSS concentraton of the Ftzroy at the Gap s 533 mgl -. The average TSS concentraton based on the long-term sedment and streamflow Table 2 s 59 mgl -. In both cases, the average TSS concentraton was sgnfcantly hgher than 250 mgl -, a value assumed by Moss et al (992) to assess sedment exports Queensland catchments. Of the four major trbutares of the Ftzroy, the Nogoa has the hghest sedment, followed by the Comet, the Isaac and then the Dawson subcatchments. The same pattern holds n terms of sedment yeld (sedment per unt area). The combned catchment area of the four major trbutares s 3,77 km 2, or 76% of the catchment area of the Ftzroy. The combned the four trbutares s 2.44 Mt yr -. If the s adjusted by takng nto account the dfference n the catchment area, the projected of the Ftzroy at the Gap, based on estmated s of the four trbutares would be 3.9 Mt yr -, whch s qute consstent wth estmated at the ste of 3.09 Mt yr -. Estmated sedment of the MacKenze was.73 Mt yr - (Table 2), some 0.47 Mt less than the combned the Nogoa, Comet and Isaac. Ths would suggest a net loss or deposton of sedments along the reaches downstream the three stes on the trbutares and along the MacKenze upstream Coolmarnga. On the other hand, the combned the Mackenze and the Dawson s.98 Mt yr -, whch s consderably less than the estmated of 3. Mt yr - for the Ftzroy at the Gap. The sedment budgets for the Dawson, MacKenze, and Ftzroy ndcate a consderable addton of sedments along the reaches between the three stes. It s hghly probable that the sedment of the MacKenze at Coolmarnga was underestmated, because t s unlkely to have dramatc fluctuatons n deposton and eroson along the lower catchment reaches. Confdence ntervals for estmates at 95% level are presented n Table 2. Predcton uncertantes were determned for ndvdual tme ntervals usng equaton (5) and then ntegrated over the 30 year perod. The average error bar (half the confdence nterval) s 74% on average, rangng 56% for the Isaac to 8% for the Comet. Sedment concentraton (mg/l),000, Runoff (mm) Nogoa Comet Isaac MacKenze Dawson Ftzroy Fgure 4. runoff versus flowweghted sedment concentraton n the Ftzroy catchment. The relatonshp between runoff and flow weghted mean sedment concentratons shows three dstnct clusters for the Ftzroy catchment. The Nogoa and Comet have the hghest sedment concentraton for a gven level of runoff n the Ftzroy catchment. However, n dry years wth low runoff, the sedment concentraton of the Nogoa s consderably lower than that of the Comet, whle durng wet years, Nogoa generates hgher sedment s. The second group conssts of the MacKenze, Dawson and Ftzroy. In ths group there s lttle dfference between the stes durng drer years. For wetter years, however, the Ftzroy has a hgher sedment concentraton, followed by the MacKenze and then the Dawson. The Isaac has by far the lowest flow-weghted sedment concentraton n the catchment, and the sedment concentraton at the Yatton does not change as much drer to wetter years as at other stes n the Ftzroy catchment. To assess the qualty of the estmated sedment, especally the effect of havng TSS concentraton data collected dfferent perods on the long-term estmates, we recalculated the mean for the perod between 994 and 2003 when TSS concentraton data were collected at all sx stes. In addton, we re-developed the ratng curves usng the TSS concentraton data snce 993, and re-calculated the estmates usng the new TSS data set a common perod of montorng, but wth a reduced sample sze. 66

7 Table 4 Streamflow and estmated sedment s for varous perods endng n 2003 n the Ftzroy catchment. Rvers Annual (GL) 994 Annual Sedment Load TSS TSS Nogoa Comet Isaac MacKenze, Dawson Ftzroy 2, Table 4 shows that the perod of ncreased water qualty montorng snce 993 has also been a perod of relatve low flows. flow for s only about 50% of the 30-year average ( ) for the Ftzroy at the Gap. The decrease of flow of the three major trbutares, namely the Nogoa, Comet, and Isaac, s much greater, rangng 42% to 62%. Ths decrease n flow would lead to a dramatc decrease n estmated sedment for the perod 994 to Table 4 shows that the decrease n sedment would be 65% for the Ftzroy, and vary 5% to 7% for the three trbutares mentoned above. If TSS concentratons for the common perod snce 993 for all stes are used, the amount of decrease n sedment s as a result of the reduced flow snce 994 s qute smlar. If the ratng curves for the common samplng perod snce 993 were appled to the 30 year perod, all stes except McKenze and Nogoa show a notceable ncrease n the estmated sedment. The ncrease n the estmated sedment for the Ftzroy at the Gap s qute dramatc. 4. CONCLUSION TSS concentratons and flow data for sx stes n the Ftzroy catchment were used to develop sedment ratng curves to estmate sedment dscharge for a common 30 year perod Sedment ratng curves are broadly smlar for all the sx stes nvestgated. Varatons n the expected sedment dscharge among the sx stes are consderably smaller than the varatons n measured TSS concentratons at a gven ste. The long-term sedment of the Ftzroy was estmated at 3.09 Mt yr - wth a 95% confdence about 74%. The estmated was hgher than prevous estmates based on extrapolatons other catchments n Queensland. The perod snce 994 when water qualty montorng ntensfed concded wth a perod of low flows. Sedment for the perod snce 994 was consderable lower than the longterm average. Most of the sedment came the Nogoa subcatchment the west. The sedment of the Ftzroy at the Gap s consstent wth the combned ts four major trbutares, namely the Nogoa, Comet, Isaac, and Dawson. 5. REFRENCES Belpero, A.P. (979), The combned use of wash and the bed materal ratng curves for the calculaton of total : an example the Burdekn Rver, Australa. Catena 6: Belpero, A.P. (983), Terrgenous sedmentaton n the central Great Barrer Reef lagoon: a model the Burdekn regon. BMR Journal of Australan Geology and Geophyscs 8(3): Duan, N. (983), Smearng estmate: A nonparametrc retransformaton method. J Amer. Stat. Assoc. 78: Fente, B., M. Joo, B. Yu, H. Hunter, N. March and C. Carroll (2005), Comparson of mean suspended s estmated by the Sednet model and ratng curves n the Ftzroy catchment, Australa. Ferguson, R. I. (986), Rver s underestmated by ratng curves. Water Resour. Res. 22: Moss, A.J., G. E. Rayment, N. Relly and E. K. Best (992), A prelmnary assessment of sedment and nutrent exports Queensland Coastal Catchments. Queensland Department of Envronment and Hertage Techncal Report No. 5. (Queensland Government, Brsbane, Australa) Nel, D, and Yu, B. (996), Fluval sedment yeld to the great Barrer Reef Lagoon: Spatal patterns and the effect of land use. In Downstream effects of Land Use. (Eds. H.M. Hunter, A. G. Eyles and G.E. Rayment ) pp Department of Natural Resources, Brsbane, Australa 67

Chapter 13: Multiple Regression

Chapter 13: Multiple Regression Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to

More information

Comparison of Regression Lines

Comparison of Regression Lines STATGRAPHICS Rev. 9/13/2013 Comparson of Regresson Lnes Summary... 1 Data Input... 3 Analyss Summary... 4 Plot of Ftted Model... 6 Condtonal Sums of Squares... 6 Analyss Optons... 7 Forecasts... 8 Confdence

More information

Statistical Evaluation of WATFLOOD

Statistical Evaluation of WATFLOOD tatstcal Evaluaton of WATFLD By: Angela MacLean, Dept. of Cvl & Envronmental Engneerng, Unversty of Waterloo, n. ctober, 005 The statstcs program assocated wth WATFLD uses spl.csv fle that s produced wth

More information

This column is a continuation of our previous column

This column is a continuation of our previous column Comparson of Goodness of Ft Statstcs for Lnear Regresson, Part II The authors contnue ther dscusson of the correlaton coeffcent n developng a calbraton for quanttatve analyss. Jerome Workman Jr. and Howard

More information

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.

More information

Correlation and Regression. Correlation 9.1. Correlation. Chapter 9

Correlation and Regression. Correlation 9.1. Correlation. Chapter 9 Chapter 9 Correlaton and Regresson 9. Correlaton Correlaton A correlaton s a relatonshp between two varables. The data can be represented b the ordered pars (, ) where s the ndependent (or eplanator) varable,

More information

STATISTICS QUESTIONS. Step by Step Solutions.

STATISTICS QUESTIONS. Step by Step Solutions. STATISTICS QUESTIONS Step by Step Solutons www.mathcracker.com 9//016 Problem 1: A researcher s nterested n the effects of famly sze on delnquency for a group of offenders and examnes famles wth one to

More information

Uncertainty in measurements of power and energy on power networks

Uncertainty in measurements of power and energy on power networks Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:

More information

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth

More information

STAT 511 FINAL EXAM NAME Spring 2001

STAT 511 FINAL EXAM NAME Spring 2001 STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte

More information

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased

More information

Negative Binomial Regression

Negative Binomial Regression STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...

More information

Statistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation

Statistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 13 The Smple Lnear Regresson Model and Correlaton 1999 Prentce-Hall, Inc. Chap. 13-1 Chapter Topcs Types of Regresson Models Determnng the Smple Lnear

More information

Chapter 11: Simple Linear Regression and Correlation

Chapter 11: Simple Linear Regression and Correlation Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests

More information

A correction model for zenith dry delay of GPS signals using regional meteorological sites. GPS-based determination of atmospheric water vapour

A correction model for zenith dry delay of GPS signals using regional meteorological sites. GPS-based determination of atmospheric water vapour Geodetc Week 00 October 05-07, Cologne S4: Appled Geodesy and GNSS A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes Xaoguang Luo Geodetc Insttute, Department of Cvl Engneerng,

More information

Supplementary Notes for Chapter 9 Mixture Thermodynamics

Supplementary Notes for Chapter 9 Mixture Thermodynamics Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects

More information

Economics 130. Lecture 4 Simple Linear Regression Continued

Economics 130. Lecture 4 Simple Linear Regression Continued Economcs 130 Lecture 4 Contnued Readngs for Week 4 Text, Chapter and 3. We contnue wth addressng our second ssue + add n how we evaluate these relatonshps: Where do we get data to do ths analyss? How do

More information

AGC Introduction

AGC Introduction . Introducton AGC 3 The prmary controller response to a load/generaton mbalance results n generaton adjustment so as to mantan load/generaton balance. However, due to droop, t also results n a non-zero

More information

Statistics for Business and Economics

Statistics for Business and Economics Statstcs for Busness and Economcs Chapter 11 Smple Regresson Copyrght 010 Pearson Educaton, Inc. Publshng as Prentce Hall Ch. 11-1 11.1 Overvew of Lnear Models n An equaton can be ft to show the best lnear

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VIII LECTURE - 34 ANALYSIS OF VARIANCE IN RANDOM-EFFECTS MODEL AND MIXED-EFFECTS EFFECTS MODEL Dr Shalabh Department of Mathematcs and Statstcs Indan

More information

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands Content. Inference on Regresson Parameters a. Fndng Mean, s.d and covarance amongst estmates.. Confdence Intervals and Workng Hotellng Bands 3. Cochran s Theorem 4. General Lnear Testng 5. Measures of

More information

Department of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6

Department of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6 Department of Quanttatve Methods & Informaton Systems Tme Seres and Ther Components QMIS 30 Chapter 6 Fall 00 Dr. Mohammad Zanal These sldes were modfed from ther orgnal source for educatonal purpose only.

More information

JAB Chain. Long-tail claims development. ASTIN - September 2005 B.Verdier A. Klinger

JAB Chain. Long-tail claims development. ASTIN - September 2005 B.Verdier A. Klinger JAB Chan Long-tal clams development ASTIN - September 2005 B.Verder A. Klnger Outlne Chan Ladder : comments A frst soluton: Munch Chan Ladder JAB Chan Chan Ladder: Comments Black lne: average pad to ncurred

More information

Chapter 3 Describing Data Using Numerical Measures

Chapter 3 Describing Data Using Numerical Measures Chapter 3 Student Lecture Notes 3-1 Chapter 3 Descrbng Data Usng Numercal Measures Fall 2006 Fundamentals of Busness Statstcs 1 Chapter Goals To establsh the usefulness of summary measures of data. The

More information

Chapter 5 Multilevel Models

Chapter 5 Multilevel Models Chapter 5 Multlevel Models 5.1 Cross-sectonal multlevel models 5.1.1 Two-level models 5.1.2 Multple level models 5.1.3 Multple level modelng n other felds 5.2 Longtudnal multlevel models 5.2.1 Two-level

More information

2016 Wiley. Study Session 2: Ethical and Professional Standards Application

2016 Wiley. Study Session 2: Ethical and Professional Standards Application 6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton

More information

Regulation No. 117 (Tyres rolling noise and wet grip adhesion) Proposal for amendments to ECE/TRANS/WP.29/GRB/2010/3

Regulation No. 117 (Tyres rolling noise and wet grip adhesion) Proposal for amendments to ECE/TRANS/WP.29/GRB/2010/3 Transmtted by the expert from France Informal Document No. GRB-51-14 (67 th GRB, 15 17 February 2010, agenda tem 7) Regulaton No. 117 (Tyres rollng nose and wet grp adheson) Proposal for amendments to

More information

Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 212. Chapters 14, 15 & 16. Professor Ahmadi, Ph.D. Department of Management

Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 212. Chapters 14, 15 & 16. Professor Ahmadi, Ph.D. Department of Management Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 1 Chapters 14, 15 & 16 Professor Ahmad, Ph.D. Department of Management Revsed August 005 Chapter 14 Formulas Smple Lnear Regresson Model: y =

More information

A LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS. Dr. Derald E. Wentzien, Wesley College, (302) ,

A LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS. Dr. Derald E. Wentzien, Wesley College, (302) , A LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS Dr. Derald E. Wentzen, Wesley College, (302) 736-2574, wentzde@wesley.edu ABSTRACT A lnear programmng model s developed and used to compare

More information

Multivariate Ratio Estimator of the Population Total under Stratified Random Sampling

Multivariate Ratio Estimator of the Population Total under Stratified Random Sampling Open Journal of Statstcs, 0,, 300-304 ttp://dx.do.org/0.436/ojs.0.3036 Publsed Onlne July 0 (ttp://www.scrp.org/journal/ojs) Multvarate Rato Estmator of te Populaton Total under Stratfed Random Samplng

More information

ITTC - Recommended Procedures and Guidelines

ITTC - Recommended Procedures and Guidelines Page of 9 able of Contents UCERAIY AALYSIS - EXAMPLE FOR WAERJE PROPULSIO ES... 2. PURPOSE OF PROCEDURE... 2 2. EXAMPLE FOR WAERJE PROPULSIO ES... 2 2. est Desgn... 2 2.2 Measurement Systems and Procedure...

More information

ECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics

ECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics ECOOMICS 35*-A Md-Term Exam -- Fall Term 000 Page of 3 pages QUEE'S UIVERSITY AT KIGSTO Department of Economcs ECOOMICS 35* - Secton A Introductory Econometrcs Fall Term 000 MID-TERM EAM ASWERS MG Abbott

More information

Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore

Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore Sesson Outlne Introducton to classfcaton problems and dscrete choce models. Introducton to Logstcs Regresson. Logstc functon and Logt functon. Maxmum Lkelhood Estmator (MLE) for estmaton of LR parameters.

More information

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have

More information

Uncertainty as the Overlap of Alternate Conditional Distributions

Uncertainty as the Overlap of Alternate Conditional Distributions Uncertanty as the Overlap of Alternate Condtonal Dstrbutons Olena Babak and Clayton V. Deutsch Centre for Computatonal Geostatstcs Department of Cvl & Envronmental Engneerng Unversty of Alberta An mportant

More information

Comparison of the Population Variance Estimators. of 2-Parameter Exponential Distribution Based on. Multiple Criteria Decision Making Method

Comparison of the Population Variance Estimators. of 2-Parameter Exponential Distribution Based on. Multiple Criteria Decision Making Method Appled Mathematcal Scences, Vol. 7, 0, no. 47, 07-0 HIARI Ltd, www.m-hkar.com Comparson of the Populaton Varance Estmators of -Parameter Exponental Dstrbuton Based on Multple Crtera Decson Makng Method

More information

Color Rendering Uncertainty

Color Rendering Uncertainty Australan Journal of Basc and Appled Scences 4(10): 4601-4608 010 ISSN 1991-8178 Color Renderng Uncertanty 1 A.el Bally M.M. El-Ganany 3 A. Al-amel 1 Physcs Department Photometry department- NIS Abstract:

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol Georgetown Unversty From the SelectedWorks of Mark J Meyer 8 Usng the estmated penetrances to determne the range of the underlyng genetc model n casecontrol desgn Mark J Meyer Neal Jeffres Gang Zheng Avalable

More information

NUMERICAL DIFFERENTIATION

NUMERICAL DIFFERENTIATION NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the

More information

Hierarchical State Estimation Using Phasor Measurement Units

Hierarchical State Estimation Using Phasor Measurement Units Herarchcal State Estmaton Usng Phasor Measurement Unts Al Abur Northeastern Unversty Benny Zhao (CA-ISO) and Yeo-Jun Yoon (KPX) IEEE PES GM, Calgary, Canada State Estmaton Workng Group Meetng July 28,

More information

Statistics MINITAB - Lab 2

Statistics MINITAB - Lab 2 Statstcs 20080 MINITAB - Lab 2 1. Smple Lnear Regresson In smple lnear regresson we attempt to model a lnear relatonshp between two varables wth a straght lne and make statstcal nferences concernng that

More information

Statistics for Economics & Business

Statistics for Economics & Business Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable

More information

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition)

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition) Count Data Models See Book Chapter 11 2 nd Edton (Chapter 10 1 st Edton) Count data consst of non-negatve nteger values Examples: number of drver route changes per week, the number of trp departure changes

More information

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:

More information

UNR Joint Economics Working Paper Series Working Paper No Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?

UNR Joint Economics Working Paper Series Working Paper No Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist? UNR Jont Economcs Workng Paper Seres Workng Paper No. 08-005 Further Analyss of the Zpf Law: Does the Rank-Sze Rule Really Exst? Fungsa Nota and Shunfeng Song Department of Economcs /030 Unversty of Nevada,

More information

A Robust Method for Calculating the Correlation Coefficient

A Robust Method for Calculating the Correlation Coefficient A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed

More information

Assessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion

Assessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

DECADAL DECLINE ( )OF LOGGERHEAD SHRIKES ON CHRISTMAS BIRD COUNTS IN ALABAMA, MISSISSIPPI, AND TENNESSEE

DECADAL DECLINE ( )OF LOGGERHEAD SHRIKES ON CHRISTMAS BIRD COUNTS IN ALABAMA, MISSISSIPPI, AND TENNESSEE DEPARTMENT OF MATHEMATICS TECHNICAL REPORT DECADAL DECLINE (1992-22)OF LOGGERHEAD SHRIKES ON CHRISTMAS BIRD COUNTS IN ALABAMA, MISSISSIPPI, AND TENNESSEE DR. STEPHEN J. STEDMAN AND DR. MICHAEL ALLEN AUGUST

More information

Linear Approximation with Regularization and Moving Least Squares

Linear Approximation with Regularization and Moving Least Squares Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...

More information

risk and uncertainty assessment

risk and uncertainty assessment Optmal forecastng of atmospherc qualty n ndustral regons: rsk and uncertanty assessment Vladmr Penenko Insttute of Computatonal Mathematcs and Mathematcal Geophyscs SD RAS Goal Development of theoretcal

More information

Developing a Data Validation Tool Based on Mendelian Sampling Deviations

Developing a Data Validation Tool Based on Mendelian Sampling Deviations Developng a Data Valdaton Tool Based on Mendelan Samplng Devatons Flppo Bscarn, Stefano Bffan and Fabola Canaves A.N.A.F.I. Italan Holsten Breeders Assocaton Va Bergamo, 292 Cremona, ITALY Abstract A more

More information

ANSWERS CHAPTER 9. TIO 9.2: If the values are the same, the difference is 0, therefore the null hypothesis cannot be rejected.

ANSWERS CHAPTER 9. TIO 9.2: If the values are the same, the difference is 0, therefore the null hypothesis cannot be rejected. ANSWERS CHAPTER 9 THINK IT OVER thnk t over TIO 9.: χ 2 k = ( f e ) = 0 e Breakng the equaton down: the test statstc for the ch-squared dstrbuton s equal to the sum over all categores of the expected frequency

More information

Topic- 11 The Analysis of Variance

Topic- 11 The Analysis of Variance Topc- 11 The Analyss of Varance Expermental Desgn The samplng plan or expermental desgn determnes the way that a sample s selected. In an observatonal study, the expermenter observes data that already

More information

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading xpermental Study on Ultmate Strength of Flexural-Falure-Type RC Beams under Impact Loadng N. Ksh 1), O. Nakano 2~, K. G. Matsuoka 1), and T. Ando 1~ 1) Dept. of Cvl ngneerng, Muroran Insttute of Technology,

More information

Chapter 14 Simple Linear Regression

Chapter 14 Simple Linear Regression Chapter 4 Smple Lnear Regresson Chapter 4 - Smple Lnear Regresson Manageral decsons often are based on the relatonshp between two or more varables. Regresson analss can be used to develop an equaton showng

More information

Operating conditions of a mine fan under conditions of variable resistance

Operating conditions of a mine fan under conditions of variable resistance Paper No. 11 ISMS 216 Operatng condtons of a mne fan under condtons of varable resstance Zhang Ynghua a, Chen L a, b, Huang Zhan a, *, Gao Yukun a a State Key Laboratory of Hgh-Effcent Mnng and Safety

More information

Research Article Green s Theorem for Sign Data

Research Article Green s Theorem for Sign Data Internatonal Scholarly Research Network ISRN Appled Mathematcs Volume 2012, Artcle ID 539359, 10 pages do:10.5402/2012/539359 Research Artcle Green s Theorem for Sgn Data Lous M. Houston The Unversty of

More information

β0 + β1xi and want to estimate the unknown

β0 + β1xi and want to estimate the unknown SLR Models Estmaton Those OLS Estmates Estmators (e ante) v. estmates (e post) The Smple Lnear Regresson (SLR) Condtons -4 An Asde: The Populaton Regresson Functon B and B are Lnear Estmators (condtonal

More information

Topic 23 - Randomized Complete Block Designs (RCBD)

Topic 23 - Randomized Complete Block Designs (RCBD) Topc 3 ANOVA (III) 3-1 Topc 3 - Randomzed Complete Block Desgns (RCBD) Defn: A Randomzed Complete Block Desgn s a varant of the completely randomzed desgn (CRD) that we recently learned. In ths desgn,

More information

28. SIMPLE LINEAR REGRESSION III

28. SIMPLE LINEAR REGRESSION III 8. SIMPLE LINEAR REGRESSION III Ftted Values and Resduals US Domestc Beers: Calores vs. % Alcohol To each observed x, there corresponds a y-value on the ftted lne, y ˆ = βˆ + βˆ x. The are called ftted

More information

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng

More information

Basic concepts and definitions in multienvironment

Basic concepts and definitions in multienvironment Basc concepts and defntons n multenvronment data: G, E, and GxE Marcos Malosett, Danela Bustos-Korts, Fred van Eeuwk, Pter Bma, Han Mulder Contents The basc concepts: ntroducton and defntons Phenotype,

More information

ANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)

ANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U) Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of

More information

x = , so that calculated

x = , so that calculated Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to

More information

Supporting Information

Supporting Information Supportng Informaton The neural network f n Eq. 1 s gven by: f x l = ReLU W atom x l + b atom, 2 where ReLU s the element-wse rectfed lnear unt, 21.e., ReLUx = max0, x, W atom R d d s the weght matrx to

More information

ESTIMATES OF VARIANCE COMPONENTS IN RANDOM EFFECTS META-ANALYSIS: SENSITIVITY TO VIOLATIONS OF NORMALITY AND VARIANCE HOMOGENEITY

ESTIMATES OF VARIANCE COMPONENTS IN RANDOM EFFECTS META-ANALYSIS: SENSITIVITY TO VIOLATIONS OF NORMALITY AND VARIANCE HOMOGENEITY ESTIMATES OF VARIANCE COMPONENTS IN RANDOM EFFECTS META-ANALYSIS: SENSITIVITY TO VIOLATIONS OF NORMALITY AND VARIANCE HOMOGENEITY Jeffrey D. Kromrey and Krstne Y. Hogarty Department of Educatonal Measurement

More information

Some basic statistics and curve fitting techniques

Some basic statistics and curve fitting techniques Some basc statstcs and curve fttng technques Statstcs s the dscplne concerned wth the study of varablty, wth the study of uncertanty, and wth the study of decsonmakng n the face of uncertanty (Lndsay et

More information

Regression Analysis. Regression Analysis

Regression Analysis. Regression Analysis Regresson Analyss Smple Regresson Multvarate Regresson Stepwse Regresson Replcaton and Predcton Error 1 Regresson Analyss In general, we "ft" a model by mnmzng a metrc that represents the error. n mn (y

More information

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours UNIVERSITY OF TORONTO Faculty of Arts and Scence December 005 Examnatons STA47HF/STA005HF Duraton - hours AIDS ALLOWED: (to be suppled by the student) Non-programmable calculator One handwrtten 8.5'' x

More information

Kernel Methods and SVMs Extension

Kernel Methods and SVMs Extension Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general

More information

AP Physics 1 & 2 Summer Assignment

AP Physics 1 & 2 Summer Assignment AP Physcs 1 & 2 Summer Assgnment AP Physcs 1 requres an exceptonal profcency n algebra, trgonometry, and geometry. It was desgned by a select group of college professors and hgh school scence teachers

More information

Effect of loading frequency on the settlement of granular layer

Effect of loading frequency on the settlement of granular layer Effect of loadng frequency on the settlement of granular layer Akko KONO Ralway Techncal Research Insttute, Japan Takash Matsushma Tsukuba Unversty, Japan ABSTRACT: Cyclc loadng tests were performed both

More information

Chapter 4. Velocity analysis

Chapter 4. Velocity analysis 1 Chapter 4 Velocty analyss Introducton The objectve of velocty analyss s to determne the sesmc veloctes of layers n the subsurface. Sesmc veloctes are used n many processng and nterpretaton stages such

More information

Developing regional flood frequency models for Victoria, Australia by using Index Flood (IF) approach

Developing regional flood frequency models for Victoria, Australia by using Index Flood (IF) approach 18 th World IMACS / MODSIM Congress, Carns, Australa 13-17 July 2009 http://mssanz.org.au/modsm09 Developng regonal flood frequency models for Vctora, Australa by usng Index Flood (IF) Masan, M. N 1. and

More information

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors Multple Lnear and Polynomal Regresson wth Statstcal Analyss Gven a set of data of measured (or observed) values of a dependent varable: y versus n ndependent varables x 1, x, x n, multple lnear regresson

More information

PHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University

PHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University PHYS 45 Sprng semester 7 Lecture : Dealng wth Expermental Uncertantes Ron Refenberger Brck anotechnology Center Purdue Unversty Lecture Introductory Comments Expermental errors (really expermental uncertantes)

More information

EURAMET.M.D-S2 Final Report Final report

EURAMET.M.D-S2 Final Report Final report Fnal report on ERAMET blateral comparson on volume of mass standards Project number: 1356 (ERAMET.M.D-S2) Volume of mass standards of 10g, 20 g, 200 g, 1 kg Zoltan Zelenka 1 ; Stuart Davdson 2 ; Cslla

More information

where I = (n x n) diagonal identity matrix with diagonal elements = 1 and off-diagonal elements = 0; and σ 2 e = variance of (Y X).

where I = (n x n) diagonal identity matrix with diagonal elements = 1 and off-diagonal elements = 0; and σ 2 e = variance of (Y X). 11.4.1 Estmaton of Multple Regresson Coeffcents In multple lnear regresson, we essentally solve n equatons for the p unnown parameters. hus n must e equal to or greater than p and n practce n should e

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

STAT 3008 Applied Regression Analysis

STAT 3008 Applied Regression Analysis STAT 3008 Appled Regresson Analyss Tutoral : Smple Lnear Regresson LAI Chun He Department of Statstcs, The Chnese Unversty of Hong Kong 1 Model Assumpton To quantfy the relatonshp between two factors,

More information

Improvement of Histogram Equalization for Minimum Mean Brightness Error

Improvement of Histogram Equalization for Minimum Mean Brightness Error Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, 7 3 Improvement of Hstogram Equalzaton for Mnmum Mean Brghtness Error AAPOG PHAHUA*,

More information

Continuous vs. Discrete Goods

Continuous vs. Discrete Goods CE 651 Transportaton Economcs Charsma Choudhury Lecture 3-4 Analyss of Demand Contnuous vs. Dscrete Goods Contnuous Goods Dscrete Goods x auto 1 Indfference u curves 3 u u 1 x 1 0 1 bus Outlne Data Modelng

More information

Answers Problem Set 2 Chem 314A Williamsen Spring 2000

Answers Problem Set 2 Chem 314A Williamsen Spring 2000 Answers Problem Set Chem 314A Wllamsen Sprng 000 1) Gve me the followng crtcal values from the statstcal tables. a) z-statstc,-sded test, 99.7% confdence lmt ±3 b) t-statstc (Case I), 1-sded test, 95%

More information

Statistics Chapter 4

Statistics Chapter 4 Statstcs Chapter 4 "There are three knds of les: les, damned les, and statstcs." Benjamn Dsrael, 1895 (Brtsh statesman) Gaussan Dstrbuton, 4-1 If a measurement s repeated many tmes a statstcal treatment

More information

Linear Regression Analysis: Terminology and Notation

Linear Regression Analysis: Terminology and Notation ECON 35* -- Secton : Basc Concepts of Regresson Analyss (Page ) Lnear Regresson Analyss: Termnology and Notaton Consder the generc verson of the smple (two-varable) lnear regresson model. It s represented

More information

REAL-TIME DETERMINATION OF INDOOR CONTAMINANT SOURCE LOCATION AND STRENGTH, PART II: WITH TWO SENSORS. Beijing , China,

REAL-TIME DETERMINATION OF INDOOR CONTAMINANT SOURCE LOCATION AND STRENGTH, PART II: WITH TWO SENSORS. Beijing , China, REAL-TIME DETERMIATIO OF IDOOR COTAMIAT SOURCE LOCATIO AD STREGTH, PART II: WITH TWO SESORS Hao Ca,, Xantng L, Wedng Long 3 Department of Buldng Scence, School of Archtecture, Tsnghua Unversty Bejng 84,

More information

Lecture 6: Introduction to Linear Regression

Lecture 6: Introduction to Linear Regression Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6

More information

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH Turbulence classfcaton of load data by the frequency and severty of wnd gusts Introducton Oscar Moñux, DEWI GmbH Kevn Blebler, DEWI GmbH Durng the wnd turbne developng process, one of the most mportant

More information

Global Sensitivity. Tuesday 20 th February, 2018

Global Sensitivity. Tuesday 20 th February, 2018 Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values

More information

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Regression Analysis

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Regression Analysis Resource Allocaton and Decson Analss (ECON 800) Sprng 04 Foundatons of Regresson Analss Readng: Regresson Analss (ECON 800 Coursepak, Page 3) Defntons and Concepts: Regresson Analss statstcal technques

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data

More information

Effective plots to assess bias and precision in method comparison studies

Effective plots to assess bias and precision in method comparison studies Effectve plots to assess bas and precson n method comparson studes Bern, November, 016 Patrck Taffé, PhD Insttute of Socal and Preventve Medcne () Unversty of Lausanne, Swtzerland Patrck.Taffe@chuv.ch

More information

/ n ) are compared. The logic is: if the two

/ n ) are compared. The logic is: if the two STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence

More information

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number

More information

DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION

DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION Internatonal Worshop ADVANCES IN STATISTICAL HYDROLOGY May 3-5, Taormna, Italy DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION by Sooyoung

More information

χ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body

χ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown

More information

Chapter 9: Statistical Inference and the Relationship between Two Variables

Chapter 9: Statistical Inference and the Relationship between Two Variables Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,

More information