Scatter Plot x

Transcription

1 Construct a scatter plot usng excel for the gven data. Determne whether there s a postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton. Complete the table and fnd the correlaton coeffcent r. The data for x and y s shown below. x y a) Scatter plot (.5 ponts) Scatter Plot y x b) Type of correlaton (postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton) ( ponts) Here the scatter plot does not show any strong pattern. Thus we may conclude that x and y are uncorrelated. c) Complete the table and fnd the correlaton coeffcent r rounded to 4 decmals. Part 1: Scatter plot (.5 ponts)

2 x y xy x y Use the last row of the table to show the column totals. From the gven data we have n 10, x -5, y, x y -8, x 85 and y 370 We have, r n x ( x ) n y ( y ) 10*( 8) ( 5)* 10*85 ( 5) 10*370 () Construct a scatter plot and nclude the regresson lne on the graph usng excel for the gven data. Determne whether there s a postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton. Complete the table and fnd the correlaton coeffcent r. (References: example 1-4 pages ; end of secton exercses 15 - pages ) In an area of the Mdwest, records were kept on the relatonshp between the ranfall (n nches) and the yeld of wheat (bushels per acre). Ran fall, x Yeld, y a) Scatter plot wth regresson lne (.5 ponts)

3 Scatter Dagram Yeld y x Ran fall b) Type of correlaton (postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton) ( ponts) The scatter plot shows that as ran fall ncreases yeld also ncreases. Thus there exst a postve lnear correlaton between Ran fall and Yeld. c) Complete the table and fnd the correlaton coeffcent r rounded to 4 decmals. (5 ponts) x y xy x y Use the last row of the table to show the column totals. From the gven data we have

4 n 9, y x 100.3, y 568.8, x y , x 13.1 and We have, r n x ( x ) n y ( y ) 9* * *13.1 (100.3) 9* (568.8) Usng the r calculated n problem test the sgnfcance of the correlaton coeffcent usng a 0.01 and the clam rho 0. Use the 7-steps hypothess test shown at the end of ths project. (References: example 7 page 505; end of secton exercses 3-8 pages ) (5 ponts) (Note: Round the computed t to 3 decmals.) Answer: Let ρ be the populaton correlaton coeffcent. 1. H 0 : ρ 0 H a : ρ 0. a We have, r n t r Snce a 0.01, from Student s t table wth (n-) 7 degrees of freedom, the crtcal value s t

5 5. Rejecton regon: Reject Ho f t < or t > Decson: Here, t > So we reject the null hypothess Ho. 7. Interpretaton: Thus the correlaton between ran fall and yeld s statstcally sgnfcant at 1% level of sgnfcance. [If the alternatve hypothess s H a : ρ > 0, use the followng Let ρ be the populaton correlaton coeffcent. 1. H 0 : ρ 0 H a : ρ > 0. a We have, r n t r Snce a 0.01, from Student s t table wth (n-) 7 degrees of freedom, the crtcal value s t Rejecton regon: Reject Ho f t > Decson: Here, t >.998

6 So we reject the null hypothess Ho. 7. Interpretaton: Thus there exst a postve correlaton between ran fall and yeld at 1% level of sgnfcance.] Secton 9.: Lnear Regresson (References: example 1-3 pages ; end of secton exercses 13 - pages ) 4. The data gven are the temperatures on randomly chosen days durng a summer class and the number of absences on those days. Temperature, x Number of absences, y a. Fnd the equaton of the regresson lne for the gven data. Round the lne values to the nearest two decmal places. (.5 ponts) Show your work. Let y denote the number of absences and x denote the temperature. Assume that x and y are lnearly related. Let y α + β x be the suggested lnear relatonshp. By the method of least squares the estmates of α and β are gven by, ˆ β n x x ( ) y ˆ x and ˆ β α n From the gven data we have n 9, x 779, y 77, x y 6995 and x We have,

7 ˆ β n x x ( ) 9* *77 9*68163 (779) y ˆ x ˆ β α n * Thus the ftted regresson equaton s Number of absences Temperature b. Usng the equaton found n part a, predct the number of absences when the temperature s 95. Round to the nearest absence. (.5 ponts) If temperature 95, the predcted value of the number of absences s Number of absences *