ISCID-CO Dunkerque/ULCO. Mathematics applied to economics and management Foundations of Descriptive and Inferential Statistics
|
|
|
- Ashley Hopkins
- 5 years ago
- Views:
Transcription
1 IMBS 1 ISCID-CO Dunkerque/ULCO Mathematics applied to economics and management Foundations of Descriptive and Inferential Statistics December Final assessment - Session 1 - Semester 1 Time allowed : 1h30 - All documents allowed Exercice 1 Answer : 7pts 2pts tables > Height<-c(165,157,168,178,171,182,182,153) > Gender<-c("1","2","2","1","2","1","1","2") > d1<-data.frame(table(height)) > d11<-data.frame(d1,"percent.freq."=d1$freq/length(height)*100, + "Cumulative.Freq."=cumsum(d1$Freq)) > # At last, we may modify the label of the second column > names(d11)[2]<-"absolute.freq." > d11 Height Absolute.Freq. Percent.Freq. Cumulative.Freq > d2<-data.frame(table(gender)) > d22<-data.frame(d2,"percent.freq."=d2$freq/length(height)*100, + "Cumulative.Freq."=cumsum(d2$Freq)) > # At last, we may modify the label of the second column > names(d22)[2]<-"absolute.freq." > d22 Gender Absolute.Freq. Percent.Freq. Cumulative.Freq pts Graphs > par(mfrow=c(2,2)) > barplot(table(height),xlab="height",ylab="absolute Freq.",main="Absolute + Freq. of Height") > barplot(table(gender),xlab="gender",ylab="absolute Freq.",main="Absolute + Freq. of Gender") > plot(ecdf(height),xlab="height",ylab="ecdf(height)",main="height ecdf") > plot(ecdf(gender),xlab="gender",ylab="ecdf(gender)",main="gender ecdf") 1/7
2 Absolute Freq. of Height Absolute Freq. of Gender Absolute Freq Absolute Freq Height 1 2 Gender Height ecdf Gender ecdf ecdf(height) ecdf(gender) Height Gender 1pt Contingency table > table(gender,height) Height Gender pts The two variables we want to compare do not belong to the same scale levels. The variable "Height" is metrically scaled while the variable "Gender" is nominally scaled. In order to describe the relation between Gender and Height, we may refer to http ://pbil.univ-lyon1.fr/r/pdf/tdr208.pdf and use the following commands : > vartot <- function(x) {res <- sum((x-mean(x)) 2) ; return(res)} > varinter <- function(x,gpe){ moyennes <- tapply(x,gpe,mean) effectifs <- tapply(x,gpe,length) res <- (sum(effectifs*(moyennes-mean(x)) 2)) return(res) } > eta2 <- function(x,gpe){res <- varinter(x,gpe)/vartot(x) ; return(res)} > eta2(height,gender) [1] The result is not significant enough to state or not a link between the two variables. Nevertheless, we may provide some descriptive measures for each distribution with respect to the gender : > split(height,gender) 2/7
3 Exercice 2 $ 1 [1] $ 2 [1] > summary(sp$ 1 ) Min. 1st Qu. Median Mean 3rd Qu. Max > summary(sp$ 2 ) Min. 1st Qu. Median Mean 3rd Qu. Max Since the measures are quite different, we may conclude that relatively to our distribution, the gender affects strongly the height. Answer : 4pts 1. 1pt > Customers<-c(907,926,506,741,789,889,874,510,529,1010, + 420,679,872,924,607,452,729,794,844,621) > WeeklySales<-c(11.20,11.05,6.84,9.21,9.42,10.08,9.45,6.73,7.24,11.77, ,7.63,9.43,9.46,7.64,6.92,8.95,9.33,10.23,7.41) > plot(weeklysales Customers,main="Scatter diagram") Scatter diagram WeeklySales Customers 2. 1pt > model<-lm(weeklysales Customers) > model Call : lm(formula = WeeklySales Customers) Coefficients : (Intercept) Customers We deduce from the previous results that b 0 = and b 1 = We may plot the trend line whose equation is Y = X help to the command : > abline(model) 3/7
4 3. 1pt The slope b 1 may be interpreted as the marginal value : when Customers increase to t%, the Weekly Sales increase to t%. 4. 1pt The average weekly Sales (in thousands in dollars) for stores that have 600 customers may be estimated help to the following command : > predict(model,list(customers=c(600))) Exercice 3 Answer : 4pts 1. 1pt > dim(iris) [1]150 5 > str(iris) > str(iris) data.frame : 150 obs. of 5 variables : $ Sepal.Length : num $ Sepal.Width : num $ Petal.Length : num $ Petal.Width : num $ Species : Factor w/ 3 levels "setosa","versicolor",.. : pt > summary(iris) Sepal.Length Sepal.Width Petal.Length Petal.Width Species Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100 setosa :50 1st Qu. : st Qu. : st Qu. : st Qu. :0.300 versicolor :50 Median :5.800 Median :3.000 Median :4.350 Median :1.300 virginica :50 Mean :5.843 Mean :3.057 Mean :3.758 Mean : rd Qu. : rd Qu. : rd Qu. : rd Qu. :1.800 Max. :7.900 Max. :4.400 Max. :6.900 Max. : pt The answer was available on internet, see http ://www2.warwick.ac.uk/fac/sci/moac/people/students/peter cock/r/iris plots/ for example. We may use the command : > pairs(iris[1 :4], main = "Edgar Anderson s Iris Data", pch = 21, bg = c("red", + "green3","blue")[unclass(iris$species)]) 4/7
5 Edgar Anderson's Iris Data Sepal.Length Sepal.Width Petal.Length Petal.Width pt > cor(iris[1 :4]) Sepal.Length Sepal.Width Petal.Length Petal.Width Sepal.Length Sepal.Width Petal.Length Petal.Width Exercice 4 Answer : 5pts 2,5pts distributions > Facebook<-c(0,11,17,16,22,17,25,30,27,27,31,35,30,45,60) > Statistics<-c(25,22,28,30,22,27,26,21,27,28,23,29,30,24,27) > class1x<-c(0,10,20,30,40,50,60) > class2x<-c(0,15,30,60) > class1y<-c(18,22,26,30) > class2y<-c(18,21,24,27,30) 5/7
6 > class3y<-c(18,20,22,24,26,28,30) > table(cut(facebook,class1x,right=f,include.lowest=t)) [0,10) [10,20) [20,30) [30,40) [40,50) [50,60] > table(cut(facebook,class2x,right=f,include.lowest=t)) [0,15) [15,30) [30,60] > table(cut(statistics,class1y,right=f,include.lowest=t)) [18,22) [22,26) [26,30] > table(cut(statistics,class2y,right=f,include.lowest=t)) [18,21) [21,24) [24,27) [27,30] > table(cut(statistics,class3y,right=f,include.lowest=t)) [18,20) [20,22) [22,24) [24,26) [26,28) [28,30] ,5pts Histograms > split.screen( figs = c( 2, 1 ) ) [1] 1 2 > split.screen( figs = c( 1, 2 ), screen = 1 ) [1] 3 4 > split.screen( figs = c( 1, 3 ), screen = 2 ) [1] > screen(3) > hist(facebook,breaks=class1x,right=f,main="facebook frequencies Histogram\n + Grouping 1",xlab="Minutes",freq=T,include.lowest=T) > screen(4) > hist(facebook,breaks=class2x,right=f,main="facebook frequencies Histogram\n + Grouping 2",xlab="Minutes",freq=T,include.lowest=T) > screen(5) > hist(statistics,breaks=class1y,right=f,main="statistics frequencies Histogram\n + Grouping 1",xlab="Grade",freq=T,include.lowest=T) > screen(6) > hist(statistics,breaks=class2y,right=f,main="statistics frequencies Histogram\n + Grouping 2",xlab="Grade",freq=T,include.lowest=T) > screen(7) > hist(statistics,breaks=class3y,right=f,main="statistics frequencies Histogram\n + Grouping 3",xlab="Grade",freq=T,include.lowest=T) 6/7
7 Facebook frequencies Histogram Grouping 1 Facebook frequencies Histogram Grouping Minutes Minutes Statistics frequencies Histogram Grouping 1 Statistics frequencies Histogram Grouping 2 Statistics frequencies Histogram Grouping Grade Grade Grade 7/7
The SAS System 18:28 Saturday, March 10, Plot of Canonical Variables Identified by Cluster
The SAS System 18:28 Saturday, March 10, 2018 1 The FASTCLUS Procedure Replace=FULL Radius=0 Maxclusters=2 Maxiter=10 Converge=0.02 Initial Seeds Cluster SepalLength SepalWidth PetalLength PetalWidth 1
1. Introduction to Multivariate Analysis
1. Introduction to Multivariate Analysis Isabel M. Rodrigues 1 / 44 1.1 Overview of multivariate methods and main objectives. WHY MULTIVARIATE ANALYSIS? Multivariate statistical analysis is concerned with
PRINCIPAL COMPONENTS ANALYSIS
PRINCIPAL COMPONENTS ANALYSIS Iris Data Let s find Principal Components using the iris dataset. This is a well known dataset, often used to demonstrate the effect of clustering algorithms. It contains
Discriminant Analysis
Chapter 16 Discriminant Analysis A researcher collected data on two external features for two (known) sub-species of an insect. She can use discriminant analysis to find linear combinations of the features
Data Mining with R. Linear Classifiers and the Perceptron Algorithm. Hugh Murrell
Data Mining with R Linear Classifiers and the Perceptron Algorithm Hugh Murrell references These slides are based on a notes by Cosma Shalizi and an essay by Charles Elkan, but are self contained and access
MULTIVARIATE HOMEWORK #5
MULTIVARIATE HOMEWORK #5 Fisher s dataset on differentiating species of Iris based on measurements on four morphological characters (i.e. sepal length, sepal width, petal length, and petal width) was subjected
Creative Data Mining
Creative Data Mining Using ML algorithms in python Artem Chirkin Dr. Daniel Zünd Danielle Griego Lecture 7 0.04.207 /7 What we will cover today Outline Getting started Explore dataset content Inspect visually
Statistics in Stata Introduction to Stata
50 55 60 65 70 Statistics in Stata Introduction to Stata Thomas Scheike Statistical Methods, Used to test simple hypothesis regarding the mean in a single group. Independent samples and data approximately
Part I. Linear Discriminant Analysis. Discriminant analysis. Discriminant analysis
Week 5 Based in part on slides from textbook, slides of Susan Holmes Part I Linear Discriminant Analysis October 29, 2012 1 / 1 2 / 1 Nearest centroid rule Suppose we break down our data matrix as by the
Linear Discriminant Analysis Based in part on slides from textbook, slides of Susan Holmes. November 9, Statistics 202: Data Mining
Linear Discriminant Analysis Based in part on slides from textbook, slides of Susan Holmes November 9, 2012 1 / 1 Nearest centroid rule Suppose we break down our data matrix as by the labels yielding (X
4 Statistics of Normally Distributed Data
4 Statistics of Normally Distributed Data 4.1 One Sample a The Three Basic Questions of Inferential Statistics. Inferential statistics form the bridge between the probability models that structure our
Discriminant Analysis (DA)
Discriminant Analysis (DA) Involves two main goals: 1) Separation/discrimination: Descriptive Discriminant Analysis (DDA) 2) Classification/allocation: Predictive Discriminant Analysis (PDA) In DDA Classification
Last time: PCA. Statistical Data Mining and Machine Learning Hilary Term Singular Value Decomposition (SVD) Eigendecomposition and PCA
Last time: PCA Statistical Data Mining and Machine Learning Hilary Term 2016 Dino Sejdinovic Department of Statistics Oxford Slides and other materials available at: http://www.stats.ox.ac.uk/~sejdinov/sdmml
Robust scale estimation with extensions
Robust scale estimation with extensions Garth Tarr, Samuel Müller and Neville Weber School of Mathematics and Statistics THE UNIVERSITY OF SYDNEY Outline The robust scale estimator P n Robust covariance
Part I Week 7 Based in part on slides from textbook, slides of Susan Holmes
Part I Week 7 Based in part on slides from textbook, slides of Susan Holmes Support Vector Machine, Random Forests, Boosting December 2, 2012 1 / 1 2 / 1 Neural networks Artificial Neural networks: Networks
1.3 Linear Functions
1.3 Linear Functions A function of the form f(x) = ax + b, where a and b are constants, is called a linear function. The graph of f(x) = ax + b or y = mx + b, is a line, with slope a (or m), and y intercept
Machine Leanring Theory and Applications: third lecture
Machine Leanring Theory and Applications: third lecture Arnak Dalalyan ENSAE PARISTECH 12 avril 2016 Framework and notation Framework and notation We observe (X i, Y i ) X Y, i = 1,..., n independent randomly
Principal Component Analysis (PCA) Principal Component Analysis (PCA)
Recall: Eigenvectors of the Covariance Matrix Covariance matrices are symmetric. Eigenvectors are orthogonal Eigenvectors are ordered by the magnitude of eigenvalues: λ 1 λ 2 λ p {v 1, v 2,..., v n } Recall:
Supervised Learning. Regression Example: Boston Housing. Regression Example: Boston Housing
Supervised Learning Unsupervised learning: To extract structure and postulate hypotheses about data generating process from observations x 1,...,x n. Visualize, summarize and compress data. We have seen
Bayesian Classification Methods
Bayesian Classification Methods Suchit Mehrotra North Carolina State University smehrot@ncsu.edu October 24, 2014 Suchit Mehrotra (NCSU) Bayesian Classification October 24, 2014 1 / 33 How do you define
3 Write an equation in point-slope form of the line through the given point and with the given slope. (2, 5); m = 0
Name: ate: 1 Write an equation in slope-intercept form of the line. y = x 3 y = 3 y = 3x + 1 y = x + 3 2 Write an equation in slope-intercept form of the line. y = 7x y = 2x + 7 y = 2x 7 y = 7x + 2 3 Write
Regression on Faithful with Section 9.3 content
Regression on Faithful with Section 9.3 content The faithful data frame contains 272 obervational units with variables waiting and eruptions measuring, in minutes, the amount of wait time between eruptions,
1.1 : (The Slope of a straight Line)
1.1 : (The Slope of a straight Line) Equations of Nonvertical Lines: A nonvertical line L has an equation of the form y mx b. The number m is called the slope of L and the point (0, b) is called the y-intercept.
STA 218: Statistics for Management
Al Nosedal. University of Toronto. Fall 2017 My momma always said: Life was like a box of chocolates. You never know what you re gonna get. Forrest Gump. Problem How much do people with a bachelor s degree
Solution to Series 10
Prof. Dr. M. Maathuis Multivariate Statistics SS 0 Solution to Series 0. a) > bumpus
A Comparison of Missing Data Handling Methods Catherine Truxillo, Ph.D., SAS Institute Inc, Cary, NC
A Comparison of Missing Data Handling Methods Catherine Truxillo, Ph.D., SAS Institute Inc, Cary, NC ABSTRACT Incomplete data presents a problem in both inferential and predictive modeling applications.
(a) Find the value of x. (4) Write down the standard deviation. (2) (Total 6 marks)
1. The following frequency distribution of marks has mean 4.5. Mark 1 2 3 4 5 6 7 Frequency 2 4 6 9 x 9 4 Find the value of x. (4) Write down the standard deviation. (Total 6 marks) 2. The following table
CS444/544: Midterm Review. Carlos Scheidegger
CS444/544: Midterm Review Carlos Scheidegger D3: DATA-DRIVEN DOCUMENTS The essential idea D3 creates a two-way association between elements of your dataset and entries in the DOM D3 operates on selections
Marquette University Executive MBA Program Statistics Review Class Notes Summer 2018
Marquette University Executive MBA Program Statistics Review Class Notes Summer 2018 Chapter One: Data and Statistics Statistics A collection of procedures and principles
SUMMER PACKET. Accelerated Algebra Name Date. Teacher Semester
Name Date Teacher Semester SUMMER PACKET Accelerated Algebra 017-018 Teacher Mrs. Robison Mrs. Miller Email krobison@gettysburg.k1.pa.us emiller@gettysburg.k1.pa.us 1 Welcome to Accelerated Algebra! I.
Review for Algebra Final Exam 2015
Review for Algebra Final Exam 2015 Could the data in the table represent a linear model. If Linear write an equation to model the relationship. x Y 4 17 2 11 0 5 2 1 4 7 Could the data in the table represent
Chapter 5 Test Review
Chapter 5 Test Review Algebra 1 CP Name: Hour: Write an equation in slope-intercept form of the line that passes through the given point and has the given slope m. 1. (-, -8); m = 3. (1, 1); m = - 3. (-1,
Applied Multivariate and Longitudinal Data Analysis
Applied Multivariate and Longitudinal Data Analysis Chapter 2: Inference about the mean vector(s) Ana-Maria Staicu SAS Hall 5220; 919-515-0644; astaicu@ncsu.edu 1 In this chapter we will discuss inference
Essential Academic Skills Subtest III: Mathematics (003)
Essential Academic Skills Subtest III: Mathematics (003) NES, the NES logo, Pearson, the Pearson logo, and National Evaluation Series are trademarks in the U.S. and/or other countries of Pearson Education,
Multivariate Linear Models in R*
Multivariate Linear Models in R* An Appendix to An R Companion to Applied Regression, third edition John Fox & Sanford Weisberg last revision: 2018-09-21 The multivariate linear model is Abstract Y = (n
NEW ENGLAND COMMON ASSESSMENT PROGRAM
NEW ENGLAND COMMON ASSESSMENT PROGRAM Released Items 2010 Grade 11 Mathematics Mathematics Items with this symbol were selected from Session One no calculators or other mathematics tools allowed. 140029.004
ALLEN PARK HIGH SCHOOL F i r s t S e m e s t e r A s s e s s m e n t R e v i e w
Algebra First Semester Assessment Review Winter 0 ALLEN PARK HIGH SCHOOL F i r s t S e m e s t e r A s s e s s m e n t R e v i e w A lgeb ra Page Winter 0 Mr. Brown Algebra First Semester Assessment Review
Classroom Assessments Based on Standards Integrated College Prep I Unit 3 CP 103A
Classroom Assessments Based on Standards Integrated College Prep I Unit 3 CP 103A Name: ID Number: Teacher Name: Score: Proficient: yes no How Tall Can He Be? The table below shows the average height in
SVM-flexible discriminant analysis
SVM-flexible discriminant analysis Huimin Peng November 20, 2014 Outline SVM Nonlinear SVM = Penalization method discriminant analysis FDA: flexible discriminant analysis penalized discriminant analysis
Section 2.3. Function Notation and Making Predictions
Function Notation and Making Predictions Using an Equation of a Linear Model to Make Predictions Example Using Function Notation with Models The table shows the average salaries of professors at fouryear
Chapter 2 Descriptive Statistics
Chapter 2 Descriptive Statistics Lecture 1: Measures of Central Tendency and Dispersion Donald E. Mercante, PhD Biostatistics May 2010 Biostatistics (LSUHSC) Chapter 2 05/10 1 / 34 Lecture 1: Descriptive
Statistics I Exercises Lesson 3 Academic year 2015/16
Statistics I Exercises Lesson 3 Academic year 2015/16 1. The following table represents the joint (relative) frequency distribution of two variables: semester grade in Estadística I course and # of hours
(Re)introduction to Statistics Dan Lizotte
(Re)introduction to Statistics Dan Lizotte 2017-01-17 Statistics The systematic collection and arrangement of numerical facts or data of any kind; (also) the branch of science or mathematics concerned
3. Find the slope of the tangent line to the curve given by 3x y e x+y = 1 + ln x at (1, 1).
1. Find the derivative of each of the following: (a) f(x) = 3 2x 1 (b) f(x) = log 4 (x 2 x) 2. Find the slope of the tangent line to f(x) = ln 2 ln x at x = e. 3. Find the slope of the tangent line to
Describe in words how the graph of each function below would differ from the graph of f (x).
MATH 111 Exam # Review (4.1-4.4, 6.1, 6.) Describe in words how the graph of each function below would differ from the graph of f (. 1. f ( x 7). f (. f ( 5 4. f ( 5. 7 f ( 6. f ( x ) 9 7. f ( 8. f ( 9.
3. Design Experiments and Variance Analysis
3. Design Experiments and Variance Analysis Isabel M. Rodrigues 1 / 46 3.1. Completely randomized experiment. Experimentation allows an investigator to find out what happens to the output variables when
Ch. 9 Pretest Correlation & Residuals
Ch. 9 Pretest Correlation & Residuals Name Period 1. The number of students in a school chorus has increased since the school first opened 6 years ago. Predicted # Residual a) Find the Linear Regression
Topic 5: Statistics 5.3 Cumulative Frequency Paper 1
Topic 5: Statistics 5.3 Cumulative Frequency Paper 1 1. The following is a cumulative frequency diagram for the time t, in minutes, taken by students to complete a task. Standard Level Write down the median.
Algebra I Final Study Guide
2011-2012 Algebra I Final Study Guide Short Answer Source: www.cityoforlando.net/public_works/stormwater/rain/rainfall.htm 1. For which one month period was the rate of change in rainfall amounts in Orlando
Review Assignment II
MATH 11012 Intuitive Calculus KSU Name:. Review Assignment II 1. Let C(x) be the cost, in dollars, of manufacturing x widgets. Fill in the table with a mathematical expression and appropriate units corresponding
Semiparametric Generalized Linear Models with the gldrm Package by Michael J. Wurm and Paul J. Rathouz
CONTRIBUTED RESEARCH ARTICLE 288 Semiparametric Generalized Linear Models with the gldrm Package by Michael J. Wurm and Paul J. Rathouz Abstract This paper introduces a new algorithm to estimate and perform
Essential Question How can you use a scatter plot and a line of fit to make conclusions about data?
. Scatter Plots and Lines of Fit Essential Question How can ou use a scatter plot and a line of fit to make conclusions about data? A scatter plot is a graph that shows the relationship between two data
Study Island. Linear and Exponential Models
Study Island Copyright 2014 Edmentum - All rights reserved. 1. A company is holding a dinner reception in a hotel ballroom. The graph represents the total cost of the ballroom rental and dinner. 3. In
Lecture 5: Classification
Lecture 5: Classification Advanced Applied Multivariate Analysis STAT 2221, Spring 2015 Sungkyu Jung Department of Statistics, University of Pittsburgh Xingye Qiao Department of Mathematical Sciences Binghamton
Exam #1 March 9, 2016
Mathematics 1372/D552, Spring 2016 Instructor: Suman Ganguli Exam #1 March 9, 2016 Name: 1. (20 points) The following data set lists the high temperatures (in degrees Fahrenheit) observed in Central Park
Advanced Studies in Applied Statistics (WBL), ETHZ Applied Multivariate Statistics Spring 2018, Week 1
Advanced Studies in Applied Statistics (WBL), ETHZ Applied Multivariate Statistics Spring 2018, Week 1 Lecturer: Beate Sick sickb@ethz.ch Remark: Much of the material have been developed together with
PreAP Algebra I Problems for the First Semester Exam
This is not a semester exam, but problems that you could use on a semester exam that are similar to some of the problems from the unit quizzes 1. Stephanie left home at 8:30 and rode her bicycle at a steady
Multivariate Statistics
Multivariate Statistics Chapter 2: Multivariate distributions and inference Pedro Galeano Departamento de Estadística Universidad Carlos III de Madrid pedro.galeano@uc3m.es Course 2016/2017 Master in Mathematical
Algebra I Exam Review
Name Algebra I Exam Review Assigned on Assignment 1/17 Final Exam Practice Units 1 and Problems 1-4 1/18 Final Exam Practice Units and 4 Problems 5-5 1/19 Practice Final Exam Multiple Choice 1-16 1/ Practice
Bivariate Data Analysis
Bivariate Data Analysis This is adapted from University of Auckland Statistics Department material. The original can be found at http://www.stat.auckland.ac.nz/~teachers/23/regression.php Types of variables
Chuck Cartledge, PhD. 20 January 2018
Big Data: Data Analysis Boot Camp Linear Regression Chuck Cartledge, PhD 20 January 2018 1/46 Table of contents (1 of 1) 1 Intro. 2 Background Vocabulary and concepts 3 Linear regression Iris data Multiple
Use slope and y-intercept to write an equation. Write an equation of the line with a slope of 1 } 2. Write slope-intercept form.
5.1 Study Guide For use with pages 282 291 GOAL Write equations of lines. EXAMPLE 1 Use slope and y-intercept to write an equation Write an equation of the line with a slope of 1 } 2 and a y-intercept
Math 1020 TEST 3 VERSION A Spring 2017
Printed Name: Section #: Instructor: Please do not ask questions during this eam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the
Math 1314 Lesson 7 Applications of the Derivative. rate of change, instantaneous rate of change, velocity, => the derivative
Math 1314 Lesson 7 Applications of the Derivative In word problems, whenever it s anything about a: rate of change, instantaneous rate of change, velocity, => the derivative average rate of change, difference
a) Graph the equation by the intercepts method. Clearly label the axes and the intercepts. b) Find the slope of the line.
Math 71 Spring 2009 TEST 1 @ 120 points Name: Write in a neat and organized fashion. Write your complete solutions on SEPARATE PAPER. You should use a pencil. For an exercise to be complete there needs
Descriptive Statistics Class Practice [133 marks]
![Descriptive Statistics Class Practice [133 marks]](/thumbs/86/93966613.jpg "Descriptive Statistics Class Practice [133 marks]")
Descriptive Statistics Class Practice [133 marks] The weekly wages (in dollars) of 80 employees are displayed in the cumulative frequency curve below. 1a. (i) (ii) Write down the median weekly wage. Find
MAT09X FINAL EXAM REVIEW C) 86 D) ) A) 14r + 37 B) 6r + 30 C) 6r + 45 D) 6r ) 3 C) 1 D) 3 2
MAT09X FINAL EXAM REVIEW NAME MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question. Perform the indicated operations ) ( ) ) 6 86 Evaluate the epression,
Module 5 Study Guide--Linear Functions
Module Stud Guide--Linear Functions The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation.. The table shows the cost of a ski rental
Algebra EOC Practice Test #1
Class: Date: Algebra EOC Practice Test #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. George is helping the manager of the local produce market expand
Assumptions, Diagnostics, and Inferences for the Simple Linear Regression Model with Normal Residuals
Assumptions, Diagnostics, and Inferences for the Simple Linear Regression Model with Normal Residuals 4 December 2018 1 The Simple Linear Regression Model with Normal Residuals In previous class sessions,
Chapter 2: Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point.
Chapter : Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point. f( ) 10, (, ) 10 1 E) none of the above. Find the slope of the tangent line to the
Introduction to Statistics
Why Statistics? Introduction to Statistics To develop an appreciation for variability and how it effects products and processes. Study methods that can be used to help solve problems, build knowledge and
Algebra 1 Third Quarter Study Guide
Algebra 1 Third Quarter Study Guide 1. Evaluate:. 2. Evaluate: 8 5 5 t. 2 s t when s = 5 and 7 Simplify. 3. 2 0 5 3 2x y x y 4. 4 3 54xy 5. 4 24 6. 3x 2 y 3 7. Is 3 a solution of? 8. A store that sells
Data Exploration Slides by: Shree Jaswal
Data Exploration Slides by: Shree Jaswal Topics to be covered Types of Attributes; Statistical Description of Data; Data Visualization; Measuring similarity and dissimilarity. Chp2 Slides by: Shree Jaswal
Analyzing Lines of Fit
4.5 Analyzing Lines of Fit Essential Question How can you analytically find a line of best fit for a scatter plot? Finding a Line of Best Fit Work with a partner. The scatter plot shows the median ages
cor(dataset$measurement1, dataset$measurement2, method= pearson ) cor.test(datavector1, datavector2, method= pearson )
Tutorial 7: Correlation and Regression Correlation Used to test whether two variables are linearly associated. A correlation coefficient (r) indicates the strength and direction of the association. A correlation
Using a graphic display calculator
12 Using a graphic display calculator CHAPTER OBJECTIVES: This chapter shows you how to use your graphic display calculator (GDC) to solve the different types of problems that you will meet in your course.
Syllabus for Grade 7. More details on each of the topics is covered in the following pages.
Syllabus for Grade 7 Chapter 1 Algebraic Reasoning Chapter 2 Integers and rational numbers Chapter 3 Number Theory Chapter 4 Rational number Chapter 5 Patterns and functions Chapter 6 Proportional Relationships
Relations and Functions
Lesson 5.1 Objectives Identify the domain and range of a relation. Write a rule for a sequence of numbers. Determine if a relation is a function. Relations and Functions You can estimate the distance of
AIM HIGH SCHOOL. Curriculum Map W. 12 Mile Road Farmington Hills, MI (248)
AIM HIGH SCHOOL Curriculum Map 2923 W. 12 Mile Road Farmington Hills, MI 48334 (248) 702-6922 www.aimhighschool.com COURSE TITLE: Statistics DESCRIPTION OF COURSE: PREREQUISITES: Algebra 2 Students will
Introduction to Statistics
Introduction to Statistics Data and Statistics Data consists of information coming from observations, counts, measurements, or responses. Statistics is the science of collecting, organizing, analyzing,
AP Statistics Semester I Examination Section I Questions 1-30 Spend approximately 60 minutes on this part of the exam.
AP Statistics Semester I Examination Section I Questions 1-30 Spend approximately 60 minutes on this part of the exam. Name: Directions: The questions or incomplete statements below are each followed by
Quantile Textbook Report
Quantile Textbook Report Algebra 1 Author Charles, Randall I., et al StateEdition West Virginia Grade Algebra 1 1 Foundations for Algebra 1.1 Variables and Expressions 750Q 1.2 Order of Operations and
For instance, we want to know whether freshmen with parents of BA degree are predicted to get higher GPA than those with parents without BA degree.
DESCRIPTIVE ANALYSIS For instance, we want to know whether freshmen with parents of BA degree are predicted to get higher GPA than those with parents without BA degree. Assume that we have data; what information
Introduction and Background to Multilevel Analysis
Introduction and Background to Multilevel Analysis Dr. J. Kyle Roberts Southern Methodist University Simmons School of Education and Human Development Department of Teaching and Learning Background and
Math 1314 Lesson 7 Applications of the Derivative
Math 1314 Lesson 7 Applications of the Derivative Recall from Lesson 6 that the derivative gives a formula for finding the slope of the tangent line to a function at any point on that function. Example
STAT 3022 Spring 2007
Simple Linear Regression Example These commands reproduce what we did in class. You should enter these in R and see what they do. Start by typing > set.seed(42) to reset the random number generator so
SESSION 5 Descriptive Statistics
SESSION 5 Descriptive Statistics Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple
Psych 10 / Stats 60, Practice Problem Set 10 (Week 10 Material), Solutions
Psych 10 / Stats 60, Practice Problem Set 10 (Week 10 Material), Solutions Part 1: Conceptual ideas about correlation and regression Tintle 10.1.1 The association would be negative (as distance increases,
Computer exercises on Experimental Design, ANOVA, and the BOOTSTRAP
Computer exercises on Experimental Design, ANOVA, and the BOOTSTRAP Exercice 1: Copy the workspace ExpDes_1.Rdata to your local D drive and load it into a R-session. Perform a sample size calculation for
Algebra 1 Enriched- Midterm Review
Algebra 1 Enriched- Midterm Review Know all vocabulary, pay attention to the highlighted words in the text, and understand the various types of directions in each of the sections of the textbook. Practice
Chapter 3: Examining Relationships
Chapter 3 Review Chapter 3: Examining Relationships 1. A study is conducted to determine if one can predict the yield of a crop based on the amount of yearly rainfall. The response variable in this study
SYSTEMS Solving Linear Systems Common Core Standards
I Systems, Lesson 1, Solving Linear Systems (r. 2018) SYSTEMS Solving Linear Systems Common Core Standards A-REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation
Core Focus on Linear Equations Block 5 Review ~ Two-Variable Data
Core Focus on Linear Equations Block 5 Review ~ Two-Variable Data Name Period Date Part I Selected Response For numbers 1a 1d, circle the type of correlation you would expect the following data sets to
Regression. Bret Hanlon and Bret Larget. December 8 15, Department of Statistics University of Wisconsin Madison.
Regression Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison December 8 15, 2011 Regression 1 / 55 Example Case Study The proportion of blackness in a male lion s nose
YISHUN JUNIOR COLLEGE 2017 JC2 Preliminary Examination
YISHUN JUNIOR COLLEGE 07 JC Preliminary Examination MATHEMATICS 8864/0 HIGHER 8 AUGUST 07 MONDAY 0800h 00h Additional materials : Answer paper List of Formulae (MF5) TIME 3 hours READ THESE INSTRUCTIONS
Algebra I Semester 1 Exam Released
Algebra I 00 0 Semester Eam Released. Find the product. 6 9 0 7 0. Find the difference of the matrices. 6 0 8 0 7 0 8 0 9 0 8 7 8 7 7 0 7 0 6 9 8 7 7 0 8 90 6 9 8 7. The distributions of two classes final
Unit 5 Test Review Systems of Linear Equations Name Class Date
Unit 5 Test Review Systems of Linear Equations Name Class Date Find the mistake - The following problems have been solved HOWEVER there could be a mistake. Each question is worth 3 points: 1pt the mistake,
********************************************************************************************************
QUESTION # 1 1. Let the random variable X represent the number of telephone lines in use by the technical support center of a software manufacturer at noon each day. The probability distribution of X is
URBANDALE COMMUNITY SCHOOL DISTRICT CURRICULUM FRAMEWORK OUTLINE. SUBJECT: Mathematics COURSE TITLE: Algebra I 2 Credits/2 Semesters
URBANDALE COMMUNITY SCHOOL DISTRICT CURRICULUM FRAMEWORK OUTLINE SUBJECT: Mathematics COURSE TITLE: Algebra I 2 Credits/2 Semesters COURSE DESCRIPTION: Algebra I provides the opportunities for students