# ST 311 Evening Problem Session Solutions Week 11

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 1. p. 175, Question 32 (Modules ) [Learning Objectives J1, J3, J9, J11-14, J17] Since 1980, average mortgage rates have fluctuated from a low of under 6% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that s offered? Here is a scatterplot of Total Mortgages in the United States (in millions of 2005 dollars) versus Interest Rate at various times over the past 26 years. R-Squared Reg Equation a) Identify the dependent and independent variables. b) Interpret the meaning of R 2 in this context? T otalm ortgages = InterestRate c) Find the correlation coefficient. If we were to measure Total Mortgages in thousands of dollars instead of millions of dollars, how would the correlation coefficient change? d) Do these data provide proof that if mortgage rates are lowered, the total mortgage amount that people will take out will increase? Explain. e) Interpret the meaning of the slope of the regression line in this context. f) Suppose we discovered a missing measurement that recorded the Total Mortgages as \$180 million for an interest rate of 14%. What would its predicted value and residual value be? How will this value affect the slope of our line? What would you expect to happen to the R 2 value? Explain. Solutions: a) The dependent variable is Total Mortgages and the independent variable is Interest Rates b) The R 2 of means that Interest Rates account for 70.6% of the variation in Total Mortgages Page 1

2 c) First make a not of the sign of the slope in this problem. Our slope here is 7.78, so we need to take the negative square root of R 2. The correlation coefficient is r = = d) These data do not indicate causation. Instead, the relationship here is one of correlation. So, it would just appear that the interest rates are correlated with the amount of mortgages. To imply causation, we would have needed to do an experiment. e) The slope of 7.78 indicates that when interest rates increase by 1%, we would expect an average decrease in total mortgages of \$7.78 million. f) The predicted value would be and the associated residual value would be ŷ = (14) = Residual = Observed P redicted = = \$68.03 million. This value will make our regression line flatter, so the new slope would be closer to 0. The R 2 value should decrease. 2. p. 204, Question 30 (Modules ) [Learning Objectives J1, J3, J9, J11-14] Here is a scatter plot of the number of wins by American League baseball teams and the average attendance at their home games for the 2006 season, and part of the regression analysis. R-Squared Reg Equation HomeAttendance = W ins. Page 2

3 a) Identify the dependent and independent variables. b) Interpret the meaning of R 2 in this context. c) Find the correlation coefficient. d) Estimate the Average Attendance for a team with 72 Wins e) Interpret the meaning of the slope of the regression line in this context. f) The St. Louis Cardinals, the 2006 World Champions, are not included in these data because they are a National League team. During the 2006 regular season, the Cardinals won 83 games and averaged 42,588 fans at their home games. Calculate the residual for this team, and explain what it means. How will this value impact the slope of the line. Explain. Solutions a) The dependent variable is Home Attendance and the independent variable is Wins b) The R 2 of means that Wins account for 48.5% of the variation in Home Attendance c) First make a not of the sign of the slope in this problem. Our slope here is , so we need to take the positive square root of R 2. The correlation coefficient is d) ŷ = (72) = r = = e) The slope of indicates that for every additional win, we would expect the average home attendance to increase by people. f) The predicted value would be and the associated residual value would be ŷ = (83) = Residual = Observed P redicted = = This residual value means that the Cardinals had an average attendance of 12,222.6 people higher than we would expect given the number of win in their season. If we included this value in our data set, it will make the slope increase. 3. p. 235, Question 30 (Modules ) [Learning Objectives J1, J9, J11-12, J14] Information was gathered about the condition and ages bridges of Tompkins County, NY built since Below you can find the corresponding scatterplot and some simple linear regression output from StatCrunch. Page 3

4 R-Squared Reg. Equation a) Identify the dependent and independent variables. Condition = year b) Interpret the meaning of the slope of the regression line in this context. c) Tompkins County is the home of the oldest covered bridge in daily use in New York. Built in 1853, it is judged to have a condition of If we use this regression to predict the condition of the covered bridge, what would its predicted value and residual value be? d) How do you think this will impact the regression slope? Explain. e) If we add the covered bridge (from c) to the data, what would you expect to happen to the R 2 value? Explain. f) The Tompkins County bridge (from c) was extensively restored in If we use that date instead of 1853, do you find the condition of the bridge remarkable? Solutions: (a) The dependent variable is Condition and the independent variable is Year (b) The slope of indicates that as we move later by one year (i.e to 1941), we would expect the average condition increase by (c) The predicted value would be ŷ = (1853) = and the associated residual value would be Residual = Observed P redicted = = Page 4

5 (d) This value will make our regression line flatter, so the new slope would be closer to 0. (e) If we add the bridge to the data, we would expect the R 2 value to decrease because we would be adding an outlier into the data set, so the line would fit worse. (f) No, if we consider the year as 1972, then we would predict the condition to be ŷ = (1972) = Which has a residual value of a little less than 1. While the observed value (of 4.523) is somewhat different than the predicted value (of ), if you look at the other bridges built in 1972, it is not unusual to see bridges with condition numbers around Additional Question 1 (Modules ) [Learning Objectives J2, J4, J8, 16] The following partial regression output explores the relationship between shoe size and height (in inches). Simple linear regression results: Dependent Variable: Height Independent Variable: shoe Sample size: 389 R (correlation coefficient) = R-sq = Estimate of error standard deviation: Parameter Estimates: Page 5

6 Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept < Slope < (a) Describe the relationship between shoe size and height shown in the scatterplot. When commenting on the strength of the relationship, include a specific number from the output that is used to determine if the relationship is strong or weak. (b) What is the equation of the regression model (report values to 2 decimal places)? (c) Would it be appropriate to use the model from part (b) to predict the height of a person with a size 4 shoe? Explain why or why not. Solutions: (a) Overall, there is a strong, positive linear relationship with no obvious outliers. The relationship is strong since r = , which is close to 1. (Note: you could also report that R 2 is close to 1: R 2 = ) (b) ŷ = x (c) No, since that is beyond the range of the data we have and we dont know if the relationship remains the same as what we see here. Page 6

### Residuals. Residuals = ª Department of ISM, University of Alabama, ST 260, M23 Residuals & Minitab. ^ e i = y i - y i

A continuation of regression analysis Lesson Objectives Continue to build on regression analysis. Learn how residual plots help identify problems with the analysis. M23-1 M23-2 Example 1: continued Case

### Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

### AP * Statistics Review. Linear Regression

AP * Statistics Review Linear Regression Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

### Regression. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between

### 31. SIMPLE LINEAR REGRESSION VI: LEVERAGE AND INFLUENCE

31. SIMPLE LINEAR REGRESSION VI: LEVERAGE AND INFLUENCE These topics are not covered in the text, but they are important. Leverage If the data set contains outliers, these can affect the leastsquares fit.

### Final Review Sheet. Mod 2: Distributions for Quantitative Data

Things to Remember from this Module: Final Review Sheet Mod : Distributions for Quantitative Data How to calculate and write sentences to explain the Mean, Median, Mode, IQR, Range, Standard Deviation,

### MULTIPLE REGRESSION EXAMPLE

MULTIPLE REGRESSION EXAMPLE For a sample of n = 166 college students, the following variables were measured: Y = height X 1 = mother s height ( momheight ) X 2 = father s height ( dadheight ) X 3 = 1 if

### Chapter 8. Linear Regression. Copyright 2012, 2008, 2005 Pearson Education, Inc.

Chapter 8 Linear Regression Copyright 2012, 2008, 2005 Pearson Education, Inc. Fat Versus Protein: An Example The following is a scatterplot of total fat versus protein for 30 items on the Burger King

### In Chapter 2, we used linear regression to describe linear relationships. The setting for this is a

Math 143 Inference on Regression 1 Review of Linear Regression In Chapter 2, we used linear regression to describe linear relationships. The setting for this is a bivariate data set (i.e., a list of cases/subjects

### Chapter 3: Describing Relationships

Chapter 3: Describing Relationships The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 3 2 Describing Relationships 3.1 Scatterplots and Correlation 3.2 Learning Targets After

### Chapter 9. Section Correlation

Chapter 9 Section 9.1 - Correlation Objectives: Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation

### SELF-TEST: SIMPLE REGRESSION

ECO 22000 McRAE SELF-TEST: SIMPLE REGRESSION Note: Those questions indicated with an (N) are unlikely to appear in this form on an in-class examination, but you should be able to describe the procedures

### Chapter 2. Looking at Data: Relationships. Introduction to the Practice of STATISTICS SEVENTH. Moore / McCabe / Craig. Lecture Presentation Slides

Chapter 2 Looking at Data: Relationships Introduction to the Practice of STATISTICS SEVENTH EDITION Moore / McCabe / Craig Lecture Presentation Slides Chapter 2 Looking at Data: Relationships 2.1 Scatterplots

### Chapter 4 Describing the Relation between Two Variables

Chapter 4 Describing the Relation between Two Variables 4.1 Scatter Diagrams and Correlation The response variable is the variable whose value can be explained by the value of the explanatory or predictor

### Relationship of two variables

Relationship of two variables A correlation exists between two variables when the values of one are somehow associated with the values of the other in some way. Scatter Plot (or Scatter Diagram) A plot

### , has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results.

BA 275 Review Problems - Week 9 (11/20/06-11/24/06) CD Lessons: 69, 70, 16-20 Textbook: pp. 520-528, 111-124, 133-141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An

### Chapter 7 9 Review. Select the letter that corresponds to the best answer.

AP Statistics Chapter 7 9 Review MULTIPLE CHOICE Name: Per: Select the letter that corresponds to the best answer. 1. The correlation between X and Y is r = 0.35. If we double each X value, increase each

### Regents Exam Questions A2.S.8: Correlation Coefficient

A2.S.8: Correlation Coefficient: Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship 1 Which statement regarding correlation

### Homework 8 Solutions

Math 17, Section 2 Spring 2011 Homework 8 Solutions Assignment Chapter 7: 7.36, 7.40 Chapter 8: 8.14, 8.16, 8.28, 8.36 (a-d), 8.38, 8.62 Chapter 9: 9.4, 9.14 Chapter 7 7.36] a) A scatterplot is given below.

### 12-1 Multiple Linear Regression Models

12-1.1 Introduction Many applications of regression analysis involve situations in which there are more than one regressor variable. A regression model that contains more than one regressor variable is

### AP STATISTICS 2006 SCORING GUIDELINES. Question 2

2006 SCING GUIDELINES Question 2 Intent of Question The primary goal of this question is to assess a student s ability to identify the estimated regression line and to identify and interpret important

### Section I: Multiple Choice Select the best answer for each question.

Chapter 15 (Regression Inference) AP Statistics Practice Test (TPS- 4 p796) Section I: Multiple Choice Select the best answer for each question. 1. Which of the following is not one of the conditions that

### Several scatterplots are given with calculated correlations. Which is which? 4) 1) 2) 3) 4) a) , b) , c) 0.002, d) 0.

AP Statistics Review Chapters 7-8 Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Suppose you were to collect data for the

### Directions: Answer the following questions on another sheet of paper

Module 3 Review Directions: Answer the following questions on another sheet of paper Questions 1-16 refer to the following situation: Is there a relationship between crime rate and the number of unemployment

Using Your TI-83/84 Calculator: Linear Correlation and Regression Elementary Statistics Dr. Laura Schultz This handout describes how to use your calculator for various linear correlation and regression

### Linear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares

Linear Regression Chapter 5 Regression Objective: To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects

### Lecture 5: Correlation and Linear Regression

Lecture 5: Correlation and Linear Regression 3.5. (Pearson) correlation coefficient The correlation coefficient measures the strength of the linear relationship between two variables. The correlation is

### Using Minitab for Regression Analysis: An extended example

Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to

### Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for

### International Statistical Institute, 56th Session, 2007: Phil Everson

Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction

### 1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

### Module 5: Multiple Regression Analysis

Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

### Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

### Chapter 7 Linear Regression

11 Part II Exploring Relationships Between Variables Chapter 7 Linear Regression 1. Cereals. Potassium 38 7Fiber 38 7( 9) 81 mg. According to the model, we expect cereal with 9 grams of fiber to have 81

### Chapter 12 : Linear Correlation and Linear Regression

Number of Faculty Chapter 12 : Linear Correlation and Linear Regression Determining whether a linear relationship exists between two quantitative variables, and modeling the relationship with a line, if

### Mod 2 Lesson 19 Interpreting Correlation

Date: Mod 2 Lesson 19 Interpreting Correlation Example 1: Positive and Negative Relationships Linear relationships can be described as either positive or negative. Below are two scatter plots that display

### Advanced High School Statistics. Preliminary Edition

Chapter 2 Summarizing Data After collecting data, the next stage in the investigative process is to summarize the data. Graphical displays allow us to visualize and better understand the important features

### Practice 3 SPSS. Partially based on Notes from the University of Reading:

Practice 3 SPSS Partially based on Notes from the University of Reading: http://www.reading.ac.uk Simple Linear Regression A simple linear regression model is fitted when you want to investigate whether

### Using R for Linear Regression

Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional

### A correlation exists between two variables when one of them is related to the other in some way.

Lecture #10 Chapter 10 Correlation and Regression The main focus of this chapter is to form inferences based on sample data that come in pairs. Given such paired sample data, we want to determine whether

### ch12 practice test SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

ch12 practice test 1) The null hypothesis that x and y are is H0: = 0. 1) 2) When a two-sided significance test about a population slope has a P-value below 0.05, the 95% confidence interval for A) does

### where b is the slope of the line and a is the intercept i.e. where the line cuts the y axis.

Least Squares Introduction We have mentioned that one should not always conclude that because two variables are correlated that one variable is causing the other to behave a certain way. However, sometimes

### How strong is a linear relationship?

Lesson 19 Interpreting Correlation Student Outcomes Students use technology to determine the value of the correlation coefficient for a given data set. Students interpret the value of the correlation coefficient

### The scatterplot indicates a positive linear relationship between waist size and body fat percentage:

STAT E-150 Statistical Methods Multiple Regression Three percent of a man's body is essential fat, which is necessary for a healthy body. However, too much body fat can be dangerous. For men between the

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

### 17. SIMPLE LINEAR REGRESSION II

17. SIMPLE LINEAR REGRESSION II The Model In linear regression analysis, we assume that the relationship between X and Y is linear. This does not mean, however, that Y can be perfectly predicted from X.

### Soci708 Statistics for Sociologists

Soci708 Statistics for Sociologists Module 11 Multiple Regression 1 François Nielsen University of North Carolina Chapel Hill Fall 2009 1 Adapted from slides for the course Quantitative Methods in Sociology

### Correlation and Regression

Correlation and Regression Scatterplots Correlation Explanatory and response variables Simple linear regression General Principles of Data Analysis First plot the data, then add numerical summaries Look

Using Your TI-NSpire Calculator: Linear Correlation and Regression Dr. Laura Schultz Statistics I This handout describes how to use your calculator for various linear correlation and regression applications.

### CHAPTER 2 AND 10: Least Squares Regression

CHAPTER 2 AND 0: Least Squares Regression In chapter 2 and 0 we will be looking at the relationship between two quantitative variables measured on the same individual. General Procedure:. Make a scatterplot

### Correlation The correlation gives a measure of the linear association between two variables. It is a coefficient that does not depend on the units tha

AMS 5 CORRELATION Correlation The correlation gives a measure of the linear association between two variables. It is a coefficient that does not depend on the units that are used to measure the data and

### Statistiek II. John Nerbonne. March 24, 2010. Information Science, Groningen Slides improved a lot by Harmut Fitz, Groningen!

Information Science, Groningen j.nerbonne@rug.nl Slides improved a lot by Harmut Fitz, Groningen! March 24, 2010 Correlation and regression We often wish to compare two different variables Examples: compare

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### Study Resources For Algebra I. Unit 1C Analyzing Data Sets for Two Quantitative Variables

Study Resources For Algebra I Unit 1C Analyzing Data Sets for Two Quantitative Variables This unit explores linear functions as they apply to data analysis of scatter plots. Information compiled and written

### Multiple Regression in SPSS STAT 314

Multiple Regression in SPSS STAT 314 I. The accompanying data is on y = profit margin of savings and loan companies in a given year, x 1 = net revenues in that year, and x 2 = number of savings and loan

### Econ 371 Problem Set #3 Answer Sheet

Econ 371 Problem Set #3 Answer Sheet 4.3 In this question, you are told that a OLS regression analysis of average weekly earnings yields the following estimated model. AW E = 696.7 + 9.6 Age, R 2 = 0.023,

### AP STATISTICS 2014 SCORING GUIDELINES

AP STATISTICS 2014 SCORING GUIDELINES Question 6 Intent of Question The primary goals of this question were to assess a student s ability to (1) calculate and interpret a residual value; (2) answer questions

### 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression

Applications 1. a. Median height is 15.7 cm. Order the 1 heights from shortest to tallest. Since 1 is even, average the two middle numbers, 15.6 cm and 15.8 cm. b. Median stride distance is 124.8 cm. Order

### Mind on Statistics. Chapter 3

Mind on Statistics Chapter 3 Section 3.1 1. Which one of the following is not appropriate for studying the relationship between two quantitative variables? A. Scatterplot B. Bar chart C. Correlation D.

### Statistical Modelling in Stata 5: Linear Models

Statistical Modelling in Stata 5: Linear Models Mark Lunt Arthritis Research UK Centre for Excellence in Epidemiology University of Manchester 08/11/2016 Structure This Week What is a linear model? How

### Simple Linear Regression in SPSS STAT 314

Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,

### Inference for Regression

Simple Linear Regression Inference for Regression The simple linear regression model Estimating regression parameters; Confidence intervals and significance tests for regression parameters Inference about

### Although scatter plots and trend lines may reveal a pattern, the relationship of the variables may indicate a correlation, but not causation.

Middletown Public Schools Mathematics Unit Planning Organizer Subject Math Grade/Course Algebra I Unit 5 Scatterplots and Trendlines Duration 14 instructional days + days reteaching/enrichment Big Idea(s)

### Assumptions in the Normal Linear Regression Model. A2: The error terms (and thus the Y s at each X) have constant variance.

Assumptions in the Normal Linear Regression Model A1: There is a linear relationship between X and Y. A2: The error terms (and thus the Y s at each X) have constant variance. A3: The error terms are independent.

### 0.1 Multiple Regression Models

0.1 Multiple Regression Models We will introduce the multiple Regression model as a mean of relating one numerical response variable y to two or more independent (or predictor variables. We will see different

### Section 14 Simple Linear Regression: Introduction to Least Squares Regression

Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship

### , then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (

Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we

### Chapter 10. The relationship between TWO variables. Response and Explanatory Variables. Scatterplots. Example 1: Highway Signs 2/26/2009

Chapter 10 Section 10-2: Correlation Section 10-3: Regression Section 10-4: Variation and Prediction Intervals The relationship between TWO variables So far we have dealt with data obtained from one variable

### 1. ε is normally distributed with a mean of 0 2. the variance, σ 2, is constant 3. All pairs of error terms are uncorrelated

STAT E-150 Statistical Methods Residual Analysis; Data Transformations The validity of the inference methods (hypothesis testing, confidence intervals, and prediction intervals) depends on the error term,

### Correlation and Simple Linear Regression

Correlation and Simple Linear Regression We are often interested in studying the relationship among variables to determine whether they are associated with one another. When we think that changes in a

### PASS Sample Size Software. Linear Regression

Chapter 855 Introduction Linear regression is a commonly used procedure in statistical analysis. One of the main objectives in linear regression analysis is to test hypotheses about the slope (sometimes

### IAPRI Quantitative Analysis Capacity Building Series. Multiple regression analysis & interpreting results

IAPRI Quantitative Analysis Capacity Building Series Multiple regression analysis & interpreting results How important is R-squared? R-squared Published in Agricultural Economics 0.45 Best article of the

### CORRELATION AND SIMPLE REGRESSION ANALYSIS USING SAS IN DAIRY SCIENCE

CORRELATION AND SIMPLE REGRESSION ANALYSIS USING SAS IN DAIRY SCIENCE A. K. Gupta, Vipul Sharma and M. Manoj NDRI, Karnal-132001 When analyzing farm records, simple descriptive statistics can reveal a

### SIMPLE REGRESSION ANALYSIS

SIMPLE REGRESSION ANALYSIS Introduction. Regression analysis is used when two or more variables are thought to be systematically connected by a linear relationship. In simple regression, we have only two

### Lesson Lesson Outline Outline

Lesson 15 Linear Regression Lesson 15 Outline Review correlation analysis Dependent and Independent variables Least Squares Regression line Calculating l the slope Calculating the Intercept Residuals and

### Solution Let us regress percentage of games versus total payroll.

Assignment 3, MATH 2560, Due November 16th Question 1: all graphs and calculations have to be done using the computer The following table gives the 1999 payroll (rounded to the nearest million dolars)

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Module 7 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. You are given information about a straight line. Use two points to graph the equation.

### Yiming Peng, Department of Statistics. February 12, 2013

Regression Analysis Using JMP Yiming Peng, Department of Statistics February 12, 2013 2 Presentation and Data http://www.lisa.stat.vt.edu Short Courses Regression Analysis Using JMP Download Data to Desktop

### 2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

### The importance of graphing the data: Anscombe s regression examples

The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 30-31, 2008 B. Weaver, NHRC 2008 1 The Objective

### Algebra I: Lesson 5-4 (5074) SAS Curriculum Pathways

Two-Variable Quantitative Data: Lesson Summary with Examples Bivariate data involves two quantitative variables and deals with relationships between those variables. By plotting bivariate data as ordered

### e = random error, assumed to be normally distributed with mean 0 and standard deviation σ

1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.

### Multiple Linear Regression

Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is

### Statistics II Final Exam - January Use the University stationery to give your answers to the following questions.

Statistics II Final Exam - January 2012 Use the University stationery to give your answers to the following questions. Do not forget to write down your name and class group in each page. Indicate clearly

### Refer to Thinking with Mathematical Models pages 82 through 84 to answer the following questions:

Name: Date: Core: Problem 4.1 Virtuan Man: Relating Body Measurements Focus Question: If you have data relating two variables, how can you check to see whether a linear model is a good fit? Refer to pages

### Simple linear regression

Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between

### Section 3 Part 1. Relationships between two numerical variables

Section 3 Part 1 Relationships between two numerical variables 1 Relationship between two variables The summary statistics covered in the previous lessons are appropriate for describing a single variable.

### Assessing Forecasting Error: The Prediction Interval. David Gerbing School of Business Administration Portland State University

Assessing Forecasting Error: The Prediction Interval David Gerbing School of Business Administration Portland State University November 27, 2015 Contents 1 Prediction Intervals 1 1.1 Modeling Error..................................

### 7. Tests of association and Linear Regression

7. Tests of association and Linear Regression In this chapter we consider 1. Tests of Association for 2 qualitative variables. 2. Measures of the strength of linear association between 2 quantitative variables.

### Stat 412/512 CASE INFLUENCE STATISTICS. Charlotte Wickham. stat512.cwick.co.nz. Feb 2 2015

Stat 412/512 CASE INFLUENCE STATISTICS Feb 2 2015 Charlotte Wickham stat512.cwick.co.nz Regression in your field See website. You may complete this assignment in pairs. Find a journal article in your field

### Regression Analysis. Data Calculations Output

Regression Analysis In an attempt to find answers to questions such as those posed above, empirical labour economists use a useful tool called regression analysis. Regression analysis is essentially a

### Linearizing Data. Lesson3. United States Population

Lesson3 Linearizing Data You may have heard that the population of the United States is increasing exponentially. The table and plot below give the population of the United States in the census years 19

### Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares

Topic 4 - Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test - Fall 2013 R 2 and the coefficient of correlation

### Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2

Lesson 4 Part 1 Relationships between two numerical variables 1 Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables

### 12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Understand linear regression with a single predictor Understand how we assess the fit of a regression model Total Sum of Squares

Using Your TI-83/84/89 Calculator: Linear Correlation and Regression Dr. Laura Schultz Statistics I This handout describes how to use your calculator for various linear correlation and regression applications.

### Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables