Activity Applying Simple Linear Regression to Your Favorite Da Many dependent variables in all areas of research serve as the subjects of regression-modeling efforts. We list five such variables here: 1. Crime rate in various communities 2. Daily maximum temperature in your town 3. Grade point average of students who have completed one aca- demic year at your college 4. Gross domestic product of the United States 5. Points scored by your favorite football team in a single game Choose one of these dependent variables, or choose some other dependent variable, for which you want to construct a predic- tion model. There may be a large number of independent variables that should be included in a prediction equation for the dependent variable you choose. List three potentially important independent variables, X1, X₂, and x3. that you think might be (individually) strongly related to your dependent variable. Next, obtain 10 data values, each of which consists of a measure of your dependent vanable y and the corresponding values of x₁, x2, and X3. a. Use the least squares formulas given in this chapter to fit three straight-line models-one for each independent variable-for predicting y. b. Interpret the sign of the estimated slope coefficient , in each case, and test the utility of each model by testing Ho: B₂ = 0 against HB, 0. What assumptions must be satisfied to ensure the validity of these tests? c. Calculate the coefficient of determination, r, for each model. Which of the independent variables predicts y best for the 10 sampled sets of data? Is this variable necessarily best in gen- eral (.e. for the entire population)? Explain.
Activity Applying Simple Linear Regression to Your Favorite Da Many dependent variables in all areas of research serve as the subjects of regression-modeling efforts. We list five such variables here: 1. Crime rate in various communities 2. Daily maximum temperature in your town 3. Grade point average of students who have completed one aca- demic year at your college 4. Gross domestic product of the United States 5. Points scored by your favorite football team in a single game Choose one of these dependent variables, or choose some other dependent variable, for which you want to construct a predic- tion model. There may be a large number of independent variables that should be included in a prediction equation for the dependent variable you choose. List three potentially important independent variables, X1, X₂, and x3. that you think might be (individually) strongly related to your dependent variable. Next, obtain 10 data values, each of which consists of a measure of your dependent vanable y and the corresponding values of x₁, x2, and X3. a. Use the least squares formulas given in this chapter to fit three straight-line models-one for each independent variable-for predicting y. b. Interpret the sign of the estimated slope coefficient , in each case, and test the utility of each model by testing Ho: B₂ = 0 against HB, 0. What assumptions must be satisfied to ensure the validity of these tests? c. Calculate the coefficient of determination, r, for each model. Which of the independent variables predicts y best for the 10 sampled sets of data? Is this variable necessarily best in gen- eral (.e. for the entire population)? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcribed Image Text:Activity Applying Simple Linear Regression to Your Favorite Data
Many dependent variables in all areas of research serve as the
subjects of regression-modeling efforts. We list five such variables
here:
1. Crime rate in various communities
2. Daily maximum temperature in your town
3. Grade point average of students who have completed one aca-
demic year at your college
4. Gross domestic product of the United States
5. Points scored by your favorite football team in a single game
Choose one of these dependent variables, or choose some
other dependent variable, for which you want to construct a predic-
tion model. There may be a large number of independent variables
that should be included in a prediction equation for the dependent
variable you choose. List three potentially important independent
variables, X₁, X₂, and x3. that you think might be (individually)
strongly related to your dependent variable. Next, obtain 10 data
values, each of which consists of a measure of your dependent
vanable y and the corresponding values of x₁, x₂, and X3.
a. Use the least squares formulas given in this chapter to fit three
straight-line models-one for each independent vanable-for
predicting y.
b. Interpret the sign of the estimated slope coefficient , in each
case, and test the utility of each model by testing Ho: B-0
against H8, 0. What assumptions must be satisfied to
ensure the validity of these tests?
c. Calculate the coefficient of determination, for each model.
Which of the independent variables predicts y best for the
10 sampled sets of data? Is this variable necessarily best in gen-
eral i.e. for the entire population)? Explain.
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