Statistics Multiple Regression A study was performed aimed at trying to further understand what factors contribute to the home size of a family in the United States Sample data was collected from a small sample to assist with the initial analysis discussion Data Definition of variables Home size (Y) home square footage in hundreds of square foot (e g 18 represents 1800 square feet) Annual Income (X1) annual income in thousands of dollars (e g 32 represents $32,000) Family Size (X2) number of people living in household Education (X3) combined years of formal education beyond high school Home size (Y) 18, 17, 26, 23, 22, 21, 33, 18, 31, 21 Annual Income (X1) 32, 36, 55, 46, 38, 60, 65, 44, 69, 50 Family Size (X2) 2, 2, 3, 4, 4, 3, 6, 3, 5, 3 Education (X3) 4, 8, 7, 0, 2, 10, 8, 8, 2, 6 Questions Find the Regression Model that includes all three independent variables Find the coefficient of determination for the Regression Model found in question 1 Interpret the meaning of the coefficient of determination in the context of the problem (a ) Find the p value for each independent variable (b ) interpret the meaning of each p value, and ( c ) determine which independent variables should be removed from the Regression Model (use Alpha 0 10) 4 Find the new Regression Model based on your analysis from question 3 5 Compare the r 2 adjusted, p value, and F value for the two regression Models found in question 1 and question 4 Did the regression model improve 6 Interret the Regression Coefficients for the Regression Model found in question 4 7 Using the Regression Model found in question 4, predict the home size for a family of 4, income of $52,000, and 6years of formal education (Note If you removed one or more of the variables from your Regression Model, only use data for the remaining variable(s) )

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Statistics Multiple Regression A study was performed aimed at trying to further understand what factors contribute to the home size of a family in the

Statistics Multiple Regression

A study was performed aimed at trying to further understand what factors contribute to the home size of a family in the United States. Sample data was collected from a small sample to assist with the initial analysis & discussion.

Data:

Definition of variables

Home size (Y) = home square footage in hundreds of square foot (e.g. 18 represents 1800 square feet)

Annual Income (X1) = annual income in thousands of dollars (e.g. 32 represents $32,000)

Family Size (X2) = number of people living in household

Education (X3) = combined years of formal education beyond high school

Home size (Y): 18, 17, 26, 23, 22, 21, 33, 18, 31, 21

Annual Income (X1): 32, 36, 55, 46, 38, 60, 65, 44, 69, 50

Family Size (X2): 2, 2, 3, 4, 4, 3, 6, 3, 5, 3

Education (X3): 4, 8, 7, 0, 2, 10, 8, 8, 2, 6

Questions

Find the Regression Model that includes all three independent variables
Find the coefficient of determination for the Regression Model found in question #1. Interpret the meaning of the coefficient of determination in the context of the problem.
(a.) Find the p-value for each independent variable.

(b.) interpret the meaning of each p-value, and ( c.) determine which independent variables should be removed from the Regression Model (use Alpha = 0.10)

4. Find the new Regression Model based on your analysis from question #3

5. Compare the r²-adjusted, p-value, and F-value for the two regression Models found in question #1 and question #4. Did the regression model improve?

6.Interret the Regression Coefficients for the Regression Model found in question #4.

7.Using the Regression Model found in question #4, predict the home size for a family of 4, income of $52,000, and 6years of formal education. (Note: If you removed one or more of the variables from your Regression Model, only use data for the remaining variable(s).)