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

1. Find the Regression Model that includes all three independent variables
2. 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.
3. (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).)