# Correlation Matrix/Regression Equation

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18. Fran's Convenience Marts are located throughout metropolitan Erie, Pennsylvania. Fran, the owner, would like to expand into other communities in northwestern Pennsylvania and southwestern New York, such as Jamestown, Corry, Meadville, and Warren. As part of her presentation to the local bank, she would like to better understand the factors that make a particular outlet profitable. She must do all the work herself, so she will not be able to study all her outlets. She selects a random sample of 15 marts and records the average daily sales (Y), the floor space (area), the number of parking spaces, and the median income of families in that ZIP code region for each. The sample information is reported below.

a. Determine the regression equation.

b. What is the value of R^2? Comment on the value.

c. Conduct a global hypothesis test to determine if any of the independent variables are different from zero.

d. Conduct individual hypothesis tests to determine if any of the independent variables can be dropped.

e. If variables are dropped, recompute the regression equation and R^2.

24. Many regions along the coast in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has resulted in many of the large grocery store chains building new stores in the region. The Kelley's Super Grocery Syores, Inc. chain is no exception. The director of planning for Kelley's Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information.

Food and income are reported in thousands of dollas per year, and the variable "Size" refers to the number of people in the household.

a. Develop a correlation matrix. Do you see any problems with multicollinearity?

b. Determine the regression equation. Discuss the regression equation. How much does an additional family member add to the amount spent on food?

c. What is the value of R^2? Can we conclude that this value is greater than 0?

d. Would you consider deleting either of the independent variables?

e. Plot the residuals in a histogram. Is there any problem with the normality assumption?

f. Plot the fitted values against the residuals. Does this plot indicate any problems with homoscedasticity?

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