Question

Regression Analysis with a Minitab output

Assume that your company owns multiple retail outlets in cities across the United States. You conduct a study to determine if daily sales levels (in hundreds of dollars) can be predicted by the number of competitors that are located within a one-mile radius of each location and city population (in thousands of people). Therefore, the dependent variable is SALES and the two independent variables are NUMBER OF COMPETITORS and CITY POPULATION. Your research team utilized Minitab software to create a Regression model. The results are shown below.

Regression Analysis: SALES vs. NUMBER OF COMPETITORS, CITY POPULATION

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value
Regression	2	160.362	80.181	15.93
NUMBER OF COMPETITORS	1	138.093	138.093	27.43
CITY POPULATION	1	2.576	2.576	0.51
Error	7	35.238	5.034
Total	9	195.600

Model Summary

S	R-sq
2.24365	81.98%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
NUMBER OF COMPETITORS	-3.245	0.620	-5.24	0.001	1.07
CITY POPULATION	0.0174	0.0243	0.72	0.498	1.07

Regression Equation

SALES

=

38.21 - 3.245 NUMBER OF COMPETITORS + 0.0174 CITY POPULATION

Study this output then answer the following questions:

1. Find the R-Square value. Report this value in the space below and comment on what this statistic indicates regarding the strength of the linear relationship between the variables.

2. Find the P-values for the two independent variables (NUMBER OF COMPETITORS and CITY POPULATION). Report these values in the space below and comment on their individual significance to the model. Specifically, address the following in your analysis:

• Which independent variable is the most significant?
• Which independent variable(s) can be proven significant at a 95% confidence level?
• Which independent variable(s) can be proven significant at a 99% confidence level?

Answer 1

R-Square value: 81.98% of the total variation in the explanatory variables in the regression model.

The p-value of number of competitors is 0.001< 0.05 hence the variable is significant

The p-value of city population is 0.498 > 0.05 hence the variable is not significant

Which independent variable is the most significant? number of competitors

• Which independent variable(s) can be proven significant at a 95% confidence level? number of competitors
• Which independent variable(s) can be proven significant at a 99% confidence level? number of competitors