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# Regression Analysis

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In trying to look at the effects of shopping center expansion, the Commerce Department decided to look at the relationship between the number of shopping centers and the retail sales for different states in the same region. It collected the data for the North Central states in the U.S. and found the following:(PLEASE SEE ATTACHED TABLE)

a). Create a scatter plot of the data using excel.

b). Find the regression equation relating retail sales and number of shopping centers.

c). Plot the regression line (using excel) on the same plot as the data. Do you think the line fits the data well? Why or why not?

d). Use the regression line to predict retail sales for each state.

e). Calculate the residuals for each state. Which state has the largest residual? Which state has the smallest? Do the residuals support your answer to part (d)?

f). Find the standard error of the estimate.

##### Solution Summary

The scatter plot of the data using Excel is created. A regression equation relating retail sales and number of shopping centers are found. The solution answers the question(s) below.

##### Solution Preview

In trying to look at the effects of shopping center expansion, the Commerce Department decided to look at the relationship between the number of shopping centers and the retail sales for different states in the same region. It collected the data for the North Central states in the U.S. and found the following:(PLEASE SEE ATTACHED TABLE)

a). Create a scatter plot of the data using excel.

Note. The graph was drawn by Maple since I am not very familiar with Excel. Sorry for that.

b). Find the regression equation relating retail sales and number of shopping centers.

Denote the number of shopping center by X and denote the retail sales by Y, we get the regression equation as follows.
Y=0.0190214X+1.33086

c). Plot the regression line (using ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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