Question

A

new retail store is analyzing their monthly revenues per shopper to quantify the effect of the age of the shopper and the number of (monthly) shoppers on their monthly revenue. The owner feels that the revenue received per shopper increases with the age of the shopper and with the number of shoppers but wants a more quantitative explanation. The multiple regression output is shown below.answer with the help of excel

Summary output

Multiple R

0.8391

R-Square

0.7841

Adj R-Square

0.7683

StErr of Estimate

150.828

Regression output

Coefficient

Std Err

t-value

p-value

Constant

-54.986

331.204

…

0.0010

Age of shopper

79.017

10.647

Not provided

0.0000

Number of shoppers

14.973

10.443

…

0.1940

​

(1) Would you recommend that this company examine any other factors to predict the monthly revenue? If yes, what other factors would you want to consider? Explain your answer.

(2) What does the scatterplot below of the residuals vs the number of monthly shoppers tell you? Is there “more work to be done”? Why or why not?

(3) Predict the monthly revenue the owner would receive from a customer that is 40 years old when the number of monthly shoppers is 20,000. No need to do the arithmetic, rather show the numbers you would add or multiply together in a formula.

(4) Notice that the t-value for the Age of shopper variable is labelled “not provided” in the regression table for this problem. Please provide the t-value calculation for the Age of shopper variable in the space below. No need to do the arithmetic, rather show the numbers you would add, multiply, subtract, or divide together in a formula below.

(5) Which input variable (i.e., explanatory variable) might you consider dropping based on a t-test? Why? Please explain convincingly.

Answer 1

1)
yes, to provide monthly revenues we have to add cost of the purchase of each shopper from retail store , because cost is most important to determine monthly revenues

2)
Please provide scatter plot for same

3)
y^ = -54.986 + 79.017 * age of shopper + 14.973 * number of shopper
here age = 40 , number of shopper = 20000
y^ = -54.986 + 79.017*40 + 14.973 * 20000

4)
t = coefficient/st error
= 79.017/10.647

5)
p-value > alpha
then that variable is insignificant
here number of shoppers has p-value = 0.1940 > 0.05
hence we might consider dropping number of shoppers

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