Question 11 options:

Mama's Pizza restaurant chain would like to understand which variable most strongly influences the amount of sales of their specialty, deep-dish pizza. They have gathered data on the number of monthly sales(in 100's) of deep-dish pizzas and the amount spent per month on advertising at 30 of their restaurants.Below are the results of the linear regression to predict the number of monthly sales(in 100's)based on monthly advertising (in $1,000's).

SUMMARY OUTPUT - Regression Model to Predict Monthly Sales(in 100's)

based on Monthly Advertising (in $1,000's)

Regression Statistics

Multiple R

0.9210

R Square

0.8482

Observations

30

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-326.55

103.05

-3.169

0.00368

-537.63

-115.47

Advertising(in $1,000's)

17.55

3.922

4.475

0.00012

9.52

25.58

Part 1:What is the independent (X) variable and the dependent (Y) variable?(2 marks)

X =

Y =

Part 2:What is the regression equation to predict monthly sales?(2 marks)

Part 3:What is the meaning of the slope? Interpret it using the words of the problem.(3 marks)

Part 4:Predict the monthly sales of one of Mama's Pizza restaurants if their monthly advertising is $55,000.(3 marks)

Part 5:Interpret the coefficient of determination (r²) using the words of the problem.(2 marks)

Part 6:At the 5% level of significance (95% confidence level), is there enough evidence to conclude that there is a linear relationship between the monthly sales and advertising expenditures? State the reasoning for your conclusion.

Hypotheses:(2 marks)Enter the correct hypothesis

H₀:

H_A:

Decision with Justification:(2 marks)Enter your answer

Conclusion (1 mark)

1. Yes, there is enough evidence to conclude there is a linear relationship betweenmonthly sales and advertising expenditures, at the 5% level of significance.
2. No, there is not enough evidence to conclude there is a linear relationship betweenmonthly sales and advertising expenditures, at the 5% level of significance.

Enter the LETTER of the correct answer

Mama's Pizza had also collected information on the average income per household in the area for each of these 30 restaurants. Below are the results of a linear regression to predict monthly sales (in 100s) based on the average household income in the area (in $1,000s).

SUMMARY OUTPUT -Regression Model to Predict Monthly Sales(in 100's) based on Average Household Income in the Area (in $1,000's)

Regression Statistics

Multiple R

0.3992

R Square

0.1594

Observations

30

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-583.86

714.23

-0.817

0.42056

-2046.9

879.2

Income

(in $1,000's)

18.29

8.68

2.107

0.04419

0.510

36.07

Part 7:Is monthly advertising or average household income a better predictor of the monthly sales? Why?(2 marks)

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