Question

1. The owner of the Original Italian Pizzeria restaurant chain would like to predict the sales of her specialty deep-dish pizza. She has gathered data on the monthly sales of deep-dish pizzas at her restaurants and observations on other potentially relevant variables for each of her 15 restaurants in Northern California. The data is found in the file “DeepDishPizza.”

a. Create two (2) scatter charts. The first one will be a scatter chart of Quantity Sold (on the y-axis) and the variable Disposable Income per Household (on the x-axis). The second one will be a scatter chart of Quantity Sold (on the y-axis) and the variable Monthly Advertising Expenditures. Be sure to label the axes correctly.

b. Using the Regression function in Data Analysis, estimate a regression equation between Quantity Sold and Disposable Income per Household. Type your estimated equation in a text box. How would you explain the interpretation of the coefficient on Disposable Income per Household and the R 2 to the owner?

c. At a level of significance of 5%, test the null hypothesis that the coefficient on Disposable Income per Household is 0. Clearly explain your answer.

d. The owner also wants to know whether advertising expenses by her firm have any effect on the number of deep-dish pizzas sold. Using the Regression function in Data Analysis, estimate a regression equation between Quantity Sold and Disposable Income per Household Type and Monthly Advertising Expenditure. Type your estimated equation in a text box. How would you now explain both estimated coefficients and the R 2 to the owner?

e. At a level of significance of 5%, test the null hypothesis that the coefficient on each independent variable is 0. Clearly explain your answer.

f. For the equation you estimated in (d), what is the interpretation of the F-test? Is it significant at a level of significance of 5%?

g. Suppose the Disposable Income per Household is equal to $43,000. Using your estimated regression equation in (d), what should the owner plan on Monthly Advertising Expenditures per restaurant if she wants to sell 58,000 deep-dish pizza per restaurant? Show your work.

Restaurant Number	Quantity Sold	Disposable Income per Household	Monthly Advertising Expenditures
1	85,300	$42,100	$64,800
2	40,500	$38,300	$42,800
3	61,800	$41,000	$58,600
4	50,800	$43,300	$46,500
5	60,600	$44,000	$50,700
6	79,400	$41,200	$60,100
7	71,400	$41,700	$55,600
8	70,700	$43,600	$57,900
9	55,600	$39,900	$52,100
10	70,900	$44,800	$60,700
11	77,200	$41,800	$64,400
12	63,200	$44,200	$55,600
13	71,100	$40,100	$60,900
14	55,500	$39,100	$47,200
15	42,100	$38,000	$46,100

Answer 1

a)

.......................

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.483483
R Square	0.233756
Adjusted R Square	0.174814
Standard Error	11962.14
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5.67E+08	5.67E+08	3.965877	0.067871
Residual	13	1.86E+09	1.43E+08
Total	14	2.43E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-58385.9	61402.83	-0.95087	0.359016	-191039	74266.82
Disposable Income per Household	2.93996	1.47629	1.991451	0.067871	-0.24937	6.129291

Y = -58385.9 + 2.93996 *x

R Square = 0.233756

.....................

c)

p value for slope = 0.067871

p value > 0.045 , not significnt

.............

d)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.93842406
R Square	0.880639716
Adjusted R Square	0.860746335
Standard Error	4914.014692
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	2	2.14E+09	1.07E+09	44.26798	2.89E-06
Residual	12	2.9E+08	24147540
Total	14	2.43E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-53658.53808	25230.92	-2.1267	0.054877	-108632
Disposable Income per Household	0.613266618	0.671587	0.913161	0.379139	-0.84999
Monthly Advertising Expenditures	1.673363643	0.207499	8.064432	3.46E-06	1.221262

y = -53658.538 +0.6132666*X1 +1.67336*x2

R Square = 0.8806

.................

e)

p value for monthly expd = 3.46313E-06

p value < 0.05, significant

.................

f)

p value = 2.89E-06

p value < 0.05

test is signifcant

modal is good

..............

Please revert back in case of any doubt.

Please upvote. Thanks in advance.