4. Data on the purchases of pizza from Papa Joe’s Pizza in a small town (in quan

Question

4. Data on the purchases of pizza from Papa Joe’s Pizza in a small town (in quantity per month), and price of the pizza (dollars per pizza), income (in dollars per year), the price of a competitor’s pizza (dollars per pizza), and the local price of a Big Mac are as follows:

a) Using regression analysis, estimate consumption as a linear function of price, income, price of Al’s pizza, and the price of a Big Mac. Write the equation, the t-stats, the R2 , the Standard Error of the Estimate, and the F-statistic. Provide interpretation of the estimation (i.e., are the signs what you'd expect; what level of significance do the coefficients have, etc…). Provide a copy of your output from your regression analysis

b) Assume that anticipated values for the next month are P = $9.05, Income = $48,703, PAL = $10.12, and PBigMac = $1.51. Predict the demand for Papa Joe’s pizza. How confident are you that the prediction is accurate (i.e., establish a confidence interval around this predicted value)? Calculate the own-price elasticity, the income elasticity, and the cross-price elasticities of demand for Papa Joe’s pizza. Explain the meaning of these elasticities.

Data:

Quantity

Price

Income

Price of Al's Pizza

Price of BigMac

2659

8.65

46639.5

10.55

2.23

2870

8.65

46822.4

10.45

2.40

2875

8.65

47005.3

10.35

2.76

2849

8.65

47499.13

10.3

1.87

2842

8.65

47499.13

10.3

1.69

2816

8.65

47096.75

10.25

1.69

3039

7.5

47096.75

10.25

1.51

3059

7.5

47462.55

10.15

2.05

3040

7.5

47462.55

10

2.23

3090

7.5

47773.48

10

3.12

2934

8.5

47773.48

10.25

3.12

2942

8.5

47773.48

10.25

3.29

2834

8.5

47919.8

9.75

2.67

2517

9.99

48194.15

9.75

1.96

2503

9.99

48377.05

9.65

1.87

2502

9.99

48194.15

9.6

2.23

2557

9.99

49108.65

10

0.98

2586

10.25

50023.15

10.25

0.98

2623

10.25

50023.15

10.2

2.05

2633

10.25

51120.55

10

2.05

2721

9.75

51502.81

10.1

0.98

2729

9.75

51694.86

10.1

0.98

2791

9.75

52024.08

10.1

2.14

2821

9.75

52126.5

10.25

2.14

Quantity

Price

Income

Price of Al's Pizza

Price of BigMac

2659

8.65

46639.5

10.55

2.23

2870

8.65

46822.4

10.45

2.40

2875

8.65

47005.3

10.35

2.76

2849

8.65

47499.13

10.3

1.87

2842

8.65

47499.13

10.3

1.69

2816

8.65

47096.75

10.25

1.69

3039

7.5

47096.75

10.25

1.51

3059

7.5

47462.55

10.15

2.05

3040

7.5

47462.55

10

2.23

3090

7.5

47773.48

10

3.12

2934

8.5

47773.48

10.25

3.12

2942

8.5

47773.48

10.25

3.29

2834

8.5

47919.8

9.75

2.67

2517

9.99

48194.15

9.75

1.96

2503

9.99

48377.05

9.65

1.87

2502

9.99

48194.15

9.6

2.23

2557

9.99

49108.65

10

0.98

2586

10.25

50023.15

10.25

0.98

2623

10.25

50023.15

10.2

2.05

2633

10.25

51120.55

10

2.05

2721

9.75

51502.81

10.1

0.98

2729

9.75

51694.86

10.1

0.98

2791

9.75

52024.08

10.1

2.14

2821

9.75

52126.5

10.25

2.14

Price of Al's Price of BigMac Quantity Price IncomePizza 2659 2870 2875 2849 2842 2816 3039 3059 3040 3090 2934 2942 2834 2517 2503 2502 2557 2586 2623 2633 2721 2729 2791 2821 8.65 46639.5 8.65 46822.4 8.65 47005.3 8.65 47499.13 8.65 47499.13 8.65 47096.75 7.5 47096.75 7.5 |47462.55 7.5 47462.55 7.5 47773.48 8.5|47773.48 8.5 47773.48 8.547919.8 9.9948194.15 9.9948377.05 9.9948194.15 9.9949108.65 10.25 50023.15 10.25 50023.15 10.25 51120.55 9.75 51502.81 9.7551694.86 9.75 52024.08 9.75 52126.5 10.55 10.45 10.35 10.3 10.3 10.25 10.25 10.15 10 10 10.25 10.25 9.75 9.75 9.65 2.23 2.40 2.76 1.87 1.69 1.69 1.51 2.05 2.23 3.12 3.12 3.29 2.67 1.96 1.87 2.23 0.98 0.98 2.05 2.05 0.98 0.98 2.14 2.14 10.25 10.2 10 10.1 10.1 10.1 10.25

Explanation / Answer

SOl:

Carry out regression in excel

we get the following output:

QUANTITY=1185.523-213.449(PRICE)+0.0497(INCOME)+101.35(Price of AI's Pizza)+40.167(Price of BigMac)

since R sq=0.955346

95.53% variation in quantity is explained by model .

good model

F stat=101.237

p<0.05

Reject Null hypothesis

Model is significant

As p values of price,income,price of Ai's Pizza and price of BigMac are <0.05

All varaibles are significant variables which can be included in model.

Solutionb:

QUANTITY=1185.523-213.449(PRICE)+0.0497(INCOME)+101.35(Price of AI's Pizza)+40.167(Price of BigMac)

QUANTITY=1185.523-213.449(9.05)+0.0497(48703)+101.35((10.12)+40.167(1.51)

=7847

SUMMARY OUTPUT Regression Statistics Multiple R 0.977418 R Square 0.955346 Adjusted R Square 0.945945 Standard Error 42.4663 Observations 24 ANOVA df SS MS F Significance F Regression 4 733067 183266.7 101.6237 1.5E-12 Residual 19 34264.34 1803.386 Total 23 767331.3 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1185.523 506.93 2.338632 0.030437 124.5063 2246.54 124.5063 2246.54 Price -213.449 13.50454 -15.8057 2.19E-12 -241.714 -185.184 -241.714 -185.184 Income 0.049769 0.006792 7.327055 6.03E-07 0.035552 0.063986 0.035552 0.063986 Price of Al's Pizza 101.3507 38.80183 2.612008 0.01714 20.13754 182.5639 20.13754 182.5639 Price of BigMac 40.16656 15.22397 2.638376 0.0162 8.302416 72.0307 8.302416 72.0307

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.