The ice cream store Cool Stuff sells exotic ice creams inclu

The ice cream store Cool Stuff sells exotic ice creams, including Tropical Cream and Green Mango. Cool Stuff has been varying the prices of these two flavors over the past 12 weeks and has recorded the sales data. The table shows the quantity sold of Tropical Cream, Q, given the price of a half gallon of Tropical Cream, p, and the price of the other flavor, Green Mango, po.

Use these data to estimate the demand function for Tropical Cream. Are the coefficients on the two prices statistically significantly different from zero at the 5% significance level? What is the R2?

Q: 84, 82, 85, 83, 82, 84, 87, 81, 82, 79, 82, 78

P: 8.5, 9, 8.75, 9.25, 9.5, 9.25, 8.25, 10, 10, 10.5, 9.5, 10.25

Po: 5.25, 6, 6, 6.5, 6.25, 6.25, 5.25, 7, 7.25, 7.25, 6.25, 7.25

What are the coefficients? the standard errors? and r^2?

What is p coefficients t value? and what is Po cofficients t value?

Are the coefficnets on the two proces statistically significantly different from zero at the 5% significance level?

Solution

The ice cream store Cool Stuff sells exotic ice creams, including Tropical Cream and Green Mango. Cool Stuff has been varying the prices of these two flavors over the past 12 weeks and has recorded the sales data. The table shows the quantity sold of Tropical Cream, Q, given the price of a half gallon of Tropical Cream, p, and the price of the other flavor, Green Mango, po.

Use these data to estimate the demand function for Tropical Cream. Are the coefficients on the two prices statistically significantly different from zero at the 5% significance level? What is the R2?

Q: 84, 82, 85, 83, 82, 84, 87, 81, 82, 79, 82, 78

P: 8.5, 9, 8.75, 9.25, 9.5, 9.25, 8.25, 10, 10, 10.5, 9.5, 10.25

Po: 5.25, 6, 6, 6.5, 6.25, 6.25, 5.25, 7, 7.25, 7.25, 6.25, 7.25

What are the coefficients? the standard errors? and r^2?

variables

coefficients

std. error

Intercept

117.8579

6.3046

P

-5.1590

1.6692

Po

2.0442

1.6495

R² = 0.843

The function Q=117.8579-5.159*P+2.0442*Po

What is p coefficients t value? and what is Po cofficients t value?

Are the coefficnets on the two proces statistically significantly different from zero at the 5% significance level?

t value for P, t=-3.091, P=0.0129 which is < 0.05, significantly different from zero at the 5% significance level.

t value for Po, t=1.239, P=0.2466 which is > 0.05, not significantly different from zero at the 5% significance level.

Regression Analysis

R²

0.843

Adjusted R²

0.809

n

12

R

0.918

k

2

Std. Error

1.079

Dep. Var.

Q

ANOVA table

Source

SS

df

MS

F

p-value

Regression

56.4333

2  

28.2167

24.22

.0002

Residual

10.4833

9  

1.1648

Total

66.9167

11  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=9)

p-value

95% lower

95% upper

Intercept

117.8579

6.3046

18.694

1.65E-08

103.5960

132.1199

P

-5.1590

1.6692

-3.091

.0129

-8.9350

-1.3831

Po

2.0442

1.6495

1.239

.2466

-1.6873

5.7757

variables	coefficients	std. error
Intercept	117.8579	6.3046
P	-5.1590	1.6692
Po	2.0442	1.6495