The Very Fresh Juice Company has developed a regression mode

The Very Fresh Juice Company has developed a regression model relating sales (y in $10,000s) with four independent variables. The four independent variables are price per unit (x1, in dollars), competitor\'s price (x2, in dollars), advertising (x3, in $1,000s) and type of container used (x4) (1 = Cans and 0 = Bottles). Part of the regression results are shown below: Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 4 283,940.60 Error 18 621,735.14 Total a. Compute the coefficient of determination and fully interpret its meaning. b. Is the regression model significant? Explain what your answer implies. Let = 0.05. c. What has been the sample size for this analysis?

Solution

y = x1 + x2 + x3 + x4

Regression Degrees of Freedom = 4

Regression Sum of Squares SSR = 283,940.6

Error Degrees of Freedom = 18

Error Sum of Squares SSE = 621,735.14

a) coefficient of determination R² = SSR / (SSR + SSE) = 283,940.6 / (283,940.6 + 621,735.14) = 0.3135 = 31.35%

It implies 31.35% of the variance in the dependent variable that is predictable from the independent variable.

b) MSE = SSE/ df error = 621,735.14/18 = 34540.84

MSR = SSR/df regression = 283,940.6/4 = 70985.15

F = MSR/MSE = 70985.15/34540.84 = 2.055

At alpha 0.05 critical F Value (4.18) = 2.927

As t < critical t we fail to reject null hypothesis and conclude that it is not significant

c) Sample size = df error + df regression + 1 = 4 + 18 + 1 = 23