Question

1.             The manager of Discount Distributing Company believes that sales of soft drinks at his store don’t change much with changes in price.  The data below show prices charged in dollars & number of cases of soft drinks sold in the 20 days following each price change:  

Yi : Cases	600	550	560	500	520	540		= 3270
Xi; Price	4.25	5.25	4.75	5.5	5	4.5		ΣXi =  29.25

The computer printout for the regression line typically looks like the following estimation line indicating is the intercept plus the slope times the X variable. The value for the standard errors of the estimates for the intercept , and for the slope are typically expressed below each term in parenthesis as follows. Note that n = 6 here (6 prices charged).

                             

                                    (110.5896)       (22.59854)

            

SSR = 3715.714            SSE = 2234.286            (Hint: SST = ?)

Based upon the information given above, you are to find the following two terms and test the hypothesis for the significance of the slope of the linear estimate below. Each part is worth 5 points.

1. The Coefficient of Determination or r² =

2. MSE =

Test the hypothesis

             

Test H₀: b₁ = 0, vs H_A: b₁ ≠ 0 at α = .05.  (2 – tailed test).

3. Find the Critical Rejection values from the table:

4. Calculate the test statistic

5. State your conclusion

Answer 1