Question

1. The manager of On-A-Budget Soda 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	Y=545	Yi = 3270
Xi; Price	4.25	5.25	4.75	5.5	5	4.5	X=4.875	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 Sb0, and for the slope Sb1are typically expressed below each term in parenthesis as follows. Note that n = 6 here (6 prices charged).

                                 Yi = 829.1429 - 58.2857 Xi   

                                    (110.5896)      (22.59854)

           

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

Find 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.

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

Sol:

SST=SSR+SSE=3715.714 + 2234.286 =5950

1. The Coefficient of Determination or r2

Rsq=1-SS error/SS total

=1-2234.286 /5950

= 0.6244897

Coefficient of Determination or r2 =0.6245

2. MSE =SSE/df=2234.286 /(n-k-1)=2234.286/(6-1-1)=2234.286/4=558.5715

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

3. Find the Critical Rejection values from the table:

df=n-k-1=6-1-1=4

t critcal two tail for alpha=0.05 and 4 df is

=T.INV.2T(0.05,4)

=2.77645

2 critical values are -2.77645 and +2.77645

4. Calculate the test statistic

t=slope/std error

= - 58.2857/(22.59854)

t=- 2.57918

5. State your conclusion

test statstic falls in the acceptance region(-2.77645 and +2.77645)

Accept Ho

There is no linear relationship between cases and price