The director of marketing at Vanguard Corporation believes that sales of the com
ID: 1159332 • Letter: T
Question
The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation: where S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 0.01 level or better. The regression output from the computer is as follows DEPENDENT VARIABLE: SR- SQUARE OBSERVATIONS: 36 F- RATIO 4.781 P- VALUE ON F 0.0150 0.2964 PARAMETER STANDARD ERROR 63821.0 0.3250 0.164 P- VALUE 0.0098 0.0228 0.0927 VARIABLE ESTIMATE INTERCEPT 175086.0 T-RATIC 2.74 2.63 0.4550 0.284 a. Does Vanguard's advertising expenditure (A) have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value. b. Does advertising by its three largest rivals affect sales of Bright Side detergent in a statistically significant way? Explain, using the appropriate p-value c. What fraction of the total variation in sales of Bright Side remains unexplained (undetermined)? What other explanatory variables might be added to this equation? d. What is the expected level of sales each week when Vanguard spends S20,000 per week and the combined advertising expenditures for the three rivals are S300,000 per week?Explanation / Answer
Ans 1/a)
For Vanguard Advertising expenditure we have t value equal to (0.455 /0.325) we know that t ratio = parameter estimate/standard error hence t value=1.4
For 5% of singnificance we need t value at least as good as value 2 if t value is less than 2 then we can say it is not significant and vice versa
For 10% of singnificance we need t value at least as good as value 1.6 if t value is less than 2 then we can say it is not significant and vice versa
For 1% of singnificance we need t value at least as good as value 2.4 if t value is less than 2 then we can say it is not significant and vice versa
calculated t=1.4 is lower than any of these critica t values for differeent confiedance levels hence Vanguard Advertising expenditure coefficient is statistically not signficant
P value for t=1.4 and DF=35 is 0.1703
Ans 1/b)
Calculated t=-1.73 that is lower than critical t which is 2.6 for larger samples and critical t value is even higher for smaller dF hence critical value t>caluclated t we can say it is satistically not significant
P Value for t=-1.73 is 0.0924
Ans 1/c)
It can be seen from R^2 as it tells us about the explanation given by independant variable 0<R^2<1
As in our case we can say 29.64% of Dependant variable is explained by independant variables such as vanguard expenditure and collective rival expenditure
We should have added other independant variables such as dummy for social networking exposure for trageted demography
Ans 1/d)
To calculate expected value of sales we have A=20,000 and R=300,000
S=a+bA+cR
=175086+0.4550(20000)-0.284(300000)
Expected Sales is $98986