A company has yearly data for its sales volumes, time (Time is equal to 1 for ye

Question

A company has yearly data for its sales volumes, time (Time is equal to 1 for year 1, 2 for year 2, etc) and advertising expenditure (Advertising). It thinks that the second two variables 1. explain sales volumes and runs a regression with Excel thatpoduces the following ANOVA table ANOVA df MS p-value Regression Residual Total 574041.8 26640.75 9 600682.5 (a) (6 marks) Provide the missing information for the following ANOVA table (reproduce it in your answer and explain how you got your answers). (b) (1 marks) What is the sample size? Explain. (c) (4 marks) At the 1% level of significance, does the fitted equation represent a significant relationship between the dependent variable and the independent variables?

Explanation / Answer

Solution:

a. df (regression) = k - 1 (k - number of treatment)

df (regression) = 3 - 1 = 2

df (residual) = 9 - 2 = 7

MS (regression) = SS (regression)/df (regression)

MS (regression) = 574041.8/2 = 287020.9

MS (residual) = SS (residual)/df (residual)

MS (residual) = 26640.75/7 = 3805.21

F = 287020.9/3805.21 = 75.42

P-value = 0.000

b. df (total) = 9

n - 1 = 9

n = 9 +1 = 10

Sample size is 10

c. Since p-value is less than 5% significance, there is significant relationship between the dependent variable and independent variables.

d. R-square = SSR/SST

R-square = 574041.8/600682.5

R-square = 0.9556

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