Question

The following data gives the monthly sales (in thousands of dollars) for different advertising expenditures (also in thousands of dollars) and sales commission percentages.

Sales                    245      138      352      322      228      275      560      366

Advertising          16.5     18.0     22.3     18.4     19.0     19.5     30.0     18.6

Commission        10.5     2.0       4.0       3.5       4.5       1.8       9.0       8.5

1. What amount of sales would this model predict for advertising expenditures of 25,000 and sales commission of 8%? [Show your code in “R Code” section. Show the answer in “Answer” section. Leave “Comments” section blank.]
2. Find the correlation coefficients for advertising expenditure and commission compared to sales. Explain the results of these findings. [Show your code in “R Code” section. Show the answer in “Answer” section. Leave “Comments” section blank.]
3. At the 5% level of significance, are advertising expenditure or sales commission percentage significant? Why? [Show your code in “R Code” section. Show the answer in “Answer” section. Include the mathematical notations of two sets of null and alternate hypotheses and the phrase “advertising expenditure” or “sales commission percentage” or “both” along with a justification in a few sentences in “Comments” section.]

Answer 1

Answer 1.

Predicted Sales = 447.9571

Answer 2.

Correlation between Advertising Expenditure and Sales is 0.851564 :- There exist very strong positive correlation between Advertising Expenditure and Monthly Sales. That is, as Advertising Expenditure increases the sales will also increase and the statistical probability that the relationship between the two occurred by chance is very low

Correlation between Commisiion and Sales is 0.4902884 :- There exist low positive correlation between Commission and Monthly Sales. That is, as Commission increases the sales will also increase but the statistical probability that the relationship between the two occurred by chance is high.

Answer 3.

Significance of Advertising Expenses

Null Hypothesis, Ho: The Advertising Expense coefficient is not significant i.e

Alternative Hypothesis, Ha: The Advertising Expense coefficient is significant i.e

In the t-test performed (given in R Code), t -value is 3.973 and p-value is 0.0106.

Decision: SInce p-value = 0.0106 < so we reject Ho at 5% level of significance and conclude that Advertising Expense is significant

Significance of Commission

Null Hypothesis, Ho: The Commission coefficient is not significant i.e

Alternative Hypothesis, Ha: The Commission coefficient is significant i.e

In the t-test performed (given in R Code), t -value is 1.587 and p-value is 0.1734.

Decision: SInce p-value = 0.1734 >   so we fai to reject Ho at 5% level of significance and conclude that Advertising Expense is not significant

R-code: