In: Statistics and Probability
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
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: