Question

A sales manager used linear regression to find the positive linear relationship between advertising expenditures and sales. the equation was calculated from the following data from 7 randomly selected advertising campaigns:

Advertising Expenditures - $8,000 / $22,000 / $15,000 / $39,000 / $32,000 / $12,000 / $45,000

Sales - $95,000 / $190,000 / $125,000 / $ 225,000 / $285,000 / $150,000 / $350,000

If the sales manager used regression equation to predict the amount of sales that he can expect for advertising expenditures of $35,000, and then used the equation to predict the amount of sales he can expect for advertising expenditures of $65,000, Which prediction would probably be more reliable and why?

Please show work

Answer 1

The linear regression is estimated based on the values of Advertising Expenditures between $8,000 and $45,000. Thus, the linear regression model estimates the relation between advertising campaigns and sales when the advertising campaigns is between $8,000 and $45,000. The regression model may not provide reliable sale estimates when the advertising campaigns is outside the range ($8,000, $45,000). This is because that the estimated model may not fit the data outside the range adequately well.

$35,000 lies inside the range ($8,000, $45,000) but the advertising expenditures of $65,000 lies outside the range. Thus, the prediction for $35,000 would probably be more reliable.