a sales manager used linear regression to find the positive linear relationship between advertising expenditures and sales. The amount of advertising expenditures used to generate the regression equation ranged from $8,000 to $45,000.
The sales manager wants to use the equation to predict the amount of sales that can be expected from advertising expenditures of $55,000 and $65,000.
Which would be more reliable, the sales predicted from the $55,000 advertising expenditure or from the $65,000 expenditure? Explain why!
I would have more confidence in the sales at the $55,000 expenditure level. Think it through, then take a shot.
To determine which sales prediction would be more reliable, we need to consider the range of advertising expenditures used to establish the linear regression equation.
In this case, the advertising expenditures used to generate the regression equation ranged from $8,000 to $45,000. This means that the sales manager is predicting sales values for advertising expenditures that extend beyond the range of data used to create the equation.
When making predictions outside the range of the data, it is important to exercise caution. Extrapolation, which refers to extending the regression equation beyond the range of the observed data, can introduce higher uncertainty and potential inaccuracies in the predictions.
In this specific scenario, the prediction for sales with a $55,000 advertising expenditure would be more reliable than the prediction for sales with a $65,000 expenditure. This is because $55,000 falls within the range of advertising expenditures used to create the regression equation, while $65,000 exceeds that range.
However, even with the $55,000 prediction being more reliable, it is still worth noting the potential limitations of extrapolation. Predictions outside the observed range should be interpreted with caution, as they are less reliable and may be more prone to inaccuracies.