Question

A marketing consultant, Sofia, has been studying the effect of increasing advertising spending on product sales. Sofia conducts several experiments, each time spending less than $1,000 in advertising. When she analyzed the relationship between x = advertising spending and y= product sales, the relationship was linear with r=0.90. Her boss is thrilled and asks her to estimate product sales for $100,000 in advertising spending. Is it appropriate for her to calculate a predicted amount of product sales with advertising spending of $100,000 ?
Yes, because the association is linear.

A

Yes, because the association is positive.

B

Yes, because the association is strong.

C

No, because the value of the correlation is not equal to 1.

D

No, because $100,000 is much greater than the values used in the experiment.

Answer 1

Answer:

• D. No, because $100,000 is much greater than the values used in the experiment.

Explanation:

Correlations, when have strong correlation coefficients, which r = 0.9 is, may be good predictors within the limits of the range of the data.

Trying to extrapolate the linear relationship between the variables, x = advertising spending and y= product sales, way beyond the limits of the data used for the study, is too risky, because the data may be linear just for some stages (ranges) but behave very different in other ranges.

As, the option D. states, $100,000 is much greater that the values used in the experiment; hence, the correlation would likely would not be a good predictor for that input.