## Related questions with answers

The manager of Colonial Furniture has been reviewing weekly advertising expenditures. During the past 6 months, all advertisements for the store have appeared in the local newspaper. The number of ads per week has varied from one to seven. The store’s sales staff has been tracking the number of customers who enter the store each week. The number of ads and the number of customers per week for the past 26 weeks were recorded. In your opinion, is it a worthwhile exercise to use the regression equation to predict the number of customers who will enter the store, given that Colonial intends to advertise five times in the newspaper? If so, find a 95% prediction interval. If not, explain why not.

Solution

VerifiedWe are tasked to estimate with $95\%$ confidence the prediction interval for the number of customers who will enter the store, given
that Colonial intends to advertise five times in
the newspaper. Let $x$ be the number of ads, and $y$ be the number of customers. From the results of part **(a)**, we know that

$\begin{align*} \hat{y} &=297.0262+21.33x.\\ s_{\varepsilon} &= 132.9675 \\ \bar{x}&= 4.1154 \\ s_x^2 &= 3.47 \\n&= 26 \end{align*}$

Also, based on the given, $x_g = 5$, and $\alpha=0.05$.

*What is the formula for the confidence interval estimator of the expected value of $y$ for a given $x$?*

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