Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

A shoe store developed the following estimated regression equation relating sales toinventory investment and advertising expenditures.$$\hat{y}=25+10 x_{1}+8 x_{2}$$where$$\begin{aligned} x_{1} &=\text { inventory investment }(\$ 1000 s) \\ x_{2} &=\text { advertising expenditures }(\$ 1000 s) \\ y &=\text { sales }(\$ 1000 s) \end{aligned}$$$\begin{array}{l}{\text { a. Predict the sales resulting from a } \$ 15,000 \text { investment in inventory and an advertising }} \\ {\text { budget of } \$ 10,000 .} \\ {\text { b. Interpret } b_{1} \text { and } b_{2} \text { in this estimated regression equation. }}\end{array}$

a. $\$ 445,000$b. The sales $y$ increase, on average, by 10 thousand dollars per thousand dollars of inventory investment.The sales $y$ increase, on average, by 8 thousand dollars per thousand dollars of advertising expenditures.

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Piedmont College

Cairn University

University of St. Thomas

Idaho State University

Lectures

0:00

02:19

A shoe store develope…

05:26

Forecasting Shoe Sales. A …

So in this question, we are given a multiple regression equation. So we have Why Hat? Which is the sales Sequels to 25 plus 10 x one plus eight x two. So we basically have to coefficients over here. The first coefficient x one is thean vant Ori investment in thousands. So tennis actually 10,000 and here x two is the amount spent on advertising. Okay. In thousands. Yeah. So our first question A asks us to predict the sales. Why resulting from a $15,000 investment in inventory smoke, I mean 1000 and in advertising budget off 10,000. So for question A, let's substitute in these values and get our value for the sales soar sails. Why, It's basically so everything is in 1000. So 25 is actually many cry 1000 less 10 times 15 1000 plus eight times 10,000. So that's 25 1000 less 150 1000 plus 80 1000 which gives us the answer off. 200 55 $1000. So that's our answer to part A. Now in part B were us to interpret B one and B two in this regression equation, so we have the coefficients here off this multiple regression equation, which are basically the estimated parameters. So we have B one is 10,000 and be to ISS. It does. So if you're interpreting coefficient, we basically say that there is an increase in why bye plus 10,000 for a one unit increasing X one provided next to is constant. And then So that's our interpretation for be one and B two, the sales Why increase on average bye plus 1000 for a one unit increase in next to with X one being constant because this is multiple regression, but this is our answer to heartbeat.

View More Answers From This Book

Find Another Textbook

03:11

The Intemal Revenue Service (IRS) provides a toll-free help line for taxpaye…

07:07

The generalized negative binomial pmf is given by$$n b(x ; r, p)=k(r, x)…

15:34

Workers in several industries were surveyed to determine the proportion of w…

02:20

The time between arrivals of vehicles at a particular intersection follows a…

06:13

The Employment and Training Administration reported that the U.S. mean unemp…

05:03

Consider the following hypothesis test:$$\begin{aligned} H_{0} : \mu &am…

02:37

How large a sample should be selected to provide a 95$\%$ confidence interva…

09:15

A production line operates with a mean filling weight of 16 ounces per conta…

17:30

The mode of a discrete random variable $X$ with pmf $p(x)$ is that value $x^…

02:06

Repeat exercise 11 for the acceptance sampling plan with $n=20$ and $c=1 .$ …