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

Constaner Reports provided extensive testing and ratings for more than 100 $\mathrm{HDTVs.} \mathrm{An}$overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following data show the price andoverall score for the ten 42 -inch plasma televisions (Consumer Reports, March $2006 ) .$$$\begin{array}{lll}{\text { Brand }} & {\text { Price }} & {\text { Score }} \\ {\text { Dell }} & {2800} & {62} \\ {\text { Hisense }} & {2800} & {62} \\ {\text { Hitachi }} & {2700} & {44} \\ {\mathrm{JVC}} & {3500} & {50} \\ {L G} & {3300} & {54}\end{array}$$$$\begin{array}{llll}{\text { Maxent }} & {2000} & {39} \\ {\text { Panasonic }} & {4000} & {66} \\ {\text { Phillips }} & {3000} & {65} \\ {\text { Proview }} & {2500} & {34} \\ {\text { Samsung }} & {3000} & {39}\end{array}$$$$\begin{array}{l}{\text { a. Use these data to develop an estimated regression equation that could be used to }} \\ {\text { predict the overall score for a } 42 \text { -inch plasma television given the price. }} \\ {\text { b. Compute } r^{2} . \text { Did the estimated regression equation provide a good fit? }} \\ {\text { c. Estimate the overall score for a } 42 \text { -inch plasma television with a price of } \$ 3200 .}\end{array}$$

a. $\hat{y}=12.017+0.013 x$b. $0.4503,$ Yesc. 53.617

Intro Stats / AP Statistics

Chapter 12

Simple Linear Regression

Linear Regression and Correlation

University of North Carolina at Chapel Hill

University of St. Thomas

Idaho State University

Boston College

Lectures

0:00

05:51

Televisions. The screen si…

03:49

An American standard analo…

00:56

An American standard telev…

01:14

Nielsen Ratings. Nielsen M…

02:35

LCD, LED, Plasma Impact: C…

00:42

consumer issues A consumer…

04:34

The following are advertis…

01:13

Your local electronics sto…

01:28

The average television is …

00:40

Ratings for a particular 2…

01:46

The total amount spent on …

00:38

TELEVISION The aspect rati…

06:21

02:49

(Exercises 13–26) For each…

Use the table which shows …

01:25

01:03

Determine whether each dat…

03:43

Use graphing software to d…

02:05

Graph the function in each…

01:11

A manufacturer of televisi…

this exercise is about linear regression and predicting an outcome using the regression equation. Now we are given this data on 42 inch TVs we have for each tv we have the price and the score. And for part A we are asked to develop a regression equation. Now we can develop our regression equation are estimated regression equation using the least squares method. And using that method means that we're finding a slope beats up one according to the first equation and the intercept according to the second formula. So let's first find this slope and let's do this on the excel spreadsheet. So we wanted to solve for the slope b. one and it has a numerator and denominator. So let's, so for the numerator and denominator separately and then divide them. Now the first step is to find the average price and the average score, and then the numerator is the sum of for each price. We subtract the average price and then multiplied by the score, subtract the average score and then we some these to get our numerator. So first make the calculation for each data pair and then some them. And then for the denominator it is the price minus the average price squared. And that is done for each price value and then we send them and so then our slope is equal to the numerator divided by the denominator. And we get .01-7. And now we can calculate the intercept. So this is 29.6 minus .01-7 Times 49.6. And this comes out to you 12.017. So our regression equation Is therefore 12.017 Plus 0.01-7 times X. So that was all part A. And now for part B were asked to calculate the coefficient of determination that is r squared, and r squared is given by the S. S. Are divided by the SST that's the sum of squares. Duty regression divided by the total sum of squares. And recall that the SSR is given by this formula and the SST is given by this formula. So let's also calculate these on the Excel spreadsheet. So we want to take I guess the first step is to calculate our predicted values for why for each price using our regression equation. So we'll call it why I had and it is equal to So it's the intercept 12.017 Plus the slope .01-7 times the price value. And we do this for each price. And it gives us the score that our regression equation would estimate. So now back to calculating the SSR and SST. And for the SSR it's for each predicted y value minus the average Y value, 49.6 and that's all squared. And we do that for each predicted Y value and then we send them. And for the SST it is the actual Wye Valley or score minus the average score. And squared, we do that for each score and then we sum them. Yeah. And her squared value is the ss are divided by the SST And we get about .45. So we can say that our regression equation is only a moderately good fit. We can say that about 40 based on the R squared value, about 45% of the variability and score is is explained by our regression equation. So that's part B. And then for part C. We are asked to estimate The score for a TV that costs $3,200, therapist saying the prices 3200. So we use our regression equation And we plug in 3200 for X, And that comes out to about 53. So we predict that the score for a 32 $100.42 inch tv, Is going to be 53.

View More Answers From This Book

Find Another Textbook

Televisions. The screen size of a television is measured diagonally from one…

An American standard analog television picture (non-HDTV), also known as NTS…

An American standard television picture is composed of approximately 485 hor…

Nielsen Ratings. Nielsen Media Research surveys TV-watching habits and provi…

LCD, LED, Plasma Impact: Curved-box TV Set To Be History In 4 Years CRT tele…

consumer issues A consumer magazine rates televisions by identifying two lev…

The following are advertised sale prices of color televisions at Anderson’s.…

Your local electronics store is having an end-of-the-year sale. The price on…

The average television is said to be on 6 hours per day. Estimate the yearly…

Ratings for a particular 2 -hour television program reveal that the greatest…

The total amount spent on plasma TVs in the United States changed from $$ 15…

TELEVISION The aspect ratio, or the ratio of the width to the height, of a w…

An American standard television picture is composed of about 485 horizontal …

(Exercises 13–26) For each description of data, identify the W’s, name the v…

Use the table which shows the number of movie theater screens (in thousands)…

The total amount spent on plasma TVs in the United States changed from 1590 …

Determine whether each data set is qualitative or quantitative.prices of…

Use graphing software to determine which of the given viewing windows displa…

Graph the function in each of the given viewing rectangles, and select the o…

A manufacturer of television sets claims that the maintenance expenditures f…

05:57

Refer to exercise $5,$ where the following data were used to imvestigate whe…

09:38

The U.S. Department of Energy's Fuel Economy Guide provides fuel effici…

06:40

A large automobile insurance company selected samples of single and married …

07:09

Almost all U.S. light-rail systems use electric cars that run on tracks buil…

01:37

Let $\mu$ denote the true $\mathrm{pH}$ of a chemical compound. A sequence o…

11:23

The data from exercise 3 follow.$$\begin{array}{r}{x_{i} 2 \quad 6 \…

11:56

The data from exercise 2 follow.$$\frac{x_{i}|3 \quad 12 \quad 6 \quad 2…

09:03

Constaner Reports provided extensive testing and ratings for more than 100 $…

10:26

$\begin{array}{l}{\text { Small cars offer higher fuel efficiency, are easy …

05:04

$$\begin{array}{c}{\text { Refer to exercise } 5 .} \\ {\text { a. Use } \al…