Problem

The data from exercise I follow. $$ \frac{x_{i}…

06:50

Problem 14 Easy Difficulty

PC World rated four component characteristics for 10 ultraportable laptop computers: features, performance, design, and price. Each characteristic was rated using a $0-100$ point
scale. An overall rating, referred to as the $P C$ World Rating, was then developed for each laptop. The following table shows the features rating and the $P C$World Rating for the 10 laptop computers $(\mathrm{PC}$ World website, February $5,2009).$
$$\begin{array}{l}{\text { a. Develop a scatter diagram with the features rating as the independent variable. }} \\ {\text { b. What does the scatter diagram developed in part (a) indicate about the relationship }} \\ {\text { between the two variables? }}\end{array}$$
$$\begin{array}{l}{\text { c. Use the least squares method to develop the estimated regression equation. }} \\ {\text { d. Predict the } P C \text { World Rating for a new laptop computer that has a features rating }} \\ {\text { of } 70 .}\end{array}$$

Answer

a. See scatter diagram
b. Positive linear relationship
c. $\hat{y}=37.122+0.518 x$
d. 73.382

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Intro Stats / AP Statistics

Essentials of Modern Business Statistics

Chapter 12

Simple Linear Regression

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Video Transcript

This exercise is about prediction using linear regression. And here we have data on ratings for pcs. So we have two different rating systems for Pcs and we want to know if the rating systems are related in any way. So for part A we were asked to make a scatter diagram with the features rating as the independent variable. So that means the futures rating should be on the X axis. So this is easy to do in itself. We select both columns of data, click on insert and then charts. We pick the scatter chart and we might want to change the X. Access to have a minimum of about 60. So that would be party. That's the scattered diagram. And if you're going to hand this in as part of an assignment, you want to give it a proper title and label the X and Y axes. Now for part B were asked if the diagram indicates any type of relationship between the features rating and the pC world rating. And as we can see, there appears to be a linear pattern in scatter with a positive slope. So we can say that the two ratings appear to be positively linearly correlated. And now for part C, we were asked to use the least squares method to produce the linear regression equation. Using the least squares method means that we're solving for the slope and intercept using these equations. So let's start with the slope piece of one. We can solve for the numerator and denominator separately and then divide them to find the quotient. Now the first step is to find the average of the features ratings and also the average for the PC world ratings. Yeah. And let's say we're going to sell for a numerator and a denominator for the numerator. We take each of the features ratings and subtract from that. The average features rating 778.4. And then we multiply that by the pc Pc World ratings. Subtract from that. The average Pc world rating, 77.7 do that for each data pair and then some of them. And for the denominator we take each features ratings, subtract from that, the average features rating and then square that do that for each features rating and then some of them. And so our slope is going to be the numerator divided by the denominator and we get 0.518 So the slope comes out 2.518 And now we can sell for the intercept Y bar on the spreadsheet was 77.7 and expire was 78.4. And this comes out to 37.1 to 2. So our regression equation yes given as follows. And then for part D. We are supposed to use our regression equation to predict the price of a lot, to predict the rating, the PC world rating of a laptop that has the features rating of 70 so here X is equal to 70. So we just plug that into our regression equation and this will give us our predicted price or rather our predicted rating. And we're predicting a Pc world rating of 73.

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