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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 performance rating, features rating,and the $P C$ World Rating for the 10 laptop computers (PC World website, February $5,$$2009 ) .$$\begin{array}{l}{\text { a. Determine the estimated regression equation that can be used to predict the } P C \text { World }} \\ {\text { Rating using the performance rating as the independent variable. }} \\ {\text { b. Determine the estimated regression equation that can be used to predict the } P C \text { World }} \\ {\text { Rating using both the performance rating and the features rating. }}\end{array}$$\begin{array}{l}{\text { c. Predict the } P C \text { World Rating for a laptop computer that has a performance rating of } 80} \\ {\text { and a features rating of } 70 .}\end{array}$

a) $\mathrm{y}=66.06+0.169 \mathrm{Performance}$b) $\mathrm{y}=39.982+0.113 \mathrm{Performance}+0.382$ Featuresc) $75.762$

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Temple University

Missouri State University

Oregon State University

University of St. Thomas

Lectures

0:00

05:15

PC World rated four compon…

01:03

To help consumers in purch…

05:07

The following data show th…

02:37

Computers. In $2004,$ abou…

03:23

Laptop computers are equip…

05:30

The regular price of a com…

just fun has three different parts. Okay, It wants to find a simple, linear regression, using the performance rating as a predictor for the overall. The general form for a simple linear regression is what at equals a plus. B Eggs E can be calculated by dividing the summer products for X and y. That's just some sweaters protest on this on the squares for why the sum of squares for Asks A and B cup by finding the mean for the wide eyes and then subtracting that people you that we calculate multiplied by the meaning of the exercise. If we run calculations on the data that they provide in the table, you can find that the mean of the eggs values for this problem is 68 a half. The mean of the Y values for this problem is 77. Sometimes this almost squares for eggs. For this problem is 2298 and 1/2 and the summer products wine. This problem is 3 90 enough. If we find the B value, we would be such or dividing the 3 90 a half Hi 2000 200 98 a half, which is a some squid and that is gonna eat well for approximate hey 0.16 not only 16 my thousands to find the a value when you take the mean of the Y values, which is still me son in half It's a fact on Devalue multiplied I the mean of the X with 68 when we simplify that for the a value we get 66 absolutely 60 sticks zero six Yeah, giving us the aggression, uh, 66 0.0 six to go luminess 2.169 where X is the performance rating and what is the big bid overall? Me for the second They want us to run a multiple direction and for this multi progression were using performance as the first predictor and features as the same thing No multiple regression we're gonna find First, the one is gonna be the same products for X one y I'm sum of squares for X two minus one of us for X more next Teoh times This other products for six to why Reminded by this sum of squares for X one times it's on the squares. Rex too. When I asked the summer products for exploiting squirrel. P two is gonna be very similar, except we're placing gates to using the excellence because some products for X two Why times a sum of squares X one minus is the hottest x one x two times the sum of products for X one y and that's divided. It has the same denominators. Sum of squares, exploiting times, a sum of squares six to minus the summer products for export thanks to school for the A value, we have the mean of the wise minus the B one eggs form minus E to and it's too me the next one and mean of extra. So the mean of X one in this problem is 16.5. Last problem. A mean of next to you. That's our features. Rating is 78 4 tens. The mean for the wise we already calculated Lost problem with seventies seven and seven minutes. Sum of squares for X one. We already calculated as 2200 nine Really enough sum of squares for X two is 284 some of products for X one by her for X one X two is 340 this summer. Products for X one. Why is to be 90.5 already in the last problem and the sun product experience to why is 147 and two tens? So we take all this information. I mean, we're gonna figure out what the B one value would be to value and the your hugging this information. And we get three mehndi and 1/2 times to 84.4 minus 3 40 times, just 1.2. And this is all divided by 3200. I am the AIDS times 284.4. Uh huh. Minus before me square. And that be one is gonna be zero point 113 for me too. We have the exact same denominator. So we have too few. All right. 8.5 I was 284 4 times reminisce 300 or be spreading. And then the numerator is just gonna slide around a little bit. So we get from 47.2 times through nine A fires minus 3 40 And okay, now and then be to value is going to be 0.38 to approximately. All right values is gonna be calculated by taking informal address. Some points. It's minus zero point when one free. I'm 68 now, Minister or other be value zero. Okay, three. I need to, I mean for X to just comedic before at a value is going to simplify to be approximately 39. We played RB one. It's a girl and a values together into the general form Or this multiple requesting yet 39 and 982 thousands No. 0.113 times. So Times x one with business performance ready What? 0.3 it's to X, which is our features reading. And that is the multiple regression. This problem for the last part. They want us to use this multiple reaction that we got to predict well. Rating. What overall rating. A computer with the performance rating of 80 and features rating. It's something you would receive. So we have our multiple regression that we miss completely and now we just have to replace the Explorer one with its printing where it was 80 and the x two giving teachers reading, which is 70 and quick calculation is gonna give us sorry. Here. Appellations gonna give us an overall rating? Uh, 75 and 762 thousands, Mrs. Parks e. So, again, the first part asked us to find a simple linear regression for yes. Using, demonstrating, Mr Predicted Second part asked us to come up with this. Multiple regression using with performance rating and feature spreading has predicted. And the third part wanted us to use that multiple regression that we calculated to figure out what the overall prediction for a computer with performance rating 80 and performance rank seven you will receive, and we kind of recently 0.7 60.

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