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Consider the following data for two variables, $x$ and $y .$$$\frac{x}{y} \left| \begin{array}{ccccc}{9} & {32} & {18} & {15} & {26} \\ \hline & {y} & {10} & {20} & {21} & {16} & {22}\end{array}\right.$$$\begin{array}{l}{\text { a. Develop an estimated regression equation for the data of the form } \hat{y}=b_{0}+b_{1} x \text { . Com- }} \\ {\text { ment on the adequacy of this equation for predicting } y .}\end{array}$$\begin{array}{l}{\text { b. Develop an estimated regression equation for the data of the form } y=b_{0}+b_{1} x+} \\ {b_{2} x^{2} . \text { Comment on the adequacy of this equation for predicting } y \text { . }} \\ {\text { c. Predict the value of } y \text { when } x=20 \text { . }}\end{array}$

a) $\hat{y}=9.315+0.424 x$b) $\hat{y}=-8.101+2.413 x-0.048 x^{2}$c) 21

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Temple University

Missouri State University

Piedmont College

Oregon State University

Lectures

0:00

15:32

Consider the following dat…

06:46

Given are five observation…

So in this question, were given some values of X and values off. Why and we're first as toe developed the regression equation between X and why so basically why he calls p zero plus p one x So let's go ahead and do That's our input. Wide range is 31 through six apartment good sex ranges a one through six click OK, put in an output range So we have a 50 output over here. Nine Take a look. So we have our regression statistics. Here are just a r squared is pretty low. Yeah, If we look, we see we have the intercept and we have the coefficient for XO. Basically, the equation that we have is all right into over here Her part eight. Why is equals to 9.315 plus point 4 to 4. Thanks. So this is basically our equation. We were asked to comment on the adequacy off this equation for predicting why. So, basically, we see from this equation we see two things. We see that the adjusted R squared it's less than 0.5. We also see that the T value for X for the coefficient of creeks is basically 0.11 which is less than 0.5 So we say that the relationship is not significant between extend one. So that's our answer to part please. Now let's move on to Part B, whereas to develop an estimated regression equation, the form wise equals two b zero b one x, me too x squared. So let's go ahead and do that. Sure. So I'm going to open up another sheet and copy these values. Yeah, I'm going to add another column for X Square. So that's to that. So that's square all off our values here. So we have equals square. Okay, so we have our two independent variables and are dependent variables. And then let's go ahead and create our multiple regression equation. So our input wide range it's no see one. Okay, 266 and our input X ranges a 1236 cos level. We're gonna keep the outward range at the same point. Now let's look at our statistics. So we see that our R squared values are much higher and we look at the equation. So basically, let's right over equation. So we have right. I used to be called to the intercept, plus 2.4 times X 90.4797 times X square. So we have our multiple regression equation here and were asked to comment on the adequacy of this equation. So we see here that are p values for okay R p values for thanks and our value for extreme are all less than 0.5 p values less than 0.454 x x square. And for our statistic, for the overall equation, we also see that the card square is much higher. It's more than and nine right here we can see that. So our square this much fires more than 0.9. And so we have ah, very good foot with clothe question now in part C, whereas to predict the value off y when x s equals to 20. So let's sub in access equals to 20 into this equation and predict our value off. Why? If we substitute here, we substitute 20 square 20 into the situation. We basically get why it's supposed to 20.96 rounded to two decimal places. That's our answer for part C. So we have part C and party over here, along with part He over here? Yeah, yeah,

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