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

In exercise I, the following estimated regression equation based on 10 observations waspresented.$$\hat{y}=29.1270+.5906 x_{1}+.4980 x_{2}$$$$\begin{array}{l}{\text { The values of SST and SSR are } 6724.125 \text { and } 6216.375, \text { respectively. }} \\ {\text { a. Find SSE. }} \\ {\text { b. Compute } R^{2} \text { . }} \\ {\text { c. Compute } R_{\text { a. }}^{2}} \\ {\text { d. Comment on the goodness of fit. }}\end{array}$$

a. 507.75b. 0.9245c. 0.9029d. Good fit

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

University of North Carolina at Chapel Hill

Cairn University

Boston College

Lectures

0:00

05:28

In exercise $1,$ the follo…

02:12

05:43

The data from exercise 2 f…

07:48

Refer to the data presente…

06:33

The following problem is r…

06:43

The following data were us…

05:59

The following data are the…

A regression was run to de…

07:01

(a) Compute the power regr…

08:31

Compute the standard error…

05:08

01:31

For the following exercise…

09:44

10:40

01:58

In Exercises $13-16,$ esti…

00:41

01:26

04:30

Use the data set in WAGE2 …

01:14

01:29

So in order to find the sum of squared errors or S. E. For the regression listed above, you must have in mind that the sum of squares total, or SST is partitioned into the summer squares through the error and the sum of squares that's due to the regression. Now, having that in mind, you can simply find out that S. E. Will be given by the summer square total minus the sum of squares due to the regression, which will result in 500 and seven 0.75. Now to determine our square or the multiple coefficient of determination, we simply divide the sum of squares. Do the error by the total of the summer squares, Which will result in 0.9245, or simply 92 45%. And this can be interpreted as how well the regression represents our data set. Now are a squared or adjusted. Multiple coefficient of determination can be given by the expression where and represents the sample size or the number of observations and P. Is the number of independent variables and the sample site is given to us. It is 10 and the number of independent variables. Well, in this case it's too, we can look here that we have X one and X two and the sample size is 10. So now it's just a matter of plugging those numbers we already calculated and getting our results So there we have it. The adjusted coefficient of determination resulted in 0.9030 or 90.30%. Now, regarding the goodness of the fit provided by the linear regression stated above, we must have in mind that the closer our values of R squared or R a squared R 21 the better the r squared value of one would mean that the data set is perfectly matched by the regression model. And in this case we had a regression coefficient of 92.45%. And then when accounting for the extra variable using the second formula, we obtained a coefficient of 90.30%, which is satisfactory and proves that there is in fact a relationship between the observed results and the predictive results that are given by the regression model, However, does this mean that any model with a regression coefficient of 90 or 95% is going to be acceptable for any given situation where you need a regression model? No. That is going to depend on the specific precision you need in a specific experiment and different experiments may require different levels of precision.

View More Answers From This Book

Find Another Textbook

Numerade Educator

07:57

A 2003 New York Times/CBSNews poll sampled 523 adults who were planning a va…

08:13

Suppose the amount of rainfall in one region during a particular month has a…

02:37

Cincinnati/NorthernKentucky International Airport hadthe secondhighest on-ti…

04:16

Let $X_{1}$ and $X_{2}$ be quantitative and verbal scores on one aptitude ex…

01:55

A survey conducted by the American Automobile Association showed that a fami…

04:14

A shoe store developed the following estimated regression equation relating …

06:21

In early $2009,$ the economy was experiencing a recession. But how was the r…

01:47

Managers of 1200 different retail outlets make twice-a-month restocking orde…

07:52

Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? S…

02:47

A well-known bank credit card firm wishes to estimate the proportion of cred…