Problem

In exercise $2,10$ observations were provided for…

03:31

Problem 11 Easy Difficulty

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

Answer

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

Related Courses

Intro Stats / AP Statistics

Essentials of Modern Business Statistics

Chapter 13

Multiple Regression

Discussion

You must be signed in to discuss.

Top Intro Stats / AP Statistics Educators

Boris M.

University of North Carolina at Chapel Hill

Intro Stats / AP Statistics Courses

Lectures

Join Course

Watch More Solved Questions in Chapter 13

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Video Transcript

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.

We have video lessons for 89.47% of the questions in this textbook