could you answer A7 to A9 please pape\' s_pubnc zo o_cUT // M 2UT 6-2017-5 I 31

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could you answer A7 to A9 please

pape' s_pubnc zo o_cUT // M 2UT 6-2017-5 I 31 3_1_1.-5.PDF AT. Which of the following statements abour the coefficient of multiple determination R in a multiple regression model is NOT true? (a) It is a measure of the proportion of variance explained by the fitted regression model (b) Its value is in the interval [0,1] (c) It does not decrease as more variables are added to the model (d) R2 near zero implies that the response variable and the explanatory variables are unrelated A8. The manager of a college wanted to model the response variable GPA (grade point averag after one year of college) using three independent variables X, X2 and X,, based on 100 observations. He tries all possible combinations of predictors and finds the top four combinations. In the following, these four combinations and the corresponding sums of square for regression and error are shown. Variables in Model SSR 374.0 385.4 380.0 386.0 SSE 26.0 14.6 20.0 14.0 Which predictors should be included in the model according to the adjusted R' criterion? (a) X, (b) X, and X (c) X and X (d)X, Xo and X, A9. Consider the model with transformed response variable This model is fitted to a set of data and gives For an individual whose explanatory variables Xi and have values of I and 2 respectively, th value of the observed untransformed response was actually 5 alue of the untransformed response variable and the associated residual are (a) 16,-11 (b) 16, 11 (c) 4, 1 (d) 4. -I e) None of these choices 5.0. For this individual, the predicte

Explanation / Answer

A 7

Option 1 : Yes, this option is correct and actually it is definition of R2 .

Option 2 : Yes, R2 can take values only in between 0 to 1.

Option 3 : No, R2 will decrease if there will be new variables got added as the variables may be insignificant in nature that will reduce the value of R2

Option 4 : Yes, that is also a correct statement. More value of R2 , more linear relationship.

A8

Here in each case SST (SSR + SSE) is equal to 400

Here we will discard the option 1 and 3 as it have high SSE/SST values then the other two model. We can say this by observation itself.

So, now we have to compare the value of adjusted R2 for model given in option 2 and option 4

for option 2 - The model is X1 & X2

R2 = 385.4/ 400 = 0.9635

Adjusted R2 = 1 - [(1 -R2) (n-1)/(n-k+1)] Here n = 100 and k = 2 (only two regressor are there)

Adjusted R2 = 1 - [ (1 - 0.9635) * (100-1)/ (100 - 2 -1)]

= 0.9627

for Option 3 : Model use x1, x2 and x3 so k = 3 here

R2 = 386/ 400 = 0.965

Adjusted R2 = 1 - [(1 -R2) (n-1)/(n-k+1)] Here n = 100 and k = 3 (only two regressor are there)

Adjusted R2 = 1 - [ (1 - 0.965) * (100-1)/ (100 - 3 -1)]

Adjusted R2 = 0.9640

so here the model given in option 4 is the best model.

A.9

Y = 0 + 1 X1 + 2 X2

putting values of regression coefficient we get

Y = -1 + X1 + 2X2

X1 = 1 and X2 = 2

by putting values in the eqution

we get

Y = -1 + 1 + 2 * 2 = 4

Y = 16

so residual = Actual - predicted value = 5 - 16 = -11

Option (a) is correct.

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