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Problem 3 [26 points]: Consider multiple linear regression with 3 explanatory variables (EVs) X, X2 and X3. Two hypothesis testings were performed on models with selected EVs, and the results were summarized by the two ANOVA tables below: Ho: E(Y | X = x) = B Ho: E(Y | X = x) = Bo + B1x + B2x2 Ho: E(Y | X = x) = B + B1x + B2x2 + B3x3 ANOVA Table Source MS P-value Regression 210.590 105.295 92.229 <1e-16 Residuals 52.517 1.142 Total 263.107 ANOVA Table Source_ MS P-value Regression 141.740 141.740 125.385 1.332e-14 Residuals 50.870 130 Total 192.610 It's known that the sample correlation between y and each of the X variables are 78.32%, 29.84% and 17.15% respectively: That is, Corr(y,x1) = 0.7832, Corr(y,x2) = 0.2984 and Corr(y,x3) = 0.1715. (a) [12 points] Replicate the table below and fill in ALL the missing values (in at least 4 significant figures). (df and RSS of Model 5: E(Y | X = x) = B + B1x + B2x2 have already been included in the table) Model Explanatory Variable(s) Null (No EV, constant only) RSS 1 2 3 4 5 6 x2 x3 x1,x2 x1,x3 x2,x3 x1,x2,x3 46 58.493 (b) [14 points] Test the hypothesis on the following mean functions: Ho: E(Y | X = x) = Bo + B1x H1: E(Y | X = x) = B + B1x + B2x2 + B3x3 You should set up the appropriate ANOVA table and follow the 4 steps of hypothesis testing as Ch3 page 49. (The p-value can be obtained from R command like "> 1-pf(Fo, df1, df2)" for the right-hand tailed probability of Fdf1, df2):

          Problem 3 [26 points]: Consider multiple linear regression with 3 explanatory variables (EVs) X, X2 and X3. Two hypothesis testings were performed on models with selected EVs, and the results were summarized by the two ANOVA tables below:

Ho: E(Y | X = x) = B
Ho: E(Y | X = x) = Bo + B1x + B2x2
Ho: E(Y | X = x) = B + B1x + B2x2 + B3x3

ANOVA Table
Source     MS       P-value
Regression 210.590 105.295 92.229 <1e-16
Residuals  52.517  1.142
Total      263.107

ANOVA Table
Source_    MS       P-value
Regression 141.740 141.740 125.385 1.332e-14
Residuals  50.870  130
Total      192.610

It's known that the sample correlation between y and each of the X variables are 78.32%, 29.84% and 17.15% respectively: That is, Corr(y,x1) = 0.7832, Corr(y,x2) = 0.2984 and Corr(y,x3) = 0.1715.

(a) [12 points] Replicate the table below and fill in ALL the missing values (in at least 4 significant figures). (df and RSS of Model 5: E(Y | X = x) = B + B1x + B2x2 have already been included in the table)

Model   Explanatory Variable(s) Null (No EV, constant only) RSS
1
2
3
4
5
6
x2
x3
x1,x2
x1,x3
x2,x3
x1,x2,x3
46
58.493

(b) [14 points] Test the hypothesis on the following mean functions:
Ho: E(Y | X = x) = Bo + B1x
H1: E(Y | X = x) = B + B1x + B2x2 + B3x3

You should set up the appropriate ANOVA table and follow the 4 steps of hypothesis testing as Ch3 page 49. (The p-value can be obtained from R command like "> 1-pf(Fo, df1, df2)" for the right-hand tailed probability of Fdf1, df2):

problem 3 26 points consider multiple linear regression with 3 explanatory variables evs x xz and xz two hypothesis testings were performed on models with selected evs and the results were 71339

Added by Peter H.

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