c) Does the addition of X significantly contribute to prediction of y after accounting for the contribution of X₂? Use=0.05- O Reject the null hypothesis O Do not reject the null hypothesis

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Use SAS output for a random sample of size 20 to answer the following questions.
Regression of y on X and X₂
1
Regression of yon X₁ X₂ and X₂
3
F1.17, 0.99 = 8.40
F3,16, 0.99 = 5.29
F1.17, 0.95 = 4.45
3,16, 0.95 = 3.24
c) Does the addition of X, significantly contribute to prediction of y after accounting for the contribution of X₁? Use a = 0.05-
O Reject the null hypothesis
O Do not reject the null hypothesis
Source
Model
Error
II...
Corrected Total 19 1855.20200
Parameter
Intercept
Number of Observations Read 20
Number of Observations Used 20
R-Square Coeff Var
Root MSE
0.818318 22.31297 4.589778
x1
x2
x3
Analysis of Variance
Sum of
DF Squares
2 1317.79841 658.89921 20.84 <.0001
x1
x2
x3
17 537.40359 31.61198
Source
Model
Error
Source DF
1
1 1309.445931
1
200.346530
Mean
Square F Value Pr> F
Type I SS
8.352481
Estimate
-36.76492528 7.01092577
0.00076294 0.00063630
1.19217421 0.56165391
4.71982137 1.53047547
Standard
Error
Source DF
Type III SS
1
30.2855361
1 94.9129162
1 200.3465296
DF Sum of Squares Mean Square F Value Pr > F
3 1518.144941 506.048314 24.02 .0001
337.057059
21.066066
1855.202000
16
Corrected Total 19
y Mean
20.57000
F2.17, 0.99 = 6.11
F4,16, 0.99 = 4.77
F2.17, 0.95 = 3.59
4,16, 0.95 = 3.01
F
Transcribed Image Text:Use SAS output for a random sample of size 20 to answer the following questions. Regression of y on X and X₂ 1 Regression of yon X₁ X₂ and X₂ 3 F1.17, 0.99 = 8.40 F3,16, 0.99 = 5.29 F1.17, 0.95 = 4.45 3,16, 0.95 = 3.24 c) Does the addition of X, significantly contribute to prediction of y after accounting for the contribution of X₁? Use a = 0.05- O Reject the null hypothesis O Do not reject the null hypothesis Source Model Error II... Corrected Total 19 1855.20200 Parameter Intercept Number of Observations Read 20 Number of Observations Used 20 R-Square Coeff Var Root MSE 0.818318 22.31297 4.589778 x1 x2 x3 Analysis of Variance Sum of DF Squares 2 1317.79841 658.89921 20.84 <.0001 x1 x2 x3 17 537.40359 31.61198 Source Model Error Source DF 1 1 1309.445931 1 200.346530 Mean Square F Value Pr> F Type I SS 8.352481 Estimate -36.76492528 7.01092577 0.00076294 0.00063630 1.19217421 0.56165391 4.71982137 1.53047547 Standard Error Source DF Type III SS 1 30.2855361 1 94.9129162 1 200.3465296 DF Sum of Squares Mean Square F Value Pr > F 3 1518.144941 506.048314 24.02 .0001 337.057059 21.066066 1855.202000 16 Corrected Total 19 y Mean 20.57000 F2.17, 0.99 = 6.11 F4,16, 0.99 = 4.77 F2.17, 0.95 = 3.59 4,16, 0.95 = 3.01 F
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