Consider the following responses and the associated values of the explanatory vari- ables: Response YX₁ X₂ Xs 1 3 1 (X'X)-¹ -3 5 -1 0 1 2 3 3 to do 0 0 -1 0 1 2 3 -2 1 0 -3 -1 0 -1 5 1 Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10,-3]', and 0 0 00 0 0 00 0 0 0/ (d) Find an estimate of the error variance o² from the SSE. (Note SSE = Y'Y - B'X'Y with 7-4=3 degrees of freedom.) (e) Setting up appropriate hypotheses, test the significance of X3 in the regression model at the 5% level of significance. (f) Find a 95% confidence interval for the mean response μy when z₁ = 1, ₂ = -3, a = -1, that is, a[1, 1, -3, -1]'.
Consider the following responses and the associated values of the explanatory vari- ables: Response YX₁ X₂ Xs 1 3 1 (X'X)-¹ -3 5 -1 0 1 2 3 3 to do 0 0 -1 0 1 2 3 -2 1 0 -3 -1 0 -1 5 1 Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10,-3]', and 0 0 00 0 0 00 0 0 0/ (d) Find an estimate of the error variance o² from the SSE. (Note SSE = Y'Y - B'X'Y with 7-4=3 degrees of freedom.) (e) Setting up appropriate hypotheses, test the significance of X3 in the regression model at the 5% level of significance. (f) Find a 95% confidence interval for the mean response μy when z₁ = 1, ₂ = -3, a = -1, that is, a[1, 1, -3, -1]'.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
![Consider the following responses and the associated values of the explanatory vari-
ables:
Response Y X₁ X₂ X3
1-3
5 -1
0 -2 0 1
0 -1
-3
1
1
0
-4
0
1
-1
3
2
-1
3 3
1
2
3
4
5
6
7
2
(X'X)-¹
t
-3
05
Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10, -3]',
and
000
0 0
0 0
00 0
(d) Find an estimate of the error variance o² from the SSE. (Note SSE = Y'Y - B'X'Y with
7-4=3 degrees of freedom.)
(e) Setting up appropriate hypotheses, test the significance of X3 in the regression model at
the 5% level of significance.
(f) Find a 95% confidence interval for the mean response μy when I₁ = 1, x₂ = −3, F3 = -1,
that is, a= [1, 1, -3, -1]'.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ea2a71-9ac4-4e85-921f-8e0d04f36029%2F9885a8b7-7baa-4b53-b9d4-94b5d389c0c5%2F2zpyq3o_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following responses and the associated values of the explanatory vari-
ables:
Response Y X₁ X₂ X3
1-3
5 -1
0 -2 0 1
0 -1
-3
1
1
0
-4
0
1
-1
3
2
-1
3 3
1
2
3
4
5
6
7
2
(X'X)-¹
t
-3
05
Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10, -3]',
and
000
0 0
0 0
00 0
(d) Find an estimate of the error variance o² from the SSE. (Note SSE = Y'Y - B'X'Y with
7-4=3 degrees of freedom.)
(e) Setting up appropriate hypotheses, test the significance of X3 in the regression model at
the 5% level of significance.
(f) Find a 95% confidence interval for the mean response μy when I₁ = 1, x₂ = −3, F3 = -1,
that is, a= [1, 1, -3, -1]'.
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VIEWStep 2: Determine an estimate of the error variance from the SSE.
VIEWStep 3: Perform the hypothesis test for the significance of X3 in the regression model.
VIEWStep 4: Determine the 95% confidence interval for the mean response ?? when ?1 =1 , ?2=− 3 and x3=-1.
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