Consider the following responses and the associated values of the explanatory vari- ables: Response YX₁ X₂ X3 1 -1 2 1 -1 -3 1 0 -4 0 1 -3 -1 2 0 -1 3 5 3 4 5 6 (X'X)-¹ = 1 0 -2 do 0 1 2 3 12 5 0 Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10, -3]', and 00 00 0 0 00 00 0 (a) Specify the multiple regression equation to represent the data and state all the assumptions for the associated multiple regression model. (b) Find an estimator for the regression vector 3 = [Bo, B₁, B₂, B₁l' and write the equation for the fitted multiple regression line. (c) Predict the value of Y when z₁ = 1, 7₂ = −3, 73 = −1. Why is the predicted value different from the observed value of Y = 2?
Consider the following responses and the associated values of the explanatory vari- ables: Response YX₁ X₂ X3 1 -1 2 1 -1 -3 1 0 -4 0 1 -3 -1 2 0 -1 3 5 3 4 5 6 (X'X)-¹ = 1 0 -2 do 0 1 2 3 12 5 0 Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10, -3]', and 00 00 0 0 00 00 0 (a) Specify the multiple regression equation to represent the data and state all the assumptions for the associated multiple regression model. (b) Find an estimator for the regression vector 3 = [Bo, B₁, B₂, B₁l' and write the equation for the fitted multiple regression line. (c) Predict the value of Y when z₁ = 1, 7₂ = −3, 73 = −1. Why is the predicted value different from the observed value of Y = 2?
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Question
![Consider the following responses and the associated values of the explanatory vari-
ables:
Response YX₁ X₂ X3
-3 5 -1
0
1
-1 -3
1
0
-4 0
1 -3 -1
2 0 -1
3 5
2
3
4
5
6
1
0 -2
0
(X'X)-¹ =
1
2
02 00
3
3
Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10, -3]',
and
/
0 0
0
0 0
0
00
00 01/
0
(a) Specify the multiple regression equation to represent the data and state all the assumptions
for the associated multiple regression model.
(b) Find an estimator for the regression vector 3= [Bo, B1, B2, B3]' and write the equation for
the fitted multiple regression line.
(c) Predict the value of Y when z₁ = 1, I₂ = −3, 73 = −1. Why is the predicted value
different from the observed value of Y = 2?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ea2a71-9ac4-4e85-921f-8e0d04f36029%2F244b7344-0e0c-40a2-a620-c7814d4d2fe1%2Ff6peg2_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following responses and the associated values of the explanatory vari-
ables:
Response YX₁ X₂ X3
-3 5 -1
0
1
-1 -3
1
0
-4 0
1 -3 -1
2 0 -1
3 5
2
3
4
5
6
1
0 -2
0
(X'X)-¹ =
1
2
02 00
3
3
Based on the conventional notations for the multiple regression model we have X'Y = [10, 14, 10, -3]',
and
/
0 0
0
0 0
0
00
00 01/
0
(a) Specify the multiple regression equation to represent the data and state all the assumptions
for the associated multiple regression model.
(b) Find an estimator for the regression vector 3= [Bo, B1, B2, B3]' and write the equation for
the fitted multiple regression line.
(c) Predict the value of Y when z₁ = 1, I₂ = −3, 73 = −1. Why is the predicted value
different from the observed value of Y = 2?
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