5.8.1 Problems 5.1 Consider the multiple regression model Y₁ = x₁B₁+x12B₂2 + x3B3+e; with the seven observations on y₁, X1, X2, and x3 given in Table 5.5. TABLE 5.5 Yi 1 1 4 0 1 -2 2 5.2 Use your answers to Fi Xi1 1 1 1 1 1 1 1 Data for Exercise 5.1 d. Find the least squares residuals ê, ê, ..., ê7. e. Find the variance estimate 6². f. Find the sample correlation between x₂ and x3. g. Find the standard error for b₂. h. Find SSE, SST, SSR, and R². x 12 0 1 * * (A) 2 -2 1 -2 0 X13 1 -2 2 1 -2 T Use a hand calculator or spreadsheet to answer the following questions: a. Calculate the observations in terms of deviations from their means. That is, find x=x₂-₂, XX-X3, and y = y₁ - y. b. Calculate Eyx, Σχ., Σ., Σ., and Σχ c. Use the expressions in Appendix 5A to find least squares estimates b₁,b₂, and b3. 1 In N
5.8.1 Problems 5.1 Consider the multiple regression model Y₁ = x₁B₁+x12B₂2 + x3B3+e; with the seven observations on y₁, X1, X2, and x3 given in Table 5.5. TABLE 5.5 Yi 1 1 4 0 1 -2 2 5.2 Use your answers to Fi Xi1 1 1 1 1 1 1 1 Data for Exercise 5.1 d. Find the least squares residuals ê, ê, ..., ê7. e. Find the variance estimate 6². f. Find the sample correlation between x₂ and x3. g. Find the standard error for b₂. h. Find SSE, SST, SSR, and R². x 12 0 1 * * (A) 2 -2 1 -2 0 X13 1 -2 2 1 -2 T Use a hand calculator or spreadsheet to answer the following questions: a. Calculate the observations in terms of deviations from their means. That is, find x=x₂-₂, XX-X3, and y = y₁ - y. b. Calculate Eyx, Σχ., Σ., Σ., and Σχ c. Use the expressions in Appendix 5A to find least squares estimates b₁,b₂, and b3. 1 In N
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please answer 1a-h. Thank you!

Transcribed Image Text:and
cients. This is a problem better handled by your
Onometric software. Taking this advice, we find
30.17 and se(EXPER) = 1.7896. Then, a 95%
5.8 Exercises
5.8.1 Problems
5.1 Consider the multiple regression model
Yi
1
1
0
1
-2
2
We estimate that the number of years of experience
maximizes wages lies between 26.7 and 33.7 years.
Y₁ = x₁B₁+x12B₂ + X13B3+e;
with the seven observations on y₁, X1, X2, and x3 given in Table 5.5.
TABLE 5.5 Data for Exercise 5.1
=(26.7, 33.7)
Xil
1
62 x 1.7896, 30.17+1.962x1.789
elds
X12
0
1
2
-2
1
-2
0
d. Find the least squares residuals ê, ê, ..., ê7.
e. Find the variance estimate 6².
f. Find the sample correlation between x₂ and x3.
g. Find the standard error for b₂.
h. Find SSE, SST, SSR, and R2.
x 13
1
-2
2
1
-2
-1
1
X=X3-3, and y = y₁ - y.
b. Calculate Exx2² Eyx, Exx, and Ex
c. Use the expressions in Appendix 5A to find least squares estimates b₁,b₂, and b3.o
WAL
the household
5.2 Use your answers to Exercise 5.1 to
a. Compute a 95% interval estimate for B₂.
b. Test the hypothesis Ho:B₂ = 1.25 against the alternative that H₁ :B₂ 1.25
This model
is provided
Use a hand calculator or spreadsheet to answer the following questions:
a. Calculate the observations in terms of deviations from their means. That is, find x2=X2-X₂₂
TABLE 5.6
Dependent v
Included ol
Variable
C
In(TOTEX
NK
AGE
R-squares
S.E. of r
Sum squ
a.
5.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman