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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
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.
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