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Solutions to various problems related to regression analysis as presented in chapter 4. Topics include calculating predicted average test scores, change in classroom average test scores, and interpreting coefficients in the context of earnings. Additionally, it covers the concept of standard error of the regression and its relation to the sum of squared residuals.

Typology: Assignments

Pre 2010

1 / 4

Download Chapter 4: Regression Analysis Solutions - Prof. Peter Michael Summers and more Assignments Introduction to Econometrics in PDF only on Docsity! Chapter 4. HW Solutions 1. (a) The predicted average test score is 520 4 5 82 22 392 36TestScore (b) The predicted change in the classroom average test score is ( 5 82 19) ( 5 82 23) 23 28TestScore (c) Using the formula for 0̂ in Equation (4.8), we know the sample average of the test scores across the 100 classrooms is 0 1 ˆ ˆ 520 4 5 82 21 4 395 85TestScore CS (d) Use the formula for the standard error of the regression (SER) in Equation (4.19) to get the sum of squared residuals: SSR=(n-2)*SER²= (100-2)* 11.5²= 12,960.5 TSS= SSR/(1-R²)= 12960.5/(1-.08)= 14,087.5 Sample variance= 1/n (TSS) Sample deviation= 11.9289 3. (a) The coefficient 9.6 shows the marginal effect of Age on AWE; that is, AWE is expected to increase by $9.6 for each additional year of age. 696.7 is the intercept of the regression line. It determines the overall level of the line. (b) SER is in the same units as the dependent variable (Y, or AWE in this example). Thus SER is measures in dollars per week. (c) R2 is unit free. (d) (i) 696.7 9.6 25 $936.7; (ii) 696.7 9.6 45 $1,128.7 (e) No. The oldest worker in the sample is 65 years old. 99 years is far outside the range of the sample data. (f) No. The distribution of earning is positively skewed and has kurtosis larger than the normal. (g) 0 1 ˆ ˆ ,Y X so that 0 1 ˆ ˆ .Y X Thus the sample mean of AWE is 696.7 9.6 41.6 $1,096.06. 4. (a) ( ) ( ) ,f m fR R R R u so that var 2( ) var( ) var( ) 2 cov( , ).f m f m fR R R R u u R R But cov( , ) 0,m fu R R thus 2var( ) var( ) var( ).f m fR R R R u With > 1, var(R Rf) > var(Rm Rf), follows because var(u) 0. (b) Yes. Using the expression in (a) 2var ( ) var ( ) ( 1) var ( ) var( ),f m f m fR R R R R R u which will be positive if 2var( ) (1 ) var ( ).m fu R R (c) 7.3% 3.5% 3.8%.m fR R Thus, the predicted returns are ˆ ˆˆ ( ) 3.5% 3.8%f m fR R R R Kellog = 3.5% + -.03(3.8%) = 3.386%. Use the same formula to get the others: Walmart = 5.97% Wastem = 6.16% Sprint = 6.464% BarnesN = 7.376% Micros = 8.326% Bestbuy = 11.67% Amazon = 13.57% 5. (a) ui represents factors other than time that influence the student’s performance on the exam including amount of time studying, aptitude for the material, and so forth. Some students will have studied more than average, other less; some students will have higher than average aptitude for the subject, others lower, and so forth. (b) Because of random assignment ui is independent of Xi. Since ui represents deviations from average E(ui) 0. Because u and X are independent E(ui|Xi) E(ui) 0. (c) (2) is satisfied if this year’s class is typical of other classes, that is, students in this year’s class can be viewed as random draws from the population of students that enroll in the class. (3) is satisfied because 0 Yi 100 and Xi can take on only two values (90 and 120). (d) (i) 49 0.24 90 70.6; 49 0.24 120 77.8; 49 0.24 150 85.0 (ii) 0.24 10 2.4. EMPIRICALS: