Solutions, Phase 2/HL
ANSWERS TO SECTION 2 The easy Regression Model
Econometrics Economics of Innovation and Development
A sama dengan Problems N = Examples (from phase 2) C = Cumputer Exercises
Solutions, Chapter 2/HL
2 . 1 Permit kids represent the number of kids born to a woman, and let educ represent years of education for the woman. A simple version relating male fertility to years of education is definitely kids sama dengan ОІ zero + ОІ1educ + u where u is the unobserved error. (i) (ii) The type of factors will be contained in u? Are these likely to be correlated with level of education? Is going to a simple regression analysis uncover ceteris paribus effects of education on fertility? Explain.
(i) Income, grow older, and family members background (such as range of siblings) are just a few options. It seems that these could be correlated with years of education. (Income and education are probably positively related; age and education could possibly be negatively correlated because ladies in more the latest cohorts have got, on average, more education; and number of brothers and sisters and education are probably in a negative way correlated. ) (ii) Not if the elements we listed in part (i) are linked to educ. Since we would like to support these elements fixed, they are really part of the problem term. But since u is definitely correlated with educ then E(u|educ) в‰ zero, and so SLR. 3 does not work out. --------------------------------------------------------------------------------------------------------------2. 2 In the basic linear regression model y=ОІ0+ОІ1x + u, suppose that E(u) в‰ zero. Letting О±0=e(u), show which the model can always be rewritten with the same slope, nevertheless new intercept and error, where the new error includes a zero anticipated value. Answers In the equation y sama dengan ОІ0 & ОІ1x + u, put and subtract О±0 from your right hand side to get sumado a = (О±0 + ОІ0) + ОІ1x + (u в€’ О±0). Call the new error elizabeth = u в€’ О±0, so that E(e) = zero. The new intercept is О±0 + ОІ0, but the slope is still ОІ1.
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Solutions, Part 2/HL 2 . 3 The following table provides the ATC results and the GPA (grade stage average) intended for 8 college students. Grade point average is founded on a four-point scale and has been rounded to the one particular digit following the decimal. College student 1 two 3 four 5 6th 7 almost 8 GPA 2 . 8 several. 4 three or more. 0 3. 5 three or more. 6 a few. 0 2 . 7 several. 7 TAKE ACTION 21 twenty four 26 28 39 25 25 31
(i) Estimation the relationship between GPA and ACT using ols; that is certainly, obtain the intercept and slope in the formula Л† Л† Л† GRADE POINT AVERAGE = ОІ 0 + ОІ1 ACT
Comment on the direction from the relationship. Does the intercept include a useful meaning here? Describe. How much larger is GPA predicted being if the ACT score is elevated by a few points? (ii) Compute the fitted respected and the residuals for each declaration, and verify that the residuals (approximately) amount to absolutely no. (iii) Precisely what is the predicted value of GPA when ever ACT =20? (iv) How much of the variance in GRADE POINT AVERAGE for the 8 college students is explained by ACT. Describe.
2 . several (i) Permit yi = GPAi, xi = ACTi, and n = 8. Then times = twenty-five. 875, con = several. 2125, в€‘ (xi вЂ“ x )(yi вЂ“ i=1
Л† y ) = your five. 8125, and в€‘ (xi вЂ“ times )2 = 56. 875. From formula (2. 9), we obtain the slope because ОІ1 sama dengan i=1
Л† five. 8125/56. 875 в‰€. 1022, rounded to four locations after the fraccion. From (2. 17), ОІ 0 = y вЂ“ Л† ОІ x в‰€ 3. 2125 вЂ“ (. 1022)25. 875 в‰€. 5681. So we could write one particular
Л† GRADE POINT AVERAGE =. 5681 +. 1022 ACT
in = almost eight.
The intercept does not have a beneficial interpretation since ACT is usually not near zero to get the Л† population of interest. If ACT is your five points larger, GPA improves by. 1022(5) =. 511.
Solutions, Chapter 2/HL
(ii) The fitted values and residuals вЂ” rounded to several decimal places вЂ” are given along with the remark number i and GRADE POINT AVERAGE in the subsequent table:
we GPA you 2 . almost eight
2 several. 4 a few 3. zero 4 a few. 5 five 3. six 6 3. 0 7 2 . six 8 several. 7
installment payments on your 7143. 0857 3. 0209. 3791 a few. 2253 вЂ“. 2253 3. 3275. 1725 3. 5319. 0681 several. 1231 вЂ“. 1231 three or more. 1231 вЂ“. 4231 several. 6341. 0659
You can validate that the commissions, as reported in the stand, sum to в€’. 0002, which is quite close to no given the inherent rounding error. Л† (iii) Once ACT sama dengan 20, GRADE POINT AVERAGE =. 5681 +...