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by: Noah Scovill

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# Econometrics HW 3 Solutions Econ 4400

Marketplace > Ohio State University > Economcs > Econ 4400 > Econometrics HW 3 Solutions
Noah Scovill
OSU
GPA 3.25

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These are the solutions for the HW 3 problem set
COURSE
Elementary Econometrics
PROF.
TYPE
Class Notes
PAGES
3
WORDS
CONCEPTS
Econometrics
KARMA
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This 3 page Class Notes was uploaded by Noah Scovill on Sunday March 20, 2016. The Class Notes belongs to Econ 4400 at Ohio State University taught by Anthony Bradfield in Fall 2015. Since its upload, it has received 13 views. For similar materials see Elementary Econometrics in Economcs at Ohio State University.

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Date Created: 03/20/16
Homework 3 9/12/2014 Name: _____________________________ Econ 4400-101 Due: 9/24/2014 Show all necessary work. Instructor: Anthony J. Bradfield All work should be done by hand, unless stated otherwise. 1. [2] ▯▯▯▯▯▯▯▯▯▯ ▯0▯▯▯ in1the model ▯ = ▯ ▯ ▯ ▯ ▯ ▯ . ▯ ▯te ou▯ the estimated regression equation. i yi x i xi– ▯▯ (xi– ▯▯2 yi– ▯▯ (xi– ▯▯▯▯▯i– ▯▯ 1 15 ▯7 2.5 6.25 5 12.5 2 -21 -8 -12.5 156.25 -31 387.5 3 -3 4 -0.5 0.25 -13 6.5 4 33 10 5.5 30.25 23 126.5 5 9 -2 -6.5 42.25 -1 6.5 6 27 16 11.5 132.25 17 195.5 ▯▯▯▯10 ▯▯▯▯4.5 367.5 735 ▯ ( )( ) ▯▯= ▯▯▯▯▯▯▯▯▯ ▯ ▯▯ = ▯▯▯ = 2 ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ = 10 – 2*4.5 = 1 ▯▯▯▯(▯▯▯▯)▯ 367.5 ▯ = 1 + 2x i i 2. [2] Calculate s , R ▯▯▯▯▯▯▯ , and verify that they are the same as the output from your (statistical) program. i y x ▯ y – ▯ (y – ▯)2 y – ▯ (y – ▯)2 ▯ – ▯ (▯ – ▯)2 i i i i ▯ i ▯ i i i i i ▯ i ▯ 1 15 ▯7 15 5 25 0 0 5 25 2 -21 -8 -15 -31 961 -6 36 -25 625 3 -3 4 9 -13 169 -12 144 -1 1 4 33 10 21 23 529 12 144 11 121 5 9 -2 -3 -1 1 12 144 -13 169 6 27 16 33 17 289 -6 36 23 529 ▯ ▯ ( )▯ ▯▯ ( )▯ ▯ ▯ ( )▯ ▯▯▯ ▯▯▯ ▯ = 1974 ▯▯▯ ▯ ▯ ▯ ▯ = 504 ▯▯▯ ▯▯▯ ▯▯ = 1470 TSS = 1974 , RSS = 504 , ESS = 1470 ▯▯▯ 504 ▯ = 1 ▯ = 1 ▯ ▯ 0.74468 ▯▯▯ 1974 ▯▯▯/(▯ ▯ ▯ ▯ 1) 504 /4 ▯ = 1 ▯ = 1 ▯ ▯ 1 ▯ 0.31915 ▯ 0.68085 ▯▯▯/(▯ ▯ 1) 1974 /5 ▯▯▯ 504 ▯ = ▯▯▯ = = = 126 ▯ ▯ ▯ ▯ 1 4 3. [2] Calculate ▯▯(▯▯), and provide ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 1 ▯▯▯ 126 ▯ ▯▯▯▯▯ = ▯ = ▯ ▯ 0.585540 ▯▯▯▯(▯ ▯ ▯▯ )▯ 367.5 ▯▯▯▯▯▯▯▯▯▯▯▯ 1 (▯▯– t ▯/▯▯ ▯▯▯▯ ▯ , ▯▯+ t ▯/▯ ▯▯▯▯▯▯▯▯) = (2 – 2.132*0.58554004, 2 + 2.132*0.58554004) = (0.75163, 3.24837) ▯▯▯▯▯▯▯▯▯▯▯▯ : (2 – 2.776*0.58554004, 2 + 2.776*0.58554004) = (0.37454, 3.62546) 1 ▯ ▯ ▯ ▯ ▯ 2 2 4. [2] Use “Homework 3 data” on Carmen, and report ▯ , ▯0, ▯1 ▯▯(▯ ▯, ▯▯(▯ ▯, ▯ ▯▯▯ ▯▯▯ ▯ , R , ▯ , and s in the regression equation CRIME ▯i▯ ▯▯0 PC1METRO ▯▯▯. i i ▯ = 25.55837 ▯▯(▯ ) = 111.1175 R = 0.3528 0 ▯ 2 ▯ 1 8.107849 ▯▯(▯▯) = 1.585068 ▯ = 0.3393 s = 57839.1882 ▯ ▯▯▯(▯▯▯ ▯ )2 = s /.▯.(▯▯) = 57839.1882/1.585068 = 23021.117 ▯ 2 2 ▯ ▯▯▯(▯▯▯ ▯ ) = (n – 1) s = 49*21.675302 = 23021.117 2 2 2 2 5. [2] Report ▯ 0 ▯1,▯▯▯(▯▯),▯▯(▯ ▯, ▯ ▯▯▯(▯▯▯ ▯ , R ▯▯▯ , and s in the regression equation CRIME ▯▯i ▯▯0 POV1RTY ▯▯▯. i i ▯ ▯ 2 ▯ 0 209.92 ▯▯(▯▯) = 135.6129 R = 0.1360 ▯ = 25.45234 ▯▯(▯ ) = 9.260437 ▯ = 0.1180 1 ▯ 2 s = 77215.04 ▯ ▯ (▯ ▯ ▯ )2= 77215.04/9.260437 = 900.40716 ▯▯▯ ▯ ▯ ▯ ▯ ▯ ▯ 2 2 2 2 6. [2] Report ▯ 0 ▯1,▯▯▯(▯▯),▯▯(▯ ▯, ▯ ▯▯▯(▯▯▯ ▯ , R ▯▯▯ , and s in the regression equation CRIME ▯▯i ▯▯0 SIN1LE ▯▯▯. i i ▯ = -878.8612 ▯▯(▯ ) = 246.8954 R = 0.4208 0 ▯ 2 ▯ 1 130.1099 ▯▯(▯▯) = 22.03329 ▯ = 0.4087 s = 51762.7955 ▯ ▯▯▯(▯▯▯ ▯ )2= 51762.7955/22.03329 = 106.62499 2 2 2 7. [2] Report ▯ 0 ▯ 1 ▯ 2 ▯3,▯▯▯(▯▯),▯▯▯(▯▯),▯▯▯(▯▯),▯▯▯(▯▯), R ▯▯▯ , and s in the regression equation CRIME ▯▯▯ ▯▯▯ PCTMETRO ▯▯▯ POVERTY ▯▯▯ SINGLE ▯▯▯. Which slope i 0 1 i 2 i 3 i i estimates are the same as from the previous three questions? 2 ▯ 0 -1197.538 ▯▯(▯▯) = 180.4874 R = 0.7224 ▯ = 0.7043 ▯ 1 7.712334 ▯▯(▯▯) = 1.109241 2 ▯ = 18.28265 ▯▯(▯ ) = 6.135958 s = 25888.2199 2 ▯ ▯ 3 89.40078 ▯▯(▯▯) = 17.83621 None of the slopes are the same as previous questions, as each holds constant the other variables.

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