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Econometrics HW 5 solutions

by: Noah Scovill

Econometrics HW 5 solutions Econ 4400

Marketplace > Ohio State University > Economcs > Econ 4400 > Econometrics HW 5 solutions
Noah Scovill
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About this Document

These are the solutions for the HW 5 problem set
Elementary Econometrics
Anthony Bradfield
Class Notes
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This 2 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 14 views. For similar materials see Elementary Econometrics in Economcs at Ohio State University.


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Date Created: 03/20/16
Homework 5 10/3/2014 Name: _____________________________ Econ 4400-101 Due: 10/10/2014 Show all necessary work. Instructor: Anthony J. Bradfield All work should be done by hand, unless stated otherwise. ▯ 1. [3] Consider the example from Homework 3 (1-3). y ▯▯ ▯ ▯▯ ▯ i ▯▯ ▯0 1 i i ▯▯= 2, ▯▯.▯.▯▯ ▯ ▯ 0.58554004, and n = 6. Suppose that you want to test whether x has any impact ▯ i on y.iWrite out the null and alternative hypotheses and carry out the test ▯▯▯▯▯▯▯▯▯▯▯▯▯▯. Does the hypothesized value fall inside or outside of the 95% CI from Homework 3? Do the two agree on whether reject or fail to reject the null hypothesis? H 0▯▯1= 0 t▯▯▯= 2.776 ▯▯▯▯▯▯▯▯▯▯▯▯ 1: (0.37454, 3.62546) reject H0if |t| >▯▯▯ ▯▯= 0 not in (0.37454, 3.62546) H A▯▯ 1 0 ▯ ▯▯▯▯▯ ▯▯▯ |t| = 3.4156503 > 2.776 ▯ reject some H 0 t = ▯= ▯▯ ▯▯▯ ▯.▯▯▯▯▯▯▯▯ ▯ reject H 0 ▯▯▯▯▯▯▯▯▯▯▯ ▯ both agree to reject H0 2. [1] Consider the example from Homework 3, problem 7. What should the relationship between POVERTY and CRIME be? Based on this, what should the null and alternative hypotheses be? There should be a positive relationship. H 0▯▯2▯ 0 H A▯▯ 2 0 3. [3] Consider the example from Homework 2, problem (5-8). Suppose that you want to test whether x ihas a positive effect on yi Write out the null and alternative hypotheses and carry ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ with a traditional test statistic. Does the hypothesized value fall inside or outside of the 95% CI? Do you reject or fail to reject the null hypothesis based on each criteria? ▯▯▯▯▯▯▯▯▯▯▯▯ : (▯ – t ▯ ▯▯▯▯ ▯, ▯ + t ▯ ▯▯▯▯ ▯) H 0▯▯1▯ 0 1 ▯ ▯/▯ ▯ ▯ ▯/▯ ▯ ▯ ▯ H A▯▯ 1 0 (-3 ▯ 3.182 ▯ , -3 + 3.182▯ ) ▯ ▯ ▯▯ ▯ ▯▯▯▯ ▯▯ ▯▯ t = ▯▯ ▯ ▯ = ▯▯/▯▯ ▯▯-8.78310066 (-4.08685991, -1.91314009) ▯ t▯= 2.353 ▯▯▯ 0 not in (-4.08685991, -1.91314009) reject H0if t> t▯ ▯ reject some H 0 t = -8.78310066 < 2.353 ▯ FTR H 0 ▯ critical value FTR, CI rejects, so they disagree 4. [2] Suppose you want to determine if the minimum wage has a positive impact on the high school drop-out rate while also controlling for high school GPA and how many years of education your parents completed. Write out the regression equation and hypotheses for this research question. yi= high school drop-out rate yi▯▯▯ 0▯▯ Mi1imumWage ▯▯▯ HSGPi ▯▯▯2ParentsEdicati3n ▯▯▯ i i H 0▯▯ 1 0 H A▯▯ 1 0 5. [1] You are considering the regression equation ClassGrade ▯▯i ▯▯▯0Class1sSkipped ▯▯▯ PreviousGP2 ▯▯▯ #ofExtraCuiricu3ars ▯▯▯. What i i do ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ to 1e? What should your hypotheses be? ▯1should be negative H 0▯▯ 1 0 H A▯▯ 1 0 6. [3] Use again "Homework 4 data." Estimate termgpa using priGPA, ACT, final, frosh, and skipped. Write out the regression equation. Predict whether frosh will be positively or negatively related to termgpa, and write out the hypotheses. Since frosh is a dummy variable, it measures whether freshmen will perform better or worse than all non-freshmen. Use Stata/other to estimate the regression equation and conduct a test of your hypotheses. Report the 95% CI from Stata/other as well and whether 0 falls outside of it. Do these two tests agree? termgpa i ▯▯▯ 0 + ▯1priGPA ▯▯i ACT 2▯▯ fiial + 3 i reject if t < -▯ ▯ 4froshi▯▯▯ 5kipped ▯▯i i 1.07 > -1.658 frosh should be negatively related to termgpa FTR H 0 H 0▯▯ 4 0 ▯▯▯▯▯▯▯▯▯▯▯▯ : 4 H A▯▯ 4 0 (-0.0392497, 0.1340984) termgpa = i.0488275 + 0.4979877priGPA + i ▯ = 0 in (-0.0392497, 0.1340984) 0.0144811ACT + 0.0i71441final + i ▯▯ FTR H 0 0.0474243frosh – 0i0501657skipped i ▯ ▯▯= 0.0474243 the tests agree; both FTR H ▯▯(▯ ) = 0.0441428 0 ▯ t = ▯.▯▯▯▯▯▯▯ = 1.07 ▯.▯▯▯▯▯▯▯ t = 1.658 ▯


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