A.1 You wish to quantify the effect of cannabis consumption on student performance. You carry out a survey asking a random sample of your fellow students about their average mark after two years of studies and number of times they have consumed cannabis in the last 30 days. Let AMi and SMi be student i’s self-reported average mark and number of times used, i = 1, ..., n, where n is the number of students in the sample.
(a) Suppose that AM is observed with measurement error while SM is observed without. That is, AMi = AMi∗+vi, where AMi∗ is the actual average mark and vi is the measurement error. The measurement error is assumed to be fully independent of (SMi, ui) with E [vi] = 0, i = 1, ..., n. Suppose that the actual average mark satisfies
AMi∗ = β0 + β1SMi + ui, (1)
and that SLR.1-SLR.5 are satisfied in the above model. Derive the (conditional on SM1, ..., SMn) mean and variance of the OLS estimator of β1 obtained by regressing AM on SM .
(b) You use the following estimator of the variance of the OLS estimator βˆ1 as described in (a) where uˆi = AMi − βˆ0 − βˆ1SMi, i = 1, ..., n. Is this a consistent estimator of the variance of β1? Explain.
(c) Consider the reverse situation: You observe the actual mark average AM ∗ but now instead of SM you observe SM i = SMi + vi where vi still satisfies the assumptions stated in (a), i = 1, ..., n. Derive the probability limit of the OLS estimator of β1 obtained by regressing AM ∗ on SM i.
(d) You obtain a consistent estimator σˆ2 of σ2 =Var(v). Use σˆ2 to develop a consistent estimator of β1.
(e) Still considering the scenario in (c), discuss how realistic the following two assumptions are, E [vi] = 0 and vi fully independent of (SMi, ui), when the measurement error is due to incorrect reporting of cannabis consumption.
(f) Suppose that you observe SM and AM without measurement error. However, some of the students that you asked to participate in the survey refused. Is this a concern regarding the validity of SLR.1-SLR.5?
A.2 You are interested in estimating the effect of per-student spending on math performance. For that purpose, you use a data set on 408 schools in the UK. For each school, the data set contains math, the percentage of students receving a passing mark in a standardized math test, together with spend, per-student spending, and enroll, number of students enrolled.
(a) You obtain the following regression results,
m^ath = −69.24 + 11.13 log(spend) + 0.22 log (enroll) , R2 = .0297.
(26.72) (3.30) (.615)
If spend increases by 10% what is the (approximate) estimated percentage change in math?
(b) Test the hypothesis that math does not change with spend against the alternative that it does increase with spend. Perform the test at a 5% and 1% level. Conclude.
(c) You conjecture that family background has an effect on student performance and would like to include poverty, the percentage of students in a given school that live in poverty, in your regression. However, this variable is not in the data set and you instead decide to include meal, the percentage of students eligible for free school meals, as an additional regressor. Is this a sensible strategy? Explain.
(d) Including meal you obtain the following results,
m^ath = −23.14 + 7.75 log(spend) − 1.26 log (enroll) − .324meal, R2 = .1893.
(24.99) (3.04) (.580) (.036)
Explain why the effect of spending on math is lower in this new regression compared to the one in (a).
(e) Interpret the coefficients on log (enroll) and meal.
(f) What do you make of the increase in R2 from the regression in (a) to the regression in (d)?
CS 340 Milestone One Guidelines and Rubric Overview: For this assignment, you will implement the fundamental operations of create, read, update,
Retail Transaction Programming Project Project Requirements: Develop a program to emulate a purchase transaction at a retail store. This
7COM1028 Secure Systems Programming Referral Coursework: Secure
Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip
CS 340 Final Project Guidelines and Rubric Overview The final project will encompass developing a web service using a software stack and impleme
