Econometric Assignment

ECON 2280 Introductory to Econometrics

Assignment 2

Name: ZHANG Jingxuan   UID: 3035027631

Q1. You are hired by the HKU to help reduce damage done to dorms by rowdy students. You estimated a cross-sectional model of last semester’s damage at each dorm as a function of the attributes of that dorm:

 𝐷𝑖̂=210+733𝐹𝑖−.805𝑆𝑖+74.0𝐴𝑖 

(253) (.752) (12.4)

N = 33, 𝑅2̅̅̅̅ = .84

where: 𝐷𝑖 = the amount of damage (in dollars) done to the ith dorm last semester

𝐹𝑖 = the percentage of the ith dorm residents who are frosh

𝑆𝑖 = the number of students who live in the ith dorm

𝐴𝑖 = the number of incidents involving alcohol that were reported to the Dean of Students Office from the ith dorm last semester (incidents involving alcohol may or may not involve damage to the dorm)

a. For each of the three slope coefficients, find their 95% confidence interval, and test if they are statistically significant by making use of the confidence intervals at level of significance of 5%. (6 points)

At the significance level of 5%, c0.025=2.045

df= n-k-1=33-3-1=29

   For the coefficient 733 of variable 𝐹:

Prob (-WF< <-WF)= Prob(733-W< <733-W)[pic 1][pic 2][pic 3][pic 4]

WF= c0.025*s.e.(=2.045*253=517.385[pic 5]

A 95% CI of = [215.615, 1250.385][pic 6]

One-tail test: H0:against H1:>0[pic 7][pic 8]

tF==2.90>2.045[pic 9]

The effect of variable F on D is statistically greater than 0 at the 5%signigicance level, thus it is statistically significant.

For the coefficient -0.805 of variable S:

Prob (-WS< <-WS)= Prob(-0.805-W< <-0.805-W)[pic 10][pic 11][pic 12][pic 13]

WS= c0.025*s.e.(=2.045*0.752=1.53784[pic 14]

A 95% CI of = [-2.34284, 0.73284][pic 15]

One-tail test: H0:against H1:>0[pic 16][pic 17]

tS==-1.07<2.045[pic 18]

The effect of variable S on D would be insignificant since the sign is unexpected.

 For the coefficient 74 of variable A:

Prob (-WA< <-WA)= Prob(74-W< <74-W)[pic 19][pic 20][pic 21][pic 22]

WA= c0.025*s.e.(=2.045*12.4=25.358[pic 23]

A 95% CI of = [48.642, 99.358][pic 24]

One-tail test: H0:against H1:>0[pic 25][pic 26]

tA==5.97>2.045[pic 27]

The effect of variable A on D is statistically insignificant.

1. What problems (omitted variables, irrelevant variables, or multicollinearity) appear to exist in this regression model? Why? (12 points)

The three problems mentioned in the question in fact all exist in this regression model.

The variable S stands for the number of students living in the ith dorm. As shown in part (a), there is of possibility that =0 in the population since the 95% CI of  is [-2.34284, 0.73284]. If =0 in the population, then undeniably an irrelevant variable S is included in the model. Although including an irrelevant variable would not exert impact on other variables, but it can make the regression model less reliable.[pic 28][pic 29][pic 30]

Apart from the above-mentioned three variables, other factors may also influence the dependent variable D. For instance, the gender or age of the student living in ith room could also affect the damage done to dorm. It is reasonable to expect female student would do less damage and also the elder student would do less damage to the dorm as well. However, such variables are omitted in the regression model.

According to the model, 𝐹 stands for the percentage of the ith dorm residents who are frosh and 𝑆 refers to the number of students who live in the ith dorm. However, F and S are strong correlated since HKU has the policy to guarantee at least one year accommodation for non-local students, which indicates the percentage for residents who are frosh (F) could be related to (S). Such multicollinearity may exist in the regression model.

Q2. Determine the sign (and, if possible, comment on the likely size) of the bias introduced by leaving a variable out of an equation in each of the following cases:

a. In an equation for annual consumption of apples in the United States, the impact on the coefficient of the price of bananas of omitting the price of oranges. (6 points)

Suppose the model including the price of oranges is model 1: x1+x2 and the model omitting the price of oranges is model 2: +x1. And we have the bias of =E(.[pic 31][pic 32][pic 33][pic 34][pic 35][pic 36]