statistics homework

finish in 8 hours 

Homework 2 Econ 4400

1 Directions

You should show enough work to demonstrate that you understand how to solve a
problem. A wrong answer with no work is worth 0 points, but a wrong answer with
some work that makes sense will get some partial credit. Stata code does not need to
be turned in.
Due Dates:
T/R Class Feb 6
W/F Class Feb 7

2 Problems

1. (10 points) Given the equation y = β0 + β1x + �. What does each part of the
equation represent? (ie is the independent variable, etc)

2. (5 points) What is the difference between a residual and an error?

3. (10 points) In figure 1, the X’s represent data points x and y. The line represents
a linear estimation of the relationship between x and y. Answer the following
questions referring to the figure:

(a) If the estimated equation is y = β̂0 + β̂1x + �, what is the approximate value
of β̂0?

(b) What is the sign of β̂1?

(c) What distance in the graph represents �̂?

4. (20 points)You are working with a small firm that invests in real estate and
have been charged with identifying homes that are priced below market value in
Columbus. You are specifically looking at homes in Upper Arlington and have
been able to collect the following data for homes sold in the past year: price,
bedrooms, bathrooms, square footage of home, and square footage of lot.

(a) (5) Write out an equation that you could estimate with OLS. (ie wagei =
β0 + β1educationi + β2agei + ….)

(b) (10) What is the expected sign of each coefficient? Why?

(c) (5) How could you use your model to identify homes that are currently
underpriced?

5. (25 points) You were recently hired to work for a Chevrolet car dealership. The
dealership plans to head to attend a wholesale auction from a rental company to
increase inventory. They are selling 120 Chevy Cruze’s. The dealership has data
on the past 120 Cruzes sold. You have been given the task of predicting the price
at which the dealership could sell the auction cars.

(a) (5) Write out an equation that you could use. (come up with at least 3
independent variables.)

(b) (10) What is the expected sign of each coefficient? Why?

(c) (5) Describe how the dealership could use your model to develop a bidding
plan with an expected margin of 20% on vehicles.

(d) (5) Suppose I wanted to use the model to identify sales people that get the
best margins. How could that be accomplished?

6. (20 points) The data set gpa small is available on Carmen to complete this ques-
tion. The dataset includes a sample of college students at Michigan State (the
textbook author is a professor at MSU). Estimate the equation: CollegeGPAi =
β0 + β1SATScorei + β2HighSchoolRanki + �i Report your regression results in
a table and interpret each coefficient. See the Stata help section for assistance.
You must produce a table that looks similar to table 1. If you hand in
something that looks like figure 2, you will not get credit.

7. (10 points) This question will later become a part of your semester long project.
You are expected to write a paper using the nlsy97 small.dta available on Carmen.
Develop a question that you would like to answer with the data set. Write out an
equation that you plan to estimate and give reasons for including each independent
variable.

3 Stata Help

The command to run an OLS regression in stata is ”regress” or ”reg” for short. Fol-
lowing the command should be a list of variables starting with the dependent variable.
So if I want to estimate y = β0 + β1x, I type ”reg y x”. Stata will return something
like figure 2. In that example, β̂0 = 2.541224 and β̂1 = 1.947394. We will learn what
the other numbers mean at a later point.

3.1 Making a Regression Table

1. Make sure the estout package is installed. (see hw 1)

2. Run regressions: ”reg y x1 x2 x3”

3. store results: eststo r1

4. Make table: esttab r1 using t1.rtf, replace label star(* 0.10 ** 0.05 *** 0.01) se

Table 1: Accpetable

(1)
GPA after fall semester

verbal/math SAT score -0.0319
(0.114)

size grad. class, 100s 0.0409∗∗

(0.0162)

rank in grad. class -0.00215∗∗∗

(0.000524)

high school percentile, from top -0.0133∗∗∗

(0.00169)

Constant 2.944∗∗∗

(0.114)
Observations 1199

Standard errors in parentheses
∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Figure 1: Scatter Plot

Figure 2: Not Acceptable