ECON 330: PRACTICE QUESTIONS

SECTION A:

Question2:

Suppose you are fitting a linear fit such that the sum of residuals is minimized. You have three possible linear lines A, B

and C. Which is the correct linear fit according to the above specification?

Q3. MCQS

1. The regression model includes a random error or disturbance term for a variety of reasons. Which

of the following is NOT one of them?

a. measurement errors in the observed variables

b. omitted influences on Y (other than X)

c. linear functional form is only an approximation

d. the observable variables do not exactly correspond with their theoretical counterparts

e. there may be approximation errors in the calculation of the least squares estimates

2. Which of the following assumptions about the error term is not part of the so called "classical

assumptions"?

a. it has a mean of zero

b. it has a constant variance

c. its value for any observation is independent of its value for any other observation

d. it is independent of the value of X

e. it has a normal distribution

3. Which of the following is NOT true?

a. the point Xbar, Ybar always lies on the regression line

b. the sum of the residuals is always zero

c. the mean of the fitted values of Y is the same as the observed values of Y

d. there are always as many points above the fitted line as there are below it

e. the regression line minimizes the sum of the squared residuals

4. In a simple linear regression model the slope coefficient measures

a. the elasticity of Y with respect to X

b. the change in Y which the model predicts for a unit change in X

c. the change in X which the model predicts for a unit change in Y

d. the ratio Y/X

e. the value of Y for any given value of X

5. Changing the units of measurement of the Y variable will affect all but which one of the

following?

a. the estimated intercept parameter

b. the estimated slope parameter

c. the Total Sum of Squares for the regression

d. R squared for the regression

e. the estimated standard errors

6. A fitted regression equation is given by Yhat = 20 + 0.75X. What is the value of the residual at

the point X=100, Y=90?

a. 5

b. -5

c. 0

d. 15

e. -5

7. What is the number of degrees of freedom for a simple bivariate linear regression with 20

observations?

a. 20

b. 22

c. 18

d. 2

8. R squared measures

a. the correlation between X and Y

b. the amount of variation in Y

c. the covariance between X and Y

d. the residual sum of squares as a proportion of the Total Sum of Squares

e. the explained sum of squares as a proportion of the Total Sum of Squares

9. One tailed tests are sometimes used to test hypotheses about regression coefficients. In which of

the following circumstances?

a. when the estimated coefficient has the sign predicted by theory

b. when you wish to use a larger significance level than 5%

c. when the sample size is large enough to use the normal approximation to the t distribution

d. when the estimated coefficient has the opposite sign to that predicted by theory

e. when you are testing a hypothesis other than that the parameter equals zero

10. The least squares estimator of the slope coefficient is unbiased means

a. the estimated slope coefficient will always be equal to the true parameter value

b. the estimated slope coefficient will get closer to the true parameter value as the size of the

sample increases

c. the estimated slope coefficient will be equal to the true parameter if the sample is large

d. the mean of the sampling distribution of the slope parameter is zero

e. if repeated samples of the same size are taken, on average their value will be equal to the true

parameter

Section B: MLR AND OMITTED VARIABLE BIAS:

Consider the following two regression models.

(i) Pricei= αo +α1 weighti +Ɛi

(ii) Pricei= βo +β1 weighti+ β2lengthi +Ui

We have the data for US automobile data for the year of 1978. The variables are defined as follows:

Table 1:

Variable name Description

make Make and Model of the automobile

price Price of the automobile

weight Weight (lbs.) of the automobile

length Length (in.) of the automobile

Black Black ==1 if color of the automobile is black, 0

otherwise

The summary statistics of the variables for the data set are listed in the table below:

Table 2:

Variable Obs Mean Std. Dev. Min Max

price 74 6165.257 2949.496 3291 15906

weight 74 3019.459 777.1936 1760 4840

length 74 187.9324 22.26634 142 233

black 74 1 0 1 1

We estimate the regression models (i) and (ii). The regression estimates are summarized in the table below.

Table 3

Regression Model(i) Regression Model(ii) Notes Titles

VARIABLES price price

weight 2.044*** 4.699***

(0.377) (1.122) Standard errors are reported in parentheses

length -97.96**

(39.17) * implies significance at 10%

Constant -6.707 10,387** ** implies significance at 5%

(1,174) (4,308) *** implies significance at 1%

Observations 74 74

R-squared 0.290 0.348

Read the three tables carefully and answer the following questions.

Q1. Interpret the coefficients of length in both regression estimates.

Q2. Interpret the constants of both regression estimates. Do these constants provide meaningful

interpretation?

Q3. The variable „length‟ is omitted in the first regression model. In what way does the omitted variable

affects the value of weight? Can you comment on the direction of bias? Can you comment on the

correlation between length and weight on the basis of the information provided?

Q4. Now I include the variable “Black” as an explanatory variable in addition to weight and length.

However, when I run the model STATA drops the “Black” variable. (The STATA output is pasted

below)

Table: 4

What do you think is the problem? What assumptions (if any) are violated?

Q5. Now consider the third regression model

Length(i)= σ +σ1weight(i)+ error

The STATA output of the estimates of the above regression is pasted below (Table 5)

Now I estimate the residuals of the above regression model and store them in a new variable called „r‟

(FYI to recover regression residuals, just type “Predict r1, residuals” immediately after the regression

output)

The summary statistics of „r‟ are listed below:

Table 6:

Variable Obs Mean Std. Dev. Min Max

r 74 7.72e-09 7.217443 -24.45176 12.53888

I will run two further regressions with the following specifications.

Regression (iii): price is regressed on r

Regression (iv): price is regressed on r and weight

Table 7

iii iv Notes Titles

VARIABLES price price Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

r -97.96** -97.96**

(46.76) (39.17)

weight 2.044***

(0.364)

Constant 6,165*** -6.707

(335.2) (1,134)

Observations 74 74

R-squared 0.057 0.348

a. Compare the coefficients of „r‟ in Table 6 with the coefficient of „length‟ reported in Table 3. Are

they equal? If yes then why?

b. What is the correlation between „r‟ and the variable „weight‟? Explain your answer

c. What will happen if I regress price on „r‟, „weight‟ and „length‟? What problem will you encounter?

1 “r” is the name that I have given to the variable. You can give some other name as well if you wish.