Part I

1. In the linear regression model,  ,

is referred to as

1. the population regression function.
2. the sample regression function.
3. exogenous variation.
4. the right-hand variable or regressor.
• In the simple linear regression model, the regression slope
1. indicates by how many percent Y increases, given a one percent increase in X.
2. when multiplied with the explanatory variable will give you the predicted Y.
3. indicates by how many units Y increases, given a one unit increase in X.
4. represents the elasticity of Y on X.
• The interpretation of the slope coefficient in the model  is as follows:
1. a 1% change in X is associated with a % change in Y.
1. a 1% change in X is associated with a change in Y of 0.01 .
1. a change in X by one unit is associated with a 100 % change in Y.
1. a change in X by one unit is associated with a  change in Y.
• The interpretation of the slope coefficient in the model is as follows:
1. a 1% change in X is associated with a % change in Y.
1. a change in X by one unit is associated with a 100* % change in Y.
1. a 1% change in X is associated with a change in Y of 0.01 .
1. a change in X by one unit is associated with a  change in Y.
• The interpretation of the slope coefficient in the model  is as follows:
1. a 1% change in X is associated with a % change in Y.
1. a change in X by one unit is associated with a  change in Y.
1. a change in X by one unit is associated with a 100 % change in Y.
1. a 1% change in X is associated with a change in Y of 0.01 .
• To decide whether or not the slope coefficient is large or small,
1. you should analyze the economic importance of a given increase in X.
2. the slope coefficient must be larger than one.
3. the slope coefficient must be statistically significant.
4. you should change the scale of the X variable if the coefficient appears to be too small.

= 607.3 + 3.85 Income – 0.0423 Income2. If income increased from 10 to 11 (\$10,000 to \$11,000), then the predicted effect on test scores would be:

1. 3.85.
2. 3.85-0.0423.
3. 2.96.
4. Cannot be calculated because the function is non-linear.

Part II:

Long Question 1:

Earnings functions attempt to find the determinants of earnings, using both continuous and binary variables. One of the central questions analyzed in this relationship is the returns to education.

Collecting data from 253 individuals, you estimate the following relationship

= 0.54 + 0.083 × Educ, R2 = 0.20, SER = 0.445

(0.14) (0.011)

where Earn is average hourly earnings and Educ is years of education.

1. What is the effect of an additional year of schooling? (notice, the dependent variable (Y) is in log, not level).
•  If you had a strong belief that years of high school education were different from college education, how would you modify the equation? What if your theory suggested that there was a “diploma effect”?
• You read in the literature that there should also be returns to on-the-job training. To approximate on-the-job training, researchers often use the so called Mincer or potential experience variable, which is defined as Exper = AgeEduc – 6. Explain the reasoning behind this approximation. Is it likely to resemble years of employment for various sub-groups of the labor force?

You incorporate the experience variable into your original regression

= -0.01 + 0.101 × Educ + 0.033 × Exper – 0.0005 × Exper2 ,

(0.16)  (0.012)              (0.006)                   (0.0001)

R2 = 0.34, SER = 0.405

• What is the effect of an additional year of experience for a person who is 40 years old and had 12 years of education?
• What is the effect of an additional year of experience for a person who is 60 years old and had 12 years of education?

Long Question 2:

Part III:

Empirical Question 1:

Using the data set TeachingRatings posted under the Exam 2 tab on Blackboard,

Carry out the following exercuses. HINT: Also, read the data description (pdf)!

1. Estimate a regression of  on  and . What is the estimated regression equation?
• Interpret all SEVEN estimated coefficients from part a.
• Which of these coefficients are statistically significant at 5% level?
• Add   and  to the regression. Is there evidence that   has a nonlinear effect on ? (Hint: in other words, is  statistically significant at 5% level)?
• Professor Smith is a man. He has cosmetic surgery that increases his beauty index from standard deviation below the average to one standard deviation above the average. What is his value of before the surgery? After the surgery?  (Hint: Calculate the average value of  and its standard deviation in Excel)

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