Eco311, Second Midterm Exam, Fall 2017.

Prof. Bill Even

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ANSWER KEY FOR FORM 1

Your row (Please circle) 1 2 3 4 5

Directions

Place your answers to all questions in the space provided. If the answer to a question is surrounded by

other work, please be sure to clearly identify the answer by circling it. Round all numerical answers to

the nearest 100th (e.g. 1.23) unless specifically told otherwise. Each question is worth 4 points unless

otherwise indicated.

A separate document with regression tables, formulae, and statistical distributions is provided and

referred to throughout the exam.

You have until the end of the class period (80 minutes) to finish the exam. If you want extra time, you

may purchase it at a price of 5 percentage points per minute.

Eco311, Second Midterm Exam, Fall 2017.

Prof. Bill Even

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For the next several questions regarding home prices, refer to the regression results in table 1.

1. (6 points) Using specification (1), construct a t-statistic for the null hypothesis that the total

family income has no effect on the value of the home owned..

a. What is the relevant t-statistic?

𝒕 = 𝟏. 𝟕𝟑𝟓

.𝟎𝟎𝟑𝟑𝟓 =𝟓𝟏𝟕.𝟗𝟏

b. What is the critical level of the t-statistic for rejecting the null hypothesis at the .10 level

(two-tailed test)?

1.64

c. Can you reject the null at the .10 level?

Yes

d. Based on the t-statistic in (a), the p-value must be

i. Less than .01

ii. Between .01 and .05

iii. Between .05 and .10

iv. Greater than .10

2. Using specification (1), construct a 99% confidence interval for the coefficient on total family

income on the house price. Show how you derived this confidence interval and circle your

answer.

1.735 ± 2.57 ∗ .00335 = (1.726,1.744)

3. Using specification (1), what is the marginal effect of an additional 10 years of age on the

predicted home value (in $) if the homeowner is currently 40 years old?

𝚫𝒗𝒂𝒍𝒖𝒆 = 𝝏𝒗𝒂𝒍𝒖𝒆𝒉

𝝏𝒂𝒈𝒆 ∗ 𝚫𝒂𝒈𝒆 = (𝟐. 𝟑𝟖𝟐 + 𝟐(−. 𝟎𝟏𝟏𝟖)∗𝟒𝟎)∗𝟏𝟎 =𝟏𝟒. 𝟑𝟖

That is, increasing age from 40 to 50 will increase predicted house value will by $14,380.

Eco311, Second Midterm Exam, Fall 2017.

Prof. Bill Even

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4. Home-owners in the sample are between the ages of 21 and 65. Based on these restrictions and

using specification (1),

a. what age minimizes the predicted home value ?

21

b. what age maximizes the predicted home value ?

65

5. In specification (2), the dependent variable is switched from value of house to its log and total

family income is replaced with its log. In one sentence, what does the coefficient of .538 imply

about the relationship between income and the value of the home? Be sure to indicate the

quantitative size of the effect of income on value of home owned and be clear about the units of

measurement.

6. (6 points) Based on specification (2),

a. provide a t-statistic for the null hypothesis that a 1% increase in income will lead to a 1%

increase in the predicted value of the home. Show how you calculated your t-statistic.

𝑡 = .538 − 1

.00132 = −350.00

b. Based on this t-statistic, can you reject the null at the .01 level of significance? In one

sentence, why or why not?

The critical value for rejection at the .01 level is 2.57 and |t|>2.57, so the null

hypothesis is rejected.