Homework 2

HW2

Hypothesis Testing and Simple Linear Regression:

1. What are the five Classic Gauss-Markov Assumptions for simple linear regression?

2. What are two reasons the sample mean may deviate from the null hypothesis? What are the steps for testing a hypothesis?

3. The average annual income of 100 randomly chosen residents of Santa Cruz is $45,221 with a standard deviation of $30,450.

a. What is the standard deviation of the mean annual income?

b. Test the 1-sided hypothesis that the average annual income is $40,000 against the alternative that it is less than $40,000 at the 10% significance level.

c. Test the 2-sided hypothesis that the average annual income is equal to $42,000 against the alternative that it is not at the 5% significance level.

d. What is the confidence interval for part (c)?

e. What is the p-value for part (b)?

f. Do you reject or fail to reject part (c)? Please write your answer and a complete, accurate, sentence.

4. The following table contains the minimum wage and unemployment rates for a sample of six states.

State	Unemployment %	Minimum wage
Alaska	6.5	$9.89
Arizona	5.1	$11.00
Arkansas	3.8	$9.25
California	4.2	$12.00
Colorado	3.7	$11.10
Florida	3.5	$8.46

a. Carefully graph unemployment and minimum wage, with unemployment on the vertical access. Draw a line that best fits the points and label the approximate intercept and slope.

b. Compute the variance and covariance for unemployment and minimum wage.

c. Estimate and the regression of a state’s unemployment rate on its minimum wage and write the resulting regression equation. Interpret the coefficient on minimum wage.

d. What is the predicted unemployment rate for a state with a minimum wage of 9 dollars?

e. If a state were to reduce its minimum wage from 10 dollars to 7 dollars, what is the predicted change in the unemployment rate?

f. What percent of the variation in unemployment is explained by the minimum wage (i.e. what is the R-squared)?

g. What assumption is required in order use regression through the origin when regressing unemployment on minimum wage? Do you think this is a reasonable assumption in this case? Explain.

h. Compute the regression through the origin coefficients and write the resulting equation.

i. What is the predicted unemployment rate for a state with a minimum wage of 9 dollars? Compare your answer to (d).

5. The following regression equation examines the relationship between house prices (in dollars) and the number of parks in a city.

a. Interpret the coefficient on the number of parks.

b. What is the predicted house price in a city with 30 parks? In a city with 50 parks?

c. How many parks would there need to be in a city in order for the predicted house price to be 1,280,300 dollars?

d. Suppose that a house in a town with 41 parks sells for 710,000 dollars. What is the error in the predicted house price?

e. New York City has 1,700 parks. What is the predicted house price in NY? Do you think this is reasonable? If no, explain the shortcoming of the regression.

You decide that a more reasonable regression would have the number of parks per 1,000 households (4 people) (HHs). You get the following result.

f. Interpret the coefficient on parks per thousand HHs.

g. What is the predicted house price in a city with 30 parks and 20,000 households?

h. What is the predicted house price in New York if there are 1,700 parks and 8 million people?

Now you regress the natural log of house price on parks per thousand households.

i. Interpret the coefficient on parks per thousand HHs.

j. What is the expected change in house price if parks per thousand increases from 1 to 1.5?