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# Econ 306 Homework 5 Fall 2016

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Capital Bike Share is a service provided in the Washington D.C. area that allows individuals to use bicycles for short-term use; individuals pick up the bike at “Point A” and then return it at “Point B.” Using data collected from this service, we want to look at the relationship between number of trips made per day and daily low temperature. This dataset comes from one single month (January) where the column “date” denotes each day of the month.

a. Run the following regression in STATA:

trips = β0 +  β1*lowtemp

b. Report the coefficient and p-value on lowtemp. Is this statistically significant?

c. Using STATA, plot the residuals (attach to this assignment). What general conclusions might you draw from looking at this plot?

d. Perform a Durbin-Watson test at the .05 level testing that there is positive serial correlation. Be sure to report the lower and upper limit critical values and test statistic. What is your decision, and what does this mean?

Suppose we have the following data on the income and consumption of non-self-employed homeowners: (Data comes from Ando & Modigliani’s “The Permanent Income and Life Cycle Hypotheses of Saving Behavior: Comparisons and Tests”)

Income Bracket (\$)

Average Income (\$)

Average Consumption (\$)

0-999

556

2760

1000-1999

1622

1930

2000-2999

2664

2740

3000-3999

3587

3515

4000-4999

4535

4350

5000-5999

5538

5320

6000-7499

6585

6250

7500-9999

8582

7460

10000-above

14033

11500

a. Run a regression to explain average consumption as a function of average income. Show your work in STATA and report your results below:

Coefficient

Std. Error

t

P > |t|

Average income

b. Use the Park test to test the residuals from the equation you ran in part a for heteroscedasticity, using average income as the potential proportionality factor Z (Use α =.05). Report the coefficient and pvalue on the proportionality factor. What do you conclude as a result?

c. Run a 5-percent White test to test for heteroscedasticity. Report the test statistic and critical value then provide your conclusion.

d. Formulate the White test regression that is used. (Write this down here) Then, run the regression in STATA. Use the output to show how STATA calculates the White test statistic (write the numbers).

e. In this example, the ranges of the income brackets are not constant, so the variables are means of ranges of differing widths. Therefore, it would seem reasonable to think that different range widths might produce different variances for the error term, making heteroscedasticity even more likely.

Re-run the regression from part a using heteroskedastic-corrected standard errors. Report your results below:

Coefficient

Std. Error

t

P > |t|

Average income

You are looking at data on determinants of housing prices. An example dataset can be found in the Excel spreadsheet: House_price.xls:

price = house price, \$1000s

lotsize  =  size of lot in square feet

sqrft = size of house in square feet

We want “price” to be our dependent variable and the other variables to be our independent variables; however, we believe that heteroskedasticity may be a concern because of the large range in housing prices. Why would taking the natural log of our variables (creating a double log form) be a possible solution to our problem? Explain. [Hint: If you are not sure, try taking the natural log of the price column to see how it changes the values]

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