# Interpreting Indicator Variables¶

In this exercise we’ll work with a (somewhat canonical) dataset on the prices, mileages, weights, and other characteristics of 74 automobiles. These data originally came from the April 1979 issue of Consumer Reports and from the United States Government EPA statistics on fuel consumption; they were compiled and published by Chambers et al. (1983).

To get the data, follow this link or go to http://www.github.com/nickeubank/MIDS_Data and download the automobile_dataset.dta file. This is a canonical example dataset used in coding examples all over the internet, and the codebook is roughly:

make            Make and Model
price           Price
mpg             Mileage (mpg)
rep78           Repair Record 1978
trunk           Trunk space (cu. ft.)
weight          Weight (lbs.)
length          Length (in.)
turn            Turn Circle (ft.)
displacement    Displacement (cu. in.)
gear_ratio      Gear Ratio
foreign         Car type


## Indicator Variables and Omitted Variable Bias¶

### Exercise 1¶

Create a new variable named guzzler that takes the value of 1 if the car’s miles per gallon (mpg) is less than 18 and takes value 0 otherwise (“guzzler” is a term for a car that consumes gas very quickly, or “guzzles gas”). Regress price on guzzler and interpret the coefficients. Do gas guzzlers cost more than the other cars? How much more?

### Exercise 2¶

Create a scatter plot of price against weight and color code your markers by the value of guzzler (red for guzzler = 1 and green for guzzler = 0).

Based on the graph you just created, do you think not controlling for weight might lead to omitted variable bias in the regression in Exercise 1? What is the direction of the bias?

### Exercise 3¶

Regress price on guzzler, weight, foreign, headroom, and displacement. Interpret the coefficients. Do the regression results confirm your guess in Q3?

### Exercise 4¶

Variable rep78 indicates the car’s repair record. The variable is poorly documented (we don’t know that the value means) but take our word for it that the values from 1-5 indicate “very poor”, “poor”, “acceptable”, “good”, and “very good” record, respectively.

Create five separate indicator variables from rep78 and regress price on indicators for values 2 through 5. Also control for headroom, weight, foreign, and displacement. Interpret the coefficients on the indicator for rep78 == 3.

(Note: You can use the C() method for creating indicator variables, but your answers will only be right if the omitted category is rep78 == 1).

## Interaction Effects¶

### Exercise 5¶

You suspect that the effect of guzzler on price may be conditioned by whether or not the car is manufactured abroad. Regress price on guzzler, foreign and their interaction, controlling for headroom, weight and displacement. Without using mathematical language, explain to your grandma what the coefficient on the interaction term means.

### Exercise 6¶

What is the price difference between a foreign guzzler and a foreign non-guzzler?

### Exercise 7¶

What is the price difference between a domestic non-guzzler and a foreign non-guzzler?

### Exercise 8¶

Regress price on foreign, mpg and their interaction, controlling for headroom, weight and displacement. Interpret the coefficients of the main independent variables. Explain in layman terms the coefficient on the interaction term.

## Absolutely positively need the solutions?¶

Don’t use this link until you’ve really, really spent time struggling with your code! Doing so only results in you cheating yourself.