The choice of the reference category has no impact the statistical results of multiple regression, including R2 and results (meaning statistical significance and b) for the other independent variables in the regression.

A researcher is using data from 106 cities to study fire department size. Specifically, she is interested in using a regression analysis to predict the number of firefighters per 10,000 population. The regression below used the independent variables percentage unemployed, percentage of adults holding a bachelor's degree, and region (NE, MW, S, or W). In these (hypothetical) data, the firefighter variable ranged from 11.28 to 24.81 (mean = 17.3, standard deviation = 3.4). Percentage unemployed ranged from 7.1 to 11.6% (mean = 9.3, s.d. = 1.1), and percentage with a bachelor's degree ranged from 16.3 to 28.7% (mean = 22.9, s.d. = 2.9) across the 106 cities.

Her regression results were as follows:

Dependent variable: number of firefighters per 10,000 population

N = 106

R² = 0.534

Sum of squared residuals = 501.82

b

Standard error of b

t

p-value

Intercept (constant)

8.56

1.34

% unemployed

-1.02

0.37

(i)

0.007

% bachelor's degree

0.74

0.54

1.37

0.173

NE dummy

2.13

0.83

2.57

0.011

MW dummy

1.52

0.68

2.24

0.027

W dummy

-0.87

0.59

-1.47

0.144

In the regression with only % unemployed and % bachelor's degree, the sum of squared residuals was 553.29.

(a) Use the results to predict the number of firefighters per 10,000 population for a city with 8% unemployment, 22% holding a bachelor's degree, and located in the Midwest. Should you trust this predicted value? Explain.

(b) If the analyst had chosen "W" as reference, what would be the b's for "NE", "MW", and "S"?

(c) If we choose "W" as reference, what happens to R², b for % unemployed, and b for % holding bachelor's degree?

(d) Assuming no collinearity issue, interpret the regression results as fully as possible.