Question

Below are results from a regression analysis. The dependent variable is the percent vote for Woodrow Wilson in 1916, measured from 0 to 100. Each observation is a New Jersey county, of which there are 20. The independent variables are the county’s percentage of Democrats (0 to 100), percentage working class (0 to 100), and the number of shark attacks that occurred in it in 1916 (0, 1, 2, . . . ). Shark attacks are rare: no county experienced more than 3.

	estimate
(Intercept)	0.327
% Democrats	0.897
% workers	-0.121
# shark attacks	-0.506

(a) How do we interpret the coefficient estimate for # shark attacks? (b) What would be the predicted vote share for Wilson in a county that is 40% Democratic, has 80% working class, and experienced no shark attacks? What about if the same county experienced 1 shark attack?

Answer 1

(a)

The coefficient estimate for the number of shark attacks was -0.506. Since it was negative, the relationship between the shark attacks and the percent vote for Woodrow Wilson in 1916 was negative, i.e., if the independent variable (number of shark attacks) was increased, then the dependent variable (percent vote) would decrease and vice versa.

Interpretation of the coefficient estimate for number of shark attacks:

For every one number increase in shark attacks,  the percent vote for Woodrow Wilson in 1916 would decrease by 0.506, that is, if a shark attack increases by one number, then the vote for Woodrow Wilson in 1916 would decrease by 0.506%

(b)

The predicted vote share for Wilson would be:

=0.327+0.897(% Democrats) - 0.121(% workers) - 0.506(number of shark attacks)

So, =0.327+0.897(40) - 0.121(80) - 0.506(0) = 26.527. Since vote share was estimated in percentage, it was 26.527%

If number of shark attacks was 1 instead of 0, then:

=0.327+0.897(40) - 0.121(80) - 0.506(1) = 26.021. Since vote share was estimated in percentage, it was 26.021%