Question

A political science model determines voter turnout based on location of a district and if voter ID laws exist in the district. A sampling of 40 districts nationwide were used.

(a) Voter Turnout = 46.3 – 3.4 * South; R² = 12.0%

                                                   (t = -1.25)                                      

where the South dummy variable takes a value of 1 if the district is in a Southern state.

Interpret the intuition of the regression and how strong an inference that is made.

(b) An additional dummy is added to the regression: ID laws is 1 if an ID law exists in the district and 0 if it does not.     

            Voter Turnout = 42.0 – 2.2* ID law – 3.4 * South – 4.7*(ID law* South); R² = 40.0%

                                                      (t = -2.00)     (t = -1.80)                (t = -2.50)

What is the purpose of study in this regression?

Compare states that are not Southern with ID laws to South states with ID laws.

Answer 1

a.) Given Regression equation:

Voter Turnout = 46.3 – 3.4 * South; R2 = 12.0%

                                                   (t = -1.25)   

Intution: As per above regression model, it states ver cleay that if voter turnout is decresed by 3.4 times if a person belongs to southern region.

Apart from southern region voter turnout remians constant at 46.3 which is practically not possible.

Inference: Since it is not capturing the variation for other regions, the R² is very less at 12% which is showing that our model is able to capture only 12% of variation. It's beacuse our model gives same voter turnout for all other regions except south.

The model is not good at all.

b.) New Model:

Voter Turnout = 42.0 – 2.2* ID law – 3.4 * South – 4.7*(ID law* South);

R2 = 40.0%

Purpose of Study:

We have added ID law variable in this equation. Now, we are checking if the voter turnout is in compliance with ID laws existing in state or not.

Also, it is possible to check that if we are expecting some total voter turnout as per voting age population and we our voter turnout becomes more or less than that. Basically its for comparison to compare the expected voter turnout with actual one.

Also adding ID law variable increases effectiveness of our model. we are able to capture other regions as well.

Why R² Increased

Now in our second equation our R² has increased from last time. This is because we are able to capture more variation this. We are able to capture the variation for other regions also which follows ID law. Thus some part of those regions are also covered beacuse of which our model able to capture more variation.

Comparison

we have to compare southern regions with other regions follwing ID Laws in bith cases.

So, considering southern region:

ID law = 1

South = 1

Voter Turnout = 42.0 -2.2-2.4-4.7

Voter Turnout = 32.7

considering other regions following ID law:

ID law = 1

South = 0

Voter turnout = 42 - 2.2 - 0 - 0

Voter turnout = 39.8

If we consider the case that ID law is followed, then voter turnout is more in other regions in total than southern region.

This is obvious because other regions include more population as compared to only southern region.

Hence voter turnout is more in that