Question
A researcher wanted to understand what factors lead to the success of Democrats winning seats in state legislatures. The researcher ran a regression model with
A researcher wanted to understand what factors lead to the success of Democrats winning seats in state legislatures. The researcher ran a regression model with percentage of Democrats in a state's legislature as the dependent variable with per capita income, percentage of union workers, percentage of state population living in an urban area, and a dummy variable for Southern states (southern state =1). The researcher hypothesized that the percentage of Democrats increases in states with more union workers, higher urban populations and in Southern states (were the Democratic Party remains strong in legislatures). The researcher hypothesized that Democrats would win a lower percentage of seats in states with higher per capita income. The researcher got the following results.
Coefficientsa | ||||||
---|---|---|---|---|---|---|
Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||
B | Std. Error | Beta | ||||
1 | (Constant) | 16.375 | 14.675 | 1.116 | .271 | |
Percapita income | .001 | .001 | .240 | 1.484 | .145 | |
Percent workers who are union members | 1.373 | .426 | .531 | 3.226 | .002 | |
Percent urban population | -.089 | .143 | -.093 | -.622 | .537 | |
Southern state? | 10.569 | 4.496 | .347 | 2.350 | .023 | |
a. Dependent Variable: Percent of state legislators who are Democrats |
R= .306
Adjusted R= .243
a. Write the results in the form of an equation.
b. Interpret the coefficients for each independent variable.
c. Do the results support the researcher's hypotheses? Why or why not?
d. What does R tell us about the goodness of fit for this particular regression analysis?
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