Question

random sample of congressional campaigns from 2002.

FUNDS: Total money raised for the campaign, in thousands of dollars DSIZE: Area of the candidate’s congressional district, in square miles FUNDCARD: 1 = campaign website allowed credit card donations, 0 = campaign website did not allow credit card donations. We wanted to know if amount of money raised for a campaign depends on the how large the district is and whether the campaign accepted credit card donations on its website.

Write one sentence identifying and interpreting the Adjusted R Square statistic. Be specific to the example.

Which independent variable has the strongest association with the dependent variable? How do you know?

Candidate Smith’s district is 471 square miles. Her campaign website allows credit card donations. How much money is she predicted to raise for the campaign? Show your calculation and write one complete sentence that includes your answer.

Answer 1

We ran a regression. Regression results

Dependent variable:
Adjusted R Square: .154

Constant (a): 673.642

FUNDCARD: 1908.063 (p = .000), Standardized Beta .361

DSIZE: .007 (p = .019), Standardized Beta .183

Write one sentence identifying and interpreting the Adjusted R Square statistic. Be specific to the example.

Coefficient of determination OR rsqaure -
It is the measure of the amount of variability in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model.

Adjusted R2 is an improved version of R2, which increases only if a signficant variable is added to the model. It penalize the model for every junk or non signficant variable that is added to the model.

In this case there are two predictor variable, hence adjusted the effect of the variable, the model explains 15.4% of the variation in the dependent variable(FUNDS)

Which independent variable has the strongest association with the dependent variable? How do you know?

The association of both variable fundcard and dsize are signficant. Hence we need to look at the standardized beta value and find which has the highest value.

We see thatn FUNDCARD has coefficient = 0.361, which is greater than that of DSIZE.

Hence FUNDCARD has a strong association with the dependent varibles.

Candidate Smith’s district is 471 square miles. Her campaign website allows credit card donations. How much money is she predicted to raise for the campaign? Show your calculation and write one complete sentence that includes your answer.

The regression equation is

FUNDS = 673.642 + 0.361 FUNDCARD + 0.183 DSIZE

Please check the table, since the table is not given in the proper manner.

We are given
DSIZE = 471
FUNDCARD = 1

Putting these values in the equation we get,

FUNDS = 673.642 + 0.361 FUNDCARD + 0.183 DSIZE
FUNDS = 673.642 + 0.361*(1) + 0.183*(471) = 760.196

Hence the predict funds is about 760.196 in Candidate Smith’s district of 471 square miles and her campaign website allows credit card donations.