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.

We ran a regression. Regression results Dependent variable: FUNDS Adjusted R Square: .154 Constant (a): 673.642 B coefficient FUNDCARD: 1908.063 (p = .000), Standardized Beta .361 B coefficient DSIZE: .007 (p = .019), Standardized Beta .183

Write the equation for the regression, using the format yhat = a + bx + bx, filling in the numbers for a and b, and the names of the variables in place of y and x. 9.

Write one sentence interpreting the b coefficient for FUNDCARD.

Write one sentence identifying and interpreting the p value for the b coefficient for FUNDCARD. Refer to the null hypothesis and show that you know what it means for this specific example.

Write one sentence interpreting the b coefficient for DSIZE.

Write one sentence identifying and interpreting the p value for the b coefficient for DSIZE. Refer to the null hypothesis and show that you know what it means for this specific example.

Answer 1

Given --> 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

Regression results,

Dependent variable: FUNDS

Adjusted R Square=0.154

Constant (a)= 673.642

β coefficient FUNDCARD= 1908.063

p value for FUNDCARD = .000

Standardized Beta for FUNDCARD = 0.361

β coefficient DSIZE= 0.007

p value for DSIZE = 0.019)

Standardized Beta for DSIZE = 0.183

1) Write the equation for the regression, using the format yhat = a + bx + bx, filling in the numbers for a and b, and the names of the variables in place of y and x.

Ans--->

Regression equation with given information is as below

FUNDS = 673.642 + 1908.063 * FUNDCARD + 0.007 * DSIZE

2) Write one sentence interpreting the b coefficient for FUNDCARD.

-> b / β coefficient for FUNDCARD is ‘1908.063’ is very high in magnitude compare to the other b / β coefficient.

3) Write one sentence identifying and interpreting the p value for the b coefficient for FUNDCARD. Refer to the null hypothesis and show that you know what it means for this specific example.

--> p value of b / β coefficient for FUNDCARD is given as 0.000. Since it is closer to the 0 the b / β coefficient for FUNDCARD is very much statistically significant. FUNDCARD significantly affect FUNDS.

4) Write one sentence interpreting the b coefficient for DSIZE.

-> b / β coefficient for DSIZE is ‘0.007’ is very low in magnitude compare to the other b / β coefficient.

5) Write one sentence identifying and interpreting the p value for the b coefficient for DSIZE. Refer to the null hypothesis and show that you know what it means for this specific example.

-> p value of b / β coefficient for DSIZE is given as 0.019. Since it is larger than 0.01, the b / β coefficient for DSIZE is not statistically significant at 90% CI.

DSIZE does not significantly affect FUNDS.

But it would be statistically significant at 80% CI.