# Bivariate Regression

In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at alpha = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.

R^2 0.519

Std. Error 6.977

N 64

ANOVA table

Source SS df MS F p-value

Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11

Residual 3,018.3339 62 48.6828

Total 6,278.4320 63

Regression output confidence interval

Variables coefficients std.error t(df=62) p-value 95%lower 95%upper

Intercept 6.5763 1.9254 3.416 .0011 2.7275 10.4252

X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563

https://brainmass.com/statistics/regression-analysis/bivariate-regression-226888

#### Solution Preview

In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.

R^2 0.519

Std. Error 6.977

N 64

ANOVA ...

#### Solution Summary

Using ouput , the solution interprets a regression analysis with the independent variable, total assets, and dependent variable, total revenue.