In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.
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 Stat p-value Lower 95% Upper 95%
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
(a) Write the fitted regression equation.
(b-1) State the degrees of freedom for a two-tailed test for zero slope, and find the critical value at α = .05.
(b-2) Choose the correct option for H0: β1 = 0 vs H1: β1 ≠ 0.
(c-1) Calculate t.
(c-2) Should the null hypothesis be rejected?
(d-1) Find the 95% confidence interval for slope.
(d-2) The confidence interval does not contain zero, which implies:
- there is a relationship between the total assets (billions) and total revenue (billions).
- there is no relationship between the total assets (billions) and total revenue (billions).
(e-1) Calculate t^2 and F.
(e-2) Calculate R^2.
(e-3) What is the percentage of variation in total revenue explained by total assets?