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.
y^ = 6.5763 + 0.0452X
(b-1) 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. (Round t critical value to 3 decimal places.)
Degrees of freedom: 62
t_crit: ±
(c-1) Calculate t. (Round your answer to 3 decimal places.)
t_calc:
(e-1) Calculate t^2 and F. (Round your answers to the nearest whole number.)
t^2:
F_calc:
(e-2) Calculate R^2.
R^2:
(e-3) What is the percentage of variation in total revenue explained by total assets? (Round your answer to 1 decimal place.)
The percentage of variation in total revenue explained by total assets is %.