the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. R2 0.519 Std. Error 6.977 n 64
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.
| R2 | 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.
yˆy^ = + X
(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 | |
| tcrit | ± |
(b-2) Choose the correct option for H0: β1 = 0 vs H1: β1 ≠ 0.
multiple choice 1
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Do not reject the null hypothesis if tcalc > 1.999
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Reject the null hypothesis if tcalc > 1.999
(c-1) Calculate t. (Round your answer to 3 decimal places.)
tcalc
(c-2) We reject the null hypothesis.
multiple choice 2
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Yes
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No
(d-1) Find the 95% confidence interval for slope. (Round your answer to 4 decimal places.)
Confidence interval is from to .
(d-2) The confidence interval does not contain zero, which implies
multiple choice 3
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there is no relationship between the total assets (billions) and total revenue (billions).
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there is a relationship between the total assets (billions) and total revenue (billions).
(e-1) Calculate t2 and F. (Round your answers to the nearest whole number.)
| t2 | |
| Fcalc |
(e-2) Calculate R2.
R2R2
(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 %
(f) Increasing assets increases income.
multiple choice 4
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Yes
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No
Note: As per the instructions we are supposed to solve first three subparts. Please repost the remaining questions.
(a)
Let y= a+bx be the regression line.
Here a is the intercept and b is the slope.
Y is the dependent and x is the independent variable.
From the given output,
The coefficient of intercept is, a=6.5763
The slope coefficient is, b=0.0452
The fitted regression equation is,
Y^ = a+bx = 6.5763+(0.0452)x
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