Discuss the below:
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 (see attached data) to find the critical value at a=.05.
c. What is your conclusion about the slope?
d. Interpret the 95 percent confidence limits for the the slope.
e. Verify that F=t^2 for the slope.
f. Describe the fit of this regression.
| R-squared |
0.519 |
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| Std. Error |
6.977 |
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| n |
64 |
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| ANOVA table |
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| Source |
SS |
df |
MS |
F |
p-value |
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| Regression |
3260.0981 |
1 |
3260.0981 |
66.97 |
1.90E-11 |
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| Residual |
3018.3339 |
62 |
48.6828 |
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| Total |
6278.432 |
63 |
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| Regression Output |
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Confidence |
Interval |
| variables |
coefficients |
std. error |
t(df=62) |
p-value |
95% lower |
95% upper |
| Intercept |
6.5763 |
1.9254 |
3.416 |
0.0011 |
2.7275 |
10.4252 |
| X1 |
0.0452 |
0.0055 |
8.183 |
1.90E-11 |
0.0342 |
0.0563 |
|
Confidence Level |
|
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0.8 |
0.9 |
0.95 |
0.98 |
0.99 |
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Significance Level for Two-Tailed Test |
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0.2 |
0.1 |
0.05 |
0.02 |
0.01 |
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Significance Level for One-Tailed Test |
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| Degrees of Freedom (v) |
0.1 |
0.05 |
0.025 |
0.01 |
0.005 |
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| 1 |
3.078 |
6.314 |
12.706 |
31.821 |
63.656 |
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| 2 |
1.886 |
2.92 |
4.303 |
6.965 |
9.925 |
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| 3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
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| 4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
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| 5 |
1.476 |
2.015 |
2.571 |
3.365 |
4.032 |
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| 6 |
1.44 |
1.943 |
2.447 |
3.143 |
3.707 |
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| 7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
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| 8 |
1.397 |
1.86 |
2.306 |
2.896 |
3.355 |
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| 9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.25 |
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| 10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
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| 11 |
1.363 |
1.796 |
2.201 |
2.718 |
3.106 |
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| 12 |
1.356 |
1.782 |
2.179 |
2.681 |
3.055 |
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| 13 |
1.35 |
1.771 |
2.16 |
2.65 |
3.012 |
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| 14 |
1.345 |
1.761 |
2.145 |
2.624 |
2.977 |
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| 15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
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| 16 |
1.337 |
1.746 |
2.12 |
2.583 |
2.921 |
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| 17 |
1.333 |
1.74 |
2.11 |
2.567 |
2.898 |
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| 18 |
1.33 |
1.734 |
2.101 |
2.552 |
2.878 |
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| 19 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
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| 20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
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| 21 |
1.323 |
1.721 |
2.08 |
2.518 |
2.831 |
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| 22 |
1.321 |
1.717 |
2.074 |
2.508 |
2.819 |
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| 23 |
1.319 |
1.714 |
2.069 |
2.5 |
2.807 |
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| 24 |
1.318 |
1.711 |
2.064 |
2.492 |
2.797 |
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| 25 |
1.316 |
1.708 |
2.06 |
2.485 |
2.787 |
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| 26 |
1.315 |
1.706 |
2.056 |
2.479 |
2.779 |
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| 27 |
1.314 |
1.703 |
2.052 |
2.473 |
2.771 |
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| 28 |
1.313 |
1.701 |
2.048 |
2.467 |
2.763 |
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| 29 |
1.311 |
1.699 |
2.045 |
2.462 |
2.756 |
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| 30 |
1.31 |
1.697 |
2.042 |
2.457 |
2.75 |
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| 31 |
1.309 |
1.696 |
2.04 |
2.453 |
2.744 |
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| 32 |
1.309 |
1.694 |
2.037 |
2.449 |
2.738 |
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| 33 |
1.308 |
1.692 |
2.035 |
2.445 |
2.733 |
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| 34 |
1.307 |
1.691 |
2.032 |
2.441 |
2.728 |
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| 35 |
1.306 |
1.69 |
2.03 |
2.438 |
2.724 |
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| 36 |
1.306 |
1.688 |
2.028 |
2.434 |
2.719 |
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| 37 |
1.305 |
1.687 |
2.026 |
2.431 |
2.715 |
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| 38 |
1.304 |
1.686 |
2.024 |
2.429 |
2.712 |
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| 39 |
1.304 |
1.685 |
2.023 |
2.426 |
2.708 |
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| 40 |
1.303 |
1.684 |
2.021 |
2.423 |
2.704 |
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| 41 |
1.303 |
1.683 |
2.02 |
2.421 |
2.701 |
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| 42 |
1.302 |
1.682 |
2.018 |
2.418 |
2.698 |
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| 43 |
1.302 |
1.681 |
2.017 |
2.416 |
2.695 |
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| 44 |
1.301 |
1.68 |
2.015 |
2.414 |
2.692 |
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| 45 |
1.301 |
1.679 |
2.014 |
2.412 |
2.69 |
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| 46 |
1.3 |
1.679 |
2.013 |
2.41 |
2.687 |
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| 47 |
1.3 |
1.678 |
2.012 |
2.408 |
2.685 |
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| 48 |
1.299 |
1.677 |
2.011 |
2.407 |
2.682 |
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| 49 |
1.299 |
1.677 |
2.01 |
2.405 |
2.68 |
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| 50 |
1.299 |
1.676 |
2.009 |
2.403 |
2.678 |
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| 55 |
1.297 |
1.673 |
2.004 |
2.396 |
2.668 |
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| 60 |
1.296 |
1.671 |
2 |
2.39 |
2.66 |
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| 65 |
1.295 |
1.669 |
1.997 |
2.385 |
2.654 |
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| 70 |
1.294 |
1.667 |
1.994 |
2.381 |
2.648 |
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| 75 |
1.293 |
1.665 |
1.992 |
2.377 |
2.643 |
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| 80 |
1.292 |
1.664 |
1.99 |
2.374 |
2.639 |
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| 85 |
1.292 |
1.663 |
1.988 |
2.371 |
2.635 |
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| 90 |
1.291 |
1.662 |
1.987 |
2.368 |
2.632 |
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| 95 |
1.291 |
1.661 |
1.985 |
2.366 |
2.629 |
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| 100 |
1.29 |
1.66 |
1.984 |
2.364 |
2.626 |
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| 110 |
1.289 |
1.659 |
1.982 |
2.361 |
2.621 |
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| 120 |
1.289 |
1.658 |
1.98 |
2.358 |
2.617 |
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| 130 |
1.288 |
1.657 |
1.978 |
2.355 |
2.614 |
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| 140 |
1.288 |
1.656 |
1.977 |
2.353 |
2.611 |
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| 150 |
1.287 |
1.655 |
1.976 |
2.351 |
2.609 |
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| ∞ |
1.282 |
1.645 |
1.96 |
2.326 |
2.576 |
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