SOLUTION: 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

Question 137307: 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 twotailed 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.
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 (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

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.
(a) Write the fitted regression equation.: Y =0.0452X + 6.5763
---------------------------------
(b) State the degrees of freedom for a two tailed test for zero slope
df = 62
------------------
and use Appendix D to find the critical value at α = .05.
Comment: I don't have your Appendix D.
--------------------------------------
(c) What is your conclusion about the slope?

(d) Interpret the 95 percent confidence limits for the slope.
We have 95% confidence that the slope is betwee. 2.7275 and 10.4252
----------------------
(e) Verify that F = t2 for the slope.
66.97 = 8.183^2
----------------------------
(f) In your own words, describe the fit of this regression.
R^2 says 51.9% of the variability between x and y is explained by
the equation.
Since R = sqrt0.519 = 0.72... the data is pretty well modeled
by the linear model.
==================
Cheers,
Stan H.
==================
--------------------
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 (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

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