Question 140653: 12.50
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 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
14.16
(a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible
causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992–2003 only.
Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your
choice to the 1992–2003 data. (f) Make a forecast for 2004, using either the fitted trend model or
a judgment forecast. Why is it best to ignore earlier years in this data set?
U.S. Manufactured General Aviation Shipments, 1966–2003
Year Planes Year Planes Year Planes Year Planes
1966 15,587 1976 15,451 1986 1,495 1996 1,053
1967 13,484 1977 16,904 1987 1,085 1997 1,482
1968 13,556 1978 17,811 1988 1,143 1998 2,115
1969 12,407 1979 17,048 1989 1,535 1999 2,421
1970 7,277 1980 11,877 1990 1,134 2000 2,714
1971 7,346 1981 9,457 1991 1,021 2001 2,538
1972 9,774 1982 4,266 1992 856 2002 2,169
1973 13,646 1983 2,691 1993 870 2003 2,090
1974 14,166 1984 2,431 1994 881
1975 14,056 1985 2,029 1995 1,028
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.
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(a) Write the fitted regression equation.
Y = 6.5763 + 0.0452X
-------------------------------
(b) 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.
df=62 ; t = 2.660
------------------------------
(c) What is your conclusion about the slope?
Since p-valu = 1.90E-11 the slope is not zero : X is statistically
significant in determining Y
------------------------------
(d) Interpret the 95 percent confidence limits for the slope.
0.0452 is in the 95% confidence interval
-------------------------------------
(e) Verify that F = t2 for the slope.
66.97 is not equal to 8.183^2
------------------------------------------
(f) In your own words, describe the fit of this regression.
Since R2 is 51.9% the reg. eq. explains only that percent
of the variability between Y and X.
-----------------------------------------------------------------
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
14.16
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Comment: This site is not suitable for graphing displays
so I will leave this question to you.
----------------------------------
(a) Plot the data on U.S. general aviation shipments.
(b) Describe the pattern and discuss possible causes.
(c) Would a fitted trend be helpful? Explain.
(d) Make a similar graph for 1992–2003 only.
Would a fitted trend be helpful in making a prediction for 2004?
(e) Fit a trend model of your choice to the 1992–2003 data.
(f) Make a forecast for 2004, using either the fitted trend model or
a judgment forecast. Why is it best to ignore earlier years in this data set?
----------------------------------------------------------
U.S. Manufactured General Aviation Shipments, 1966–2003
Year Planes Year Planes Year Planes Year Planes
1966 15,587 1976 15,451 1986 1,495 1996 1,053
1967 13,484 1977 16,904 1987 1,085 1997 1,482
1968 13,556 1978 17,811 1988 1,143 1998 2,115
1969 12,407 1979 17,048 1989 1,535 1999 2,421
1970 7,277 1980 11,877 1990 1,134 2000 2,714
1971 7,346 1981 9,457 1991 1,021 2001 2,538
1972 9,774 1982 4,266 1992 856 2002 2,169
1973 13,646 1983 2,691 1993 870 2003 2,090
1974 14,166 1984 2,431 1994 881
1975 14,056 1985 2,029 1995 1,028
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Cheers,
Stan H.
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