document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140653>Question 140653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12.50\r<BR>\n" );
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document.write( "In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64<BR>\n" );
document.write( "large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two tailed<BR>\n" );
document.write( "test for zero slope, and use Appendix D to find the critical value at &#945; = .05. (c) What is your<BR>\n" );
document.write( "conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify<BR>\n" );
document.write( "that F = t2 for the slope. (f) In your own words, describe the fit of this regression. <BR>\n" );
document.write( "R2 0.519<BR>\n" );
document.write( "Std. Error 6.977<BR>\n" );
document.write( "n 64<BR>\n" );
document.write( "ANOVA table<BR>\n" );
document.write( "Source SS df MS F p-value<BR>\n" );
document.write( "Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11<BR>\n" );
document.write( "Residual 3,018.3339 62 48.6828<BR>\n" );
document.write( "Total 6,278.4320 63 <BR>\n" );
document.write( "Regression output confidence interval<BR>\n" );
document.write( "variables coefficients std. error t (df = 62) p-value 95% lower 95% upper<BR>\n" );
document.write( "Intercept 6.5763 1.9254 3.416 .0011 2.7275 10.4252<BR>\n" );
document.write( "X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563\r<BR>\n" );
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document.write( "14.16\r<BR>\n" );
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document.write( "(a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible<BR>\n" );
document.write( "causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992–2003 only.<BR>\n" );
document.write( "Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your<BR>\n" );
document.write( "choice to the 1992–2003 data. (f) Make a forecast for 2004, using either the fitted trend model or<BR>\n" );
document.write( "a judgment forecast. Why is it best to ignore earlier years in this data set? <BR>\n" );
document.write( "U.S. Manufactured General Aviation Shipments, 1966–2003<BR>\n" );
document.write( "Year Planes Year Planes Year Planes Year Planes<BR>\n" );
document.write( "1966 15,587 1976 15,451 1986 1,495 1996 1,053<BR>\n" );
document.write( "1967 13,484 1977 16,904 1987 1,085 1997 1,482<BR>\n" );
document.write( "1968 13,556 1978 17,811 1988 1,143 1998 2,115<BR>\n" );
document.write( "1969 12,407 1979 17,048 1989 1,535 1999 2,421<BR>\n" );
document.write( "1970 7,277 1980 11,877 1990 1,134 2000 2,714<BR>\n" );
document.write( "1971 7,346 1981 9,457 1991 1,021 2001 2,538<BR>\n" );
document.write( "1972 9,774 1982 4,266 1992 856 2002 2,169<BR>\n" );
document.write( "1973 13,646 1983 2,691 1993 870 2003 2,090<BR>\n" );
document.write( "1974 14,166 1984 2,431 1994 881<BR>\n" );
document.write( "1975 14,056 1985 2,029 1995 1,028\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102373 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.<BR>\n" );
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document.write( "(a) Write the fitted regression equation.<BR>\n" );
document.write( "Y = 6.5763 + 0.0452X<BR>\n" );
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document.write( "(b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at &#945; = .05. <BR>\n" );
document.write( "df=62 ; t = 2.660<BR>\n" );
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document.write( "(c) What is your conclusion about the slope? <BR>\n" );
document.write( "Since p-valu = 1.90E-11 the slope is not zero : X is statistically <BR>\n" );
document.write( "significant in determining Y<BR>\n" );
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document.write( "(d) Interpret the 95 percent confidence limits for the slope. <BR>\n" );
document.write( "0.0452 is in the 95% confidence interval<BR>\n" );
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document.write( "(e) Verify that F = t2 for the slope.<BR>\n" );
document.write( "66.97 is not equal to  8.183^2 <BR>\n" );
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document.write( "(f) In your own words, describe the fit of this regression.<BR>\n" );
document.write( "Since R2 is 51.9% the reg. eq. explains only that percent <BR>\n" );
document.write( "of the variability between Y and X. <BR>\n" );
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document.write( "R2 0.519<BR>\n" );
document.write( "Std. Error 6.977<BR>\n" );
document.write( "n 64<BR>\n" );
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document.write( "ANOVA table<BR>\n" );
document.write( "Source..... SS....... df... MS........ F..... p-value<BR>\n" );
document.write( "Regression 3,260.0981 1.. 3,260.0981 66.97... 1.90E-11<BR>\n" );
document.write( "Residual.. 3,018.3339 62... 48.6828<BR>\n" );
document.write( "Total..... 6,278.4320 63 <BR>\n" );
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document.write( "Regression output confidence interval<BR>\n" );
document.write( "variables coefficients std. error.. t (df = 62). p-value 95% lower 95% upper<BR>\n" );
document.write( "Intercept..... 6.5763.. 1.9254......... 3.416.... .0011... 2.7275... 10.4252<BR>\n" );
document.write( "X1............ 0.0452.. 0.0055......... 8.183 ...1.90E-11. 0.0342.... 0.0563 <BR>\n" );
document.write( "14.16 <BR>\n" );
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document.write( "Comment: This site is not suitable for graphing displays<BR>\n" );
document.write( "so I will leave this question to you.<BR>\n" );
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document.write( "(a) Plot the data on U.S. general aviation shipments.<BR>\n" );
document.write( "(b) Describe the pattern and discuss possible causes. <BR>\n" );
document.write( "(c) Would a fitted trend be helpful? Explain.<BR>\n" );
document.write( "(d) Make a similar graph for 1992–2003 only.<BR>\n" );
document.write( "Would a fitted trend be helpful in making a prediction for 2004?<BR>\n" );
document.write( "(e) Fit a trend model of your choice to the 1992–2003 data.<BR>\n" );
document.write( "(f) Make a forecast for 2004, using either the fitted trend model or<BR>\n" );
document.write( "a judgment forecast. Why is it best to ignore earlier years in this data set?<BR>\n" );
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document.write( "U.S. Manufactured General Aviation Shipments, 1966–2003<BR>\n" );
document.write( "Year Planes Year Planes Year Planes Year Planes<BR>\n" );
document.write( "1966 15,587 1976 15,451 1986 1,495 1996 1,053<BR>\n" );
document.write( "1967 13,484 1977 16,904 1987 1,085 1997 1,482<BR>\n" );
document.write( "1968 13,556 1978 17,811 1988 1,143 1998 2,115<BR>\n" );
document.write( "1969 12,407 1979 17,048 1989 1,535 1999 2,421<BR>\n" );
document.write( "1970 7,277 1980 11,877 1990 1,134 2000 2,714<BR>\n" );
document.write( "1971 7,346 1981 9,457 1991 1,021 2001 2,538<BR>\n" );
document.write( "1972 9,774 1982 4,266 1992 856 2002 2,169<BR>\n" );
document.write( "1973 13,646 1983 2,691 1993 870 2003 2,090<BR>\n" );
document.write( "1974 14,166 1984 2,431 1994 881<BR>\n" );
document.write( "1975 14,056 1985 2,029 1995 1,028 \r<BR>\n" );
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document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );