document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183491>Question 183491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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 &#945; = .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.\r<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\r<BR>\n" );
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document.write( "ANOVA table\r<BR>\n" );
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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\r<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\r<BR>\n" );
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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" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137747 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=137747\">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 = 0.0452X + 6.5763  <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<BR>\n" );
document.write( "crit value: t = 2.00<BR>\n" );
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document.write( "(c) What is your conclusion about the slope?<BR>\n" );
document.write( "The p-value is less than 5% so reject Ho that the slope is zero.<BR>\n" );
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document.write( "(d) Interpret the 95 percent confidence limits for the slope. <BR>\n" );
document.write( "With 95% confidence we can say the slope is between 0.0342. and  0.0563<BR>\n" );
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document.write( "(e) Verify that F = t2 for the slope. <BR>\n" );
document.write( "66.97 = 8.183^2\r<BR>\n" );
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document.write( "(f) In your own words, describe the fit of this regression.<BR>\n" );
document.write( "The p-value for the Regression of 1.90E-11 is strong evidence that<BR>\n" );
document.write( "X and Y are strongly related.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<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" );
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.......0.0011... 2.7275.. 10.4252<BR>\n" );
document.write( "X1.......... 0.0452.. 0.0055..... 8.183...... 1.90E-11..0.0342... 0.0563<BR>\n" );
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