document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178531>Question 178531</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh></A><BR>\n" );
document.write( ": <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 fittedregression 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 theslope. (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-<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<BR>\n" );
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 #134100 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=134100\">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" );
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 ; crit. value = 1.96 (I do not have the same D-chart you may have)<BR>\n" );
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document.write( "(c) What is your conclusion about the slope? <BR>\n" );
document.write( "Since p-value = 1.9E-11, reject hypothesis that the slope is zero<BR>\n" );
document.write( "----------------------------------<BR>\n" );
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 = 8.8183^2<BR>\n" );
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document.write( "(f) In your own words, describe the fit of this regression.<BR>\n" );
document.write( "Since R^2 is 51.9% the fit is good.\r<BR>\n" );
document.write( "\n" );
document.write( "--------------- <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( "-------------------------<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-<BR>\n" );
document.write( "Residual.. 3,018.3339 62 48.6828 <BR>\n" );
document.write( "Total..... 6,278.4320 63<BR>\n" );
document.write( "----------------------------------- <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................0.0011.. 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( "=========================================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );