document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138776>Question 138776</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh>APPLIED STATISTICS IN BUSINESS AND ECONOMICS</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s<BR>\n" );
document.write( "employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed<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.\r<BR>\n" );
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document.write( "R2 0.202<BR>\n" );
document.write( "Std. Error 6.816<BR>\n" );
document.write( "n 35\r<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 387.6959 1 387.6959 8.35 .0068<BR>\n" );
document.write( "Residual 1,533.0614 33 46.4564<BR>\n" );
document.write( "Total 1,920.7573 34\r<BR>\n" );
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document.write( "Regression output confidence interval<BR>\n" );
document.write( "variables coefficients std. error t (df = 33) p-value 95% lower 95% upper<BR>\n" );
document.write( "Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331<BR>\n" );
document.write( "Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101278 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=101278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the following regression, <BR>\n" );
document.write( "X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees. <BR>\n" );
document.write( "(a) Write the fitted regression equation.<BR>\n" );
document.write( "Income Tax = 0.0343 (weekly pay) +30.7963<BR>\n" );
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document.write( "(b) State the degrees of freedom for a two tailed for zero slope, and use Appendix D to find the critical value at &#945; = .05.<BR>\n" );
document.write( "df=33 ; t = 1.96<BR>\n" );
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document.write( "(c) What is your conclusion about the slope? <BR>\n" );
document.write( "Since p-value is less than 5% Reject Ho that the correlation is zero.<BR>\n" );
document.write( "Accept the slope value of 0.0343<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 state that the slope is between 0.0101 and 0.0584<BR>\n" );
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document.write( "(e) Verify that F = t2 for the slope.<BR>\n" );
document.write( "8.35 = 2.889^2<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 only 0.202 only 20.2% of the correlation between<BR>\n" );
document.write( "the variables is explained by the regression equation.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( "----------<BR>\n" );
document.write( "R2 0.202 Std. Error 6.816 n 35 <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 387.6959 1  387.6959 8.35 .0068<BR>\n" );
document.write( "Residual 1,533.0614 33  46.4564<BR>\n" );
document.write( "Total 1,   920.7573 34 <BR>\n" );
document.write( "Regression output confidence interval<BR>\n" );
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document.write( "variables coefficients std. error t (df = 33) p-value 95% lower 95% upper<BR>\n" );
document.write( "Intercept 30.7963 ........6.4078... 4.806        .0000     17.7595 43.8331<BR>\n" );
document.write( "Slope      0.0343 ........0.0119... 2.889....... .0068..... 0.0101 0.0584<BR>\n" );
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