document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137309>Question 137309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed 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<BR>\n" );
document.write( "that F = t2 for the slope. (f) In your own words, describe the fit of this regression.\r<BR>\n" );
document.write( "\n" );
document.write( "R2-------------0.202<BR>\n" );
document.write( "Std. Error-----6.816<BR>\n" );
document.write( "N--------------35<BR>\n" );
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" );
document.write( "variables---coeffic.--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\r<BR>\n" );
document.write( "\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 #100461 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=100461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the following regression, 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( "Y = 0.0343X + 30.7963<BR>\n" );
document.write( "--------------------------<BR>\n" );
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: df=33; 1.645<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "(c) What is your conclusion about the slope?<BR>\n" );
document.write( "0.0343 is in the 95% confidence interval<BR>\n" );
document.write( "--------------- <BR>\n" );
document.write( "(d) Interpret the 95 percent confidence limits for the slope.<BR>\n" );
document.write( "With 95% condifidence we can say the slope is between the lower and the upper limit.<BR>\n" );
document.write( "---------------- <BR>\n" );
document.write( "(e) Verify that F = t2 for the slope.<BR>\n" );
document.write( " 8.35 = 2.889^2<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "(f) In your own words, describe the fit of this regression.<BR>\n" );
document.write( "Since R^2 = 0.202 only 20% of the variation between X and y is explained<BR>\n" );
document.write( "by the regression equation.  R = sqrt(R^2) = 0.449 shows the Regression<BR>\n" );
document.write( "equation weak as a linear predictor.<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "========================= <BR>\n" );
document.write( "R2-------------0.202<BR>\n" );
document.write( "Std. Error-----6.816<BR>\n" );
document.write( "N--------------35<BR>\n" );
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" );
document.write( "variables---coeffic.--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" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );