document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193517>Question 1193517</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the data below, determine the value of the error estimate S^2\r<BR>\n" );
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document.write( ". Give your answer to two decimal places.\r<BR>\n" );
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document.write( "∑xi=422,∑yi=5313,∑y2i=2512988\r<BR>\n" );
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document.write( "∑xiyi=191328,n=12,β^1=3.221 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825573 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=825573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Refer to this page to refresh your memory on the formulas needed<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.public.asu.edu/~gwaissi/ASM-e-book/module208.html\">https://www.public.asu.edu/~gwaissi/ASM-e-book/module208.html</a><BR>\n" );
document.write( "Specifically check out the section labeled \"4. Calculate the sums of squares\"\r<BR>\n" );
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document.write( "Also, check out the bottom of page 2 on this PDF<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www2.isye.gatech.edu/~hsharp/math3070/section3_4.pdf\">https://www2.isye.gatech.edu/~hsharp/math3070/section3_4.pdf</a><BR>\n" );
document.write( "I'm talking about the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SS_{xy} = \sum xy - \frac{(\sum x)(\sum y)}{n}\"><BR>\n" );
document.write( "Through substitution we can say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SS_{yy} = \sum y*y - \frac{(\sum y)(\sum y)}{n}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SS_{yy} = \sum y^2 - \frac{(\sum y)^2}{n}\">\r<BR>\n" );
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document.write( "As a final reference page, check out the top of page 2 of this PDF<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://users.stat.ufl.edu/~winner/statnotescomp/regression.pdf\">https://users.stat.ufl.edu/~winner/statnotescomp/regression.pdf</a><BR>\n" );
document.write( "where it reads <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \text{The (unbiased) estimate of the error variance } \sigma^2 \text{ is } s^2 = \text{MSE} = \frac{\text{SSE}}{n-2}\">\r<BR>\n" );
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document.write( "Now onto the problem at hand.\r<BR>\n" );
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document.write( "I will drop the subscript 'i' to simplify things a bit<BR>\n" );
document.write( "So instead of saying something like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sum x_i = 422\"><BR>\n" );
document.write( "I'll simply refer to it as <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sum x = 422\">\r<BR>\n" );
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document.write( "Given info:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sum x = 422\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sum y = 5313\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sum y^2 = 2512988\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sum xy = 191328\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n = 12\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \hat{\beta_1} = 3.221\">\r<BR>\n" );
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document.write( "Use some of the given info to say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SST = SS_{yy}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SST = \sum y^2 - \frac{(\sum y)^2}{n}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SST = 2512988 - \frac{(5313)^2}{12}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SST = 160,657.25\">\r<BR>\n" );
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document.write( "and furthermore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSR = \hat{\beta_1}*SS_{xy}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSR  = \hat{\beta_1}*\left(\sum xy - \frac{(\sum x)(\sum y)}{n}\right)\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSR  = 3.221*\left(191328 - \frac{(422)(5313)}{12}\right)\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSR  = 14,454.2375\">\r<BR>\n" );
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document.write( "Now we can compute the SSE<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSE = SST - SSR\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSE = SS_{yy} - \hat{\beta_1}*SS_{xy}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSE = 160,657.25 - 14,454.2375\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large SSE = 146,203.0125\">\r<BR>\n" );
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document.write( "Finally,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s^2 = \frac{SSE}{n-2}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s^2 = \frac{146,203.0125}{12-2}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s^2 = 14,620.30125\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s^2 = 14,620.30\">\r<BR>\n" );
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document.write( "Answer: <font color=red>14,620.30</font><BR>\n" );
document.write( "Delete the comma if needed<BR>\n" );
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