document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=766645>Question 766645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following sample observations were randomly selected.<BR>\n" );
document.write( "X: 4,5,3,6,10<BR>\n" );
document.write( "Y: 4,6,5,7,7<BR>\n" );
document.write( "a. Determine the regression equation.<BR>\n" );
document.write( "b. Determine the value of &#374; when X is 7. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467105 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The regression equation minimizes the square of the difference between the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > values of the sample points and a line of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%2Ax%2Bb ALIGN=MIDDLE  ALT=\"y=a%2Ax%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Carrying out the math, this gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28N%2ASxy-Sx%2ASy%29%2FD ALIGN=MIDDLE  ALT=\"a+=+%28N%2ASxy-Sx%2ASy%29%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%28Sy%2ASxx-Sx%2ASxy%29%2FD ALIGN=MIDDLE  ALT=\"b+=+%28Sy%2ASxx-Sx%2ASxy%29%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=N%2ASxx-Sx%2ASx ALIGN=MIDDLE  ALT=\"D=N%2ASxx-Sx%2ASx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" >=number of samples, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sx+ ALIGN=MIDDLE  ALT=\"Sx+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sy ALIGN=MIDDLE  ALT=\"Sy\"   DISABLED_style= \"max-width:90%; height:auto;\" >=sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sxx ALIGN=MIDDLE  ALT=\"Sxx\"   DISABLED_style= \"max-width:90%; height:auto;\" >=sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sxy ALIGN=MIDDLE  ALT=\"Sxy\"   DISABLED_style= \"max-width:90%; height:auto;\" >=sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay ALIGN=MIDDLE  ALT=\"x%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=53%2F146=0.363 ALIGN=MIDDLE  ALT=\"a=53%2F146=0.363\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=275%2F73=3.767 ALIGN=MIDDLE  ALT=\"b=275%2F73=3.767\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%2Bb+=+921%2F146+=+6.308 ALIGN=MIDDLE  ALT=\"7a%2Bb+=+921%2F146+=+6.308\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );