document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159471>Question 159471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a homework question.  I do not understand about regression lines.\r<BR>\n" );
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document.write( "The question is:  Find the equation of the regression line:\r<BR>\n" );
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document.write( "x     12    14    10     9     15  8<BR>\n" );
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document.write( "y     29    35    28    23     36  18\r<BR>\n" );
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document.write( "Multiple choice answer:\r<BR>\n" );
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document.write( "y = -1.2 + 2.4x<BR>\n" );
document.write( "y = 1.2 + 2.4x<BR>\n" );
document.write( "y = 2.4 + 1.2x<BR>\n" );
document.write( "y = -2.4 + 1.2x\r<BR>\n" );
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document.write( "Which is the correct answer? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117658 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A regression line is the best fit of a straight line using the data points.<BR>\n" );
document.write( "It doesn't necessarily go through all or any of the points but fits the data best (least error at each of the data points).<BR>\n" );
document.write( "A regression analysis uses the data to find the slope, m, of the line, and the y-intercept, b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's see if we can guess the solution without doing a full blown regression analysis. <BR>\n" );
document.write( "I'm not sure if that was the intent of the problem.<BR>\n" );
document.write( "First look at the data,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-2%2C+18%2C+-5%2C+45%2Cgrid%28+1+%29%2C%0D%0Acircle%28+12%2C+29%2C+.2+%29%2C%0D%0Acircle%28+14%2C+35%2C+.2+%29%2C%0D%0Acircle%28+10%2C+28%2C+.2+%29%2C%0D%0Acircle%28+9%2C+23%2C+.2+%29%2C%0D%0Acircle%28+15%2C+36%2C+.2+%29%2C%0D%0Acircle%28+8%2C+18%2C+.2+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can guess the approximate slope by using the first and last points,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bapx%5D=%2836-18%29%2F%2815-8%29=2.57 ALIGN=MIDDLE  ALT=\"m%5Bapx%5D=%2836-18%29%2F%2815-8%29=2.57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the answer must be 2.4, closer to 2.4 than 1.2.<BR>\n" );
document.write( "You know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5Bave%5D-mx%5Bave%5D ALIGN=MIDDLE  ALT=\"b=y%5Bave%5D-mx%5Bave%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bave%5D=%2812%2B14%2B10%2B9%2B15%2B9%29%2F6=11.333 ALIGN=MIDDLE  ALT=\"x%5Bave%5D=%2812%2B14%2B10%2B9%2B15%2B9%29%2F6=11.333\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bave%5D=%2829%2B35%2B28%2B23%2B36%2B18%29%2F6=28.167 ALIGN=MIDDLE  ALT=\"x%5Bave%5D=%2829%2B35%2B28%2B23%2B36%2B18%29%2F6=28.167\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5Bave%5D-mx%5Bave%5D ALIGN=MIDDLE  ALT=\"b=y%5Bave%5D-mx%5Bave%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=28.167-%282.4%29%2811.333%29 ALIGN=MIDDLE  ALT=\"b=28.167-%282.4%29%2811.333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=28.167-27.2 ALIGN=MIDDLE  ALT=\"b=28.167-27.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0.97 ALIGN=MIDDLE  ALT=\"b=0.97\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The closest answer is 1.2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.2%2B2.4x ALIGN=MIDDLE  ALT=\"y=1.2%2B2.4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The value for b was off because of roundoff error in m. <BR>\n" );
document.write( "The actual calculated value for m=2.3814, with b=1.178.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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