document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136359>Question 1136359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hours Studied: 1,   3,   3,    4,    4,   2<BR>\n" );
document.write( "Test Score :    70, 80, 85, 90, 85, 75\r<BR>\n" );
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document.write( "The table shows the number of hours<BR>\n" );
document.write( "students studied and their score on a<BR>\n" );
document.write( "math test in Ms. Aduke’s class.\r<BR>\n" );
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document.write( "Write an equation for the trend line. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754128 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> basically, you plot the points and then draw a straight line that minimizes the distnce from that straight line to all the points.\r<BR>\n" );
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document.write( "there is software that does that for you, but you can also eyeball the graph and get reasonably close to what the software would have generated.\r<BR>\n" );
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document.write( "here's my eyeball estimate.\r<BR>\n" );
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document.write( "i looked at the graph and drew a straight line that i felt was closest to all the points on the graph.\r<BR>\n" );
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document.write( "i then took two points on the line in the graph to make my equation.\r<BR>\n" );
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document.write( "the points i chose were (1,72) and (4,88).\r<BR>\n" );
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document.write( "the slope of the line was (88 - 72) / (4 - 1) = 16 / 3 = 5.33 rounded to two dedcimal places.\r<BR>\n" );
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document.write( "the slope intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "the equation became y = 5.33 * x + b\r<BR>\n" );
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document.write( "i then took one of the points on the line that i previously chose to make the slope to find the y-intercept.\r<BR>\n" );
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document.write( "the point i chose was (1,72).\r<BR>\n" );
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document.write( "i replace y with 72 and x with 1 to get 72 = 5.33 * 1 + b\r<BR>\n" );
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document.write( "i then solved for b to get b = 72 - 5.33 = 66.67.\r<BR>\n" );
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document.write( "the y-intercept was 66.67 and the equation became y = 5.33 * x + 6.67.\r<BR>\n" );
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document.write( "here's what the software generated.\r<BR>\n" );
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document.write( "the equation from the software is y = 63.90243902439 + 5.9756097560976x\r<BR>\n" );
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document.write( "when displayed in descending order of degree, the equation becomes:\r<BR>\n" );
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document.write( "y = 5.9756097560976 * x + 63.90243902439\r<BR>\n" );
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document.write( "i compawred what the software gave me to what i created manmually.\r<BR>\n" );
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document.write( "here's the two equations.\r<BR>\n" );
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document.write( "software generated is y = 5.98 * x + 63.90 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "manually generated is y = 5.33 * x + 66.67 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "i then graphed both of these equations on the same graph to see how much they differed from each other.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "the software generated line is in red.\r<BR>\n" );
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document.write( "the manually generated line is in blue.\r<BR>\n" );
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document.write( "if you have the software generator, that is preferable.\r<BR>\n" );
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document.write( "if not, then manually generated will have to do.\r<BR>\n" );
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document.write( "the software generated one that i used can be found at <a  rel=nofollow HREF= \"http://www.alcula.com/calculators/statistics/linear-regression/\" target = \"_blank\">http://www.alcula.com/calculators/statistics/linear-regression/</a>\r<BR>\n" );
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