document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011186>Question 1011186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following are the scores of 15 students obtained in<BR>\n" );
document.write( "the midterm and final examinations in a course in<BR>\n" );
document.write( "probability and statistics \r<BR>\n" );
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document.write( "Midterm<BR>\n" );
document.write( "Exam, x 70 50 80 75 90 85 60 80 65 30 85 80 70 65 40<BR>\n" );
document.write( "Final<BR>\n" );
document.write( "Exam, y 85 60 75 80 90 75 50 75 75 50 75 90 65 55 60<BR>\n" );
document.write( "(i) Find the equation of the least square line to fit these<BR>\n" );
document.write( "data,<BR>\n" );
document.write( "(ii) Estimate the final examination scores of a student<BR>\n" );
document.write( "who received a score of 74 in the midterm<BR>\n" );
document.write( "examination.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627328 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Steps in using least square method<BR>\n" );
document.write( "1) calculate the mean of the x values (midterm grade)<BR>\n" );
document.write( "2) calculate the mean of the y values (final grade)<BR>\n" );
document.write( "3) calculate the slope of the line of best fit<BR>\n" );
document.write( "slope = (summation from i = 1 to 15 of (xi - xmean)*(yi - ymean)) / (summation of i = 1 to 15 of (xi - xmean)^2) <BR>\n" );
document.write( "4) compute the y intercept using<BR>\n" );
document.write( "b = ymean - (slope*xmean)<BR>\n" );
document.write( "5) you now have the equation of the line using least square method<BR>\n" );
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document.write( "1) xmean = 68.33<BR>\n" );
document.write( "2) ymean = 70.67<BR>\n" );
document.write( "3) slope = 2466.67 / 4183.33 = 0.59<BR>\n" );
document.write( "4) b = 70.67 - (0.59 * 68.33) = 30.36<BR>\n" );
document.write( "5) y = 0.59x + 30.36<BR>\n" );
document.write( "now if x = 74 then <BR>\n" );
document.write( "y = (0.59*74) + 30.36 =  74.02<BR>\n" );
document.write( "using our line using least square method, we expect a student who gets a 74 on the midterm to get a 74 on the final\r<BR>\n" );
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