document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019231>Question 1019231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "I am having a lot of difficulty forming an equation for c in terms of t from the following table\r<BR>\n" );
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document.write( "t  1  1.5  2  2.5  3  5<BR>\n" );
document.write( "c 50 60 70 80 90 130\r<BR>\n" );
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document.write( "could you please show your workings as to how you arrived at the equation.\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635211 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=635211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we use linear regression for this problem<BR>\n" );
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document.write( "we want to determine the following formula<BR>\n" );
document.write( "c(t) = a + bt<BR>\n" );
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document.write( "we have N = 6 pairs of data, first we calculate<BR>\n" );
document.write( "tc and t^2 for each pair<BR>\n" );
document.write( "t c tc t^2<BR>\n" );
document.write( "1 50 50 1<BR>\n" );
document.write( "1.5 60 90 2.25 <BR>\n" );
document.write( "2 70 140 4<BR>\n" );
document.write( "2.5 80 200 6.25<BR>\n" );
document.write( "3 90 270 9<BR>\n" );
document.write( "3.5 130 455 12.25<BR>\n" );
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document.write( "summation of t's   =  13.5<BR>\n" );
document.write( "summation of c's   =   480<BR>\n" );
document.write( "summation of tc's  =  1205<BR>\n" );
document.write( "summation of t^2's = 34.75<BR>\n" );
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document.write( "slope(b) = ((N * summation of tc's) - (summation of t's * summation of c's)) / ((N * summation of t^2's) - (summation of t's)^2)<BR>\n" );
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document.write( "b = ((6 * 1205) - (13.5 * 480)) / ((6 * 34.75) - (13.5)^2)<BR>\n" );
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document.write( "b = 28.571428571 approx 28.57<BR>\n" );
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document.write( "intercept(a) = (summation of the c's -(b*summation of t's)) / N<BR>\n" );
document.write( "a = (480 - (28.57 * 13.5)) / 6<BR>\n" );
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document.write( "a = 15.7175 approx 15.72<BR>\n" );
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document.write( "equation for c is<BR>\n" );
document.write( "c(t) = 28.57x + 15.72<BR>\n" );
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document.write( " </SPAN>\n" );
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