document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=313163>Question 313163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm stumped.\r<BR>\n" );
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document.write( "Given an array of known X and Y values, and a list of *new* X values, how can I solve for what the new Y value will be ?\r<BR>\n" );
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document.write( "A bit more detail: In Excel, I plotted these known X and Y values by means of a XY Scatter Chart, then asked it to create me a Trend Line, showing me the formula. The formula, for this data, is: y = 14.132x² - 63.03x + 79.647. I need to know how to actually *arrive* at that formula by a more manual means.\r<BR>\n" );
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document.write( "Thanks! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #223913 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=223913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Check out the link below for the particulars.<BR>\n" );
document.write( "You can do this all within an EXCEL spreadsheet. <BR>\n" );
document.write( "You're trying to fit <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a0%2Ba1%2Ax%2Ba2%2Ax%5E2 ALIGN=MIDDLE  ALT=\"y=a0%2Ba1%2Ax%2Ba2%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >to the given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > sets of data (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xi ALIGN=MIDDLE  ALT=\"xi\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=yi ALIGN=MIDDLE  ALT=\"yi\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
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document.write( "You need to create a matrix of values.<BR>\n" );
document.write( "[X]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cb%2Cc%2Cd%2Cc%2Cd%2Ce%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cb%2Cc%2Cd%2Cc%2Cd%2Ce%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=N ALIGN=MIDDLE  ALT=\"a=N\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sum%28xi%2C1%2CN%29 ALIGN=MIDDLE  ALT=\"b=sum%28xi%2C1%2CN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sum%28xi%5E2%2C1%2CN%29 ALIGN=MIDDLE  ALT=\"c=sum%28xi%5E2%2C1%2CN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sum%28xi%5E3%2C1%2CN%29 ALIGN=MIDDLE  ALT=\"d=sum%28xi%5E3%2C1%2CN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=sum%28xi%5E4%2C1%2CN%29 ALIGN=MIDDLE  ALT=\"e=sum%28xi%5E4%2C1%2CN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then create another matrix of values,<BR>\n" );
document.write( "[Y]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C1%2Cp%2Cq%2Cr%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C1%2Cp%2Cq%2Cr%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=sum%28yi%2C1%2CN%29 ALIGN=MIDDLE  ALT=\"p=sum%28yi%2C1%2CN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=sum%28xi%2Ayi%2C1%2CN%29 ALIGN=MIDDLE  ALT=\"q=sum%28xi%2Ayi%2C1%2CN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sum%28xi%5E2%2Ayi%2C1%2CN%29 ALIGN=MIDDLE  ALT=\"r=sum%28xi%5E2%2Ayi%2C1%2CN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you have the coefficients a0,a1, and a2. <BR>\n" );
document.write( "[a]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C1%2Ca0%2Ca1%2Ca2%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C1%2Ca0%2Ca1%2Ca2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The matrix equation you need to solve is,<BR>\n" );
document.write( "[X][a]=[Y]<BR>\n" );
document.write( "[a]=[X]inv[Y]<BR>\n" );
document.write( "So find the inverse of [X] and matrix multiply by [Y]. <BR>\n" );
document.write( "That will provide you the coefficients of the least square fit quadratic, [a].<BR>\n" );
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document.write( "http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html </SPAN>\n" );
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