document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156170>Question 156170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need help<BR>\n" );
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document.write( "This is linear regression<BR>\n" );
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document.write( "I have these two lists<BR>\n" );
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document.write( "Let's say the left side is<BR>\n" );
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document.write( "Still heartbeat rate ! Racing heartbeat rate<BR>\n" );
document.write( "... 50..........................   166<BR>\n" );
document.write( "... 60..........................   168<BR>\n" );
document.write( "... 70..........................   170<BR>\n" );
document.write( "... 80..........................   172<BR>\n" );
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document.write( "I was told to use the first \"x\" as 0, and base the others on \"0\"<BR>\n" );
document.write( "(For example, this is how you would write it in the calculator: 50 = 0, 60 = 10,  70 = 20, 80 = 30<BR>\n" );
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document.write( "If you put this in a calculator, using (0,10,20,30)as L1, (166,168,170,172) as L2<BR>\n" );
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document.write( "I get the regression line formula, of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B+166+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B+166+\"   DISABLED_style= \"max-width:90%; height:auto;\" > It has told me to predict<BR>\n" );
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document.write( "Still heartbeat rate ! Racing heartbeat rate<BR>\n" );
document.write( "... 40..........................   ???<BR>\n" );
document.write( "... 65..........................   ???<BR>\n" );
document.write( "... 84..........................   ???<BR>\n" );
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document.write( "If I put in the numbers ( -10, 15, 34)(based on the first \"50\" = 0<BR>\n" );
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document.write( "Using the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B+166+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B+166+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(-10) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B+166+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B+166+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2%28-10%29+%2B+166+ ALIGN=MIDDLE  ALT=\"+y+=+0.2%28-10%29+%2B+166+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-2%29+%2B+166+ ALIGN=MIDDLE  ALT=\"+y+=+%28-2%29+%2B+166+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+164+ ALIGN=MIDDLE  ALT=\"+y+=+164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The other solutions are ( 169, and 172.8 )<BR>\n" );
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document.write( "Now, I found that if you just use the numbers themselves (50, 60, 70, 80) Instead of (0,10,20,30)<BR>\n" );
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document.write( "You come up with a different equation<BR>\n" );
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document.write( "The new equation = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B+156+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B+156+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( The book I got this problem from, has this answer/equation)<BR>\n" );
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document.write( "If I predict the same heart rates ( 40, 65, 84)<BR>\n" );
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document.write( "If I use the new equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B156+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B156+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(40) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B156+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B156+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2%2840%29+%2B156+ ALIGN=MIDDLE  ALT=\"+y+=+0.2%2840%29+%2B156+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+8+%2B156+ ALIGN=MIDDLE  ALT=\"+y+=+8+%2B156+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+164+ ALIGN=MIDDLE  ALT=\"+y+=+164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I get the same predictions, so which regression line is correct<BR>\n" );
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document.write( "(A)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B+166+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B+166+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(B) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0.2x+%2B156+ ALIGN=MIDDLE  ALT=\"+y+=+0.2x+%2B156+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Is it \"A\" or \"B\", my question is, \"How do you know which regression line formula  is correct?\" It can be an infinite number of equations, depending on what you use for \"L1\"<BR>\n" );
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document.write( "Do you only use the First Number in list as \"0\" if it is a year?<BR>\n" );
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document.write( "Thanks ahead of time, Levi<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 #115040 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=115040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using the orinal set of numbers gives you the equation you want: <BR>\n" );
document.write( "y = 0.2x + 156<BR>\n" );
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document.write( "Making the 50 becomes 0 change sinply<BR>\n" );
document.write( "moved the regression line 10 to the left.<BR>\n" );
document.write( "The y-value for 50 in the 1st set and 0<BR>\n" );
document.write( "in the 2nd set are the same because you<BR>\n" );
document.write( "only translated the x values.<BR>\n" );
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document.write( "Each of your sets of x/y pairs gives rise<BR>\n" );
document.write( "to a different regression line.  I don't<BR>\n" );
document.write( "know who told you to traslate 50 to 0;<BR>\n" );
document.write( "you might ask them, why?<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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