document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704868>Question 704868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If theres a positive correlation between data does it matter which set of data is represented on the x axis </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434428 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Positive correlation means:<BR>\n" );
document.write( "1) there is a correlation (we agree that the x and y values are related)<BR>\n" );
document.write( "2) the slope of the graph is positive (the larger the x, the larger the y)<BR>\n" );
document.write( "A negative correlation would give a graph with negative slope (larger x values correspond to smaller y values)<BR>\n" );
document.write( "A correlation of any kind could be weak or strong.<BR>\n" );
document.write( "A weak correlation shows a lot of scatter (the statistician notices the correlation, but other people may not see it). That is the kind of correlation that we see in biology, pharmacology, medicine, epidemiology.<BR>\n" );
document.write( "If there is a strong correlation, everyone agrees that the variables are related. That's what we want in analytical chemistry, physics, and engineering.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Consider the following (x,y) strongly positively correlated data points:<BR>\n" );
document.write( "(1.0,1.1), (2.0,2.2),  (3.0,3.3), (4.0,3.9), (5.0,4.8)<BR>\n" );
document.write( "Linear regression says:<BR>\n" );
document.write( "r=0.9946, slope=0.91, y-intercept=0.24<BR>\n" );
document.write( "Predictions: y(0.0)=0.33, y(6.0)=0.91(6.0)+0.33=5.79<BR>\n" );
document.write( "give us predicted points (0.0,0.33), (6.0,5.79) for the regression line<BR>\n" );
document.write( " <BR>\n" );
document.write( "Reversing them, the (x,y) pairs would be:<BR>\n" );
document.write( "(1.1,1.0), (2.2,2.0), (3.3,3.0), (3.9,4.0), (4.8,5.0)<BR>\n" );
document.write( "Linear regression says:<BR>\n" );
document.write( "r=0.9946, slope=1.087, y-intercept=-0.326<BR>\n" );
document.write( "y=1.087x-0.326  --> x=(y+0.326)/1.087<BR>\n" );
document.write( "Predictions: x(0.33)=(0.0+0.326)/1.087=0.60, x(5.79)=(5.79+0.326)/1.087=5.63<BR>\n" );
document.write( "give us predicted points (0.24,0.45), (5.79, 5.63) for the regression line<BR>\n" );
document.write( " <BR>\n" );
document.write( "Conclusion:<BR>\n" );
document.write( "Even with obviously strongly correlated data,<BR>\n" );
document.write( "for the same data points, the correlation coefficient, r, is the same,<BR>\n" );
document.write( "but the calculated regression line is a bit different, and depends on what we take as the x.<BR>\n" );
document.write( "Points (1.0,1.1), (2.0,2.2),  (3.0,3.3), (4.0,3.9), (5.0,4.8)<BR>\n" );
document.write( "and the two regression lines (green and blue) are plotted below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C6%2C-1%2C6%2C%0D%0Agrid%281%29%0D%0Acircle%281.0%2C1.1%2C0.1%29%2Ccircle%282.0%2C2.2%2C0.1%29%2Ccircle%283.0%2C3.3%2C0.1%29%2C%0D%0Acircle%284.0%2C3.9%2C0.1%29%2Ccircle%285.0%2C4.8%2C0.1%29%2C%0D%0Ablue%28line%280%2C0.33%2C6%2C5.79%29%29%2Cgreen%28line%280.33%2C0.60%2C5.79%2C5.63%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If I had made up a set of points more widely scattered, the difference would be more dramatic. </SPAN>\n" );
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