document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006176>Question 1006176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Physics: I collected some data from Pendulum experiment and I used excel to graph these data in scatter plot and I think the period is proportional to the length. \r<BR>\n" );
document.write( "\n" );
document.write( "What is the most appropriate linear relation for this graph? e.g. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=kx+ ALIGN=MIDDLE  ALT=\"+y=kx+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2=kx+ ALIGN=MIDDLE  ALT=\"+y%5E2=kx+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Length(m)|Period(T)Sec|\r<BR>\n" );
document.write( "\n" );
document.write( "0.30     |1.254       |<BR>\n" );
document.write( "0.28     |1.232       |<BR>\n" );
document.write( "0.26     |1.204       |<BR>\n" );
document.write( "0.24     |1.160       |<BR>\n" );
document.write( "0.22     |1.106       |<BR>\n" );
document.write( "0.20     |1.044       |<BR>\n" );
document.write( "0.18     |1.010       |<BR>\n" );
document.write( "0.16     |1.006       |<BR>\n" );
document.write( "0.14     |1.004       |<BR>\n" );
document.write( "0.12     |0.916       |<BR>\n" );
document.write( "0.10     |0.820       |<BR>\n" );
document.write( "--------------- </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622313 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=622313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I plotted your data as points and found the regression line. The regression line does NOT go through the origin. So y = k*x is a bad choice. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Instead I did a power regression and the calculator shows f(x) = 1.92875x^(0.35929)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how if we plug x = 0.12 into f(x) we get f(0.12) = 1.92875*(0.12)^(0.35929) = 0.90039892737524 which is somewhat close to 0.916. It's going to be a bit off because regression curves aren't perfect. Try other x values of the points in your data list.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Side Note: if you still need the regression line, then it is y = 2.01727x + 0.66527 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );