document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206835>Question 1206835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following sample observations were randomly selected:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "x:\r<BR>\n" );
document.write( "\n" );
document.write( " 11\r<BR>\n" );
document.write( "\n" );
document.write( " 2\r<BR>\n" );
document.write( "\n" );
document.write( "11\r<BR>\n" );
document.write( "\n" );
document.write( " 5\r<BR>\n" );
document.write( "\n" );
document.write( " 9\r<BR>\n" );
document.write( "\n" );
document.write( " 11\r<BR>\n" );
document.write( "\n" );
document.write( "20\r<BR>\n" );
document.write( "\n" );
document.write( "1\r<BR>\n" );
document.write( "\n" );
document.write( "y:\r<BR>\n" );
document.write( "\n" );
document.write( "8\r<BR>\n" );
document.write( "\n" );
document.write( "1\r<BR>\n" );
document.write( "\n" );
document.write( "2\r<BR>\n" );
document.write( "\n" );
document.write( "3\r<BR>\n" );
document.write( "\n" );
document.write( "7\r<BR>\n" );
document.write( "\n" );
document.write( "16\r<BR>\n" );
document.write( "\n" );
document.write( "4\r<BR>\n" );
document.write( "\n" );
document.write( "20\r<BR>\n" );
document.write( "\n" );
document.write( "                      <BR>\n" );
document.write( "a. Determine the coefficient of correlation. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Coefficient of correlation           \r<BR>\n" );
document.write( "\n" );
document.write( "                      \r<BR>\n" );
document.write( "\n" );
document.write( "b. Determine the coefficient of determination. (Round the intermediate calculations to 2 decimal places and final answer to 4 decimal places.)\r<BR>\n" );
document.write( "\n" );
document.write( "       <BR>\n" );
document.write( "Coefficient of determination           \r<BR>\n" );
document.write( "\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 #844532 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i used the regression calculator at <a  rel=nofollow HREF= \"https://www.statskingdom.com/linear-regression-calculator.html\" target = \"_blank\">https://www.statskingdom.com/linear-regression-calculator.html</a> to solve this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "there are lots of them on the web.<BR>\n" );
document.write( "just pick the one that you understand the most, after doing some research.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "hear are the results from using his calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/040903.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/040904.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "information you want to pay attention to is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula is y = -.2591 * x + 9.892.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-.2591 is the slope of the regression line.<BR>\n" );
document.write( "9.892 is the y-intercapt (value of y when value of x is 0).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r = -.2293 which is a very small correlation in a downward direction, meaning as value of x goes up, value of y goes down.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r^2 = .05257. meaning only about 5% of the y-values are directly as a consequence of the x-values, meaning that the correlation is very weak.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p-value of .5849 is much higher than a critical p-value of .05 meaning that there is not sufficient evidence that the correlation is different than the assumed status quo.<BR>\n" );
document.write( "this means that, if there was an assumed correlation different from this, this data would not be strong enough to say it should be this correlation instead.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a reference that includes how to interpret p-value in a regression analysis.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://statisticsbyjim.com/regression/interpret-coefficients-p-values-regression/\" target = \"_blank\">https://statisticsbyjim.com/regression/interpret-coefficients-p-values-regression/</a> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );