document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187775>Question 1187775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A study is conducted to determine the relationship between a driver’s age and the number of <BR>\n" );
document.write( "accidents he/she has over a 1-year period. The data are shown below. Test the significance of the <BR>\n" );
document.write( "correlation coefficient at <BR>\n" );
document.write( "a= 0.01. <BR>\n" );
document.write( "Driver’s age (x)    = 16 24 18 17 23 27 32<BR>\n" );
document.write( "No.of accidents (y) =3 2 5 2 0 1 1<BR>\n" );
document.write( "a. Draw the scatter plot. <BR>\n" );
document.write( "b. Compute the value of the correlation coefficient. <BR>\n" );
document.write( "c. Test the significance of the correlation coefficient at a = 0.01. <BR>\n" );
document.write( "d. Determine the regression line equation. <BR>\n" );
document.write( "e. Predict the number of accidents of a driver who is 28.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819208 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=819208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the following regression tool ill help you answer at least some of these questions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.graphpad.com/quickcalcs/linear1/\" target = \"_blank\">https://www.graphpad.com/quickcalcs/linear1/</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "hee are the results.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/112601.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/112602.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "answers to some of your requirements and questions are showon below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a. Draw the scatter plot.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the scatter plot with the linear regression line are shown above.<BR>\n" );
document.write( "they indicate a negative correlation, i.e. as the age of the driver goes up, the number of accidents over a one year period goes down.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b. Compute the value of the correlation coefficient.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this software shows the R^2, which is a goodness of fit indicater.<BR>\n" );
document.write( "the correlation coefficient is equal to the square root of the goodness of fit indicator.<BR>\n" );
document.write( "it also takes the sign of the correlation into account.<BR>\n" );
document.write( "R^2 = .3722.<BR>\n" );
document.write( "R = plus or minus sqrt(.3722) = minus .61008, in this case.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c. Test the significance of the correlation coefficient at a = 0.01.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the p-value of the correlation is .1458.<BR>\n" );
document.write( "this is well above the critical p-value of plus or minus .01.<BR>\n" );
document.write( "this indicates the results of the correlation are not significant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d. Determine the regression line equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the regression line equation is y = -.1701 * x + 5.816.<BR>\n" );
document.write( "the slope of the line is equal to -.1701.<BR>\n" );
document.write( "the y-intercept of the line is equal to 5.816.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e. Predict the number of accidents of a driver who is 28.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to predict the number of accidents in a 1 year time, replace x in the regression equation with 28 and solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = -.1701 * 28 + 5.98 = 1.0532.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the prediction is that a driver who is 28 years old will have approximately 1.0532 accidents, on average, in one year's time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );