document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144763>Question 144763</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A 10-year study conducted by the American Heart Association provided data on how age related to the risk of strokes.  Suppose that the following data was obtained in a follow-up study. Risk is interpreted as the probability that the patient will have a stroke over the next 10-year,\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "Patient Risk       Age<BR>\n" );
document.write( " <BR>\n" );
document.write( "1       <BR>\n" );
document.write( " 12<BR>\n" );
document.write( " 57<BR>\n" );
document.write( " <BR>\n" );
document.write( "2<BR>\n" );
document.write( " 24<BR>\n" );
document.write( " 67<BR>\n" );
document.write( " <BR>\n" );
document.write( "3<BR>\n" );
document.write( " 13<BR>\n" );
document.write( " 58<BR>\n" );
document.write( " <BR>\n" );
document.write( "4<BR>\n" );
document.write( " 56<BR>\n" );
document.write( " 86<BR>\n" );
document.write( " <BR>\n" );
document.write( "5<BR>\n" );
document.write( " 28<BR>\n" );
document.write( " 59<BR>\n" );
document.write( " <BR>\n" );
document.write( "6<BR>\n" );
document.write( " 51<BR>\n" );
document.write( " 76<BR>\n" );
document.write( " <BR>\n" );
document.write( "7<BR>\n" );
document.write( " 31<BR>\n" );
document.write( " 78<BR>\n" );
document.write( " <BR>\n" );
document.write( "8<BR>\n" );
document.write( " 18<BR>\n" );
document.write( " 56<BR>\n" );
document.write( " <BR>\n" );
document.write( "9<BR>\n" );
document.write( " 37<BR>\n" );
document.write( " 80<BR>\n" );
document.write( " <BR>\n" );
document.write( "10<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 78<BR>\n" );
document.write( " <BR>\n" );
document.write( "11<BR>\n" );
document.write( " 22<BR>\n" );
document.write( " 71<BR>\n" );
document.write( " <BR>\n" );
document.write( "12<BR>\n" );
document.write( " 36<BR>\n" );
document.write( " 70<BR>\n" );
document.write( " <BR>\n" );
document.write( "13<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 67<BR>\n" );
document.write( " <BR>\n" );
document.write( "14<BR>\n" );
document.write( " 48<BR>\n" );
document.write( " 77<BR>\n" );
document.write( " <BR>\n" );
document.write( "15<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 60<BR>\n" );
document.write( " <BR>\n" );
document.write( "16<BR>\n" );
document.write( " 36<BR>\n" );
document.write( " 82<BR>\n" );
document.write( " <BR>\n" );
document.write( "17<BR>\n" );
document.write( " 8<BR>\n" );
document.write( " 66<BR>\n" );
document.write( " <BR>\n" );
document.write( "18<BR>\n" );
document.write( " 34<BR>\n" );
document.write( " 80<BR>\n" );
document.write( " <BR>\n" );
document.write( "19<BR>\n" );
document.write( " 3<BR>\n" );
document.write( " 62<BR>\n" );
document.write( " <BR>\n" );
document.write( "20<BR>\n" );
document.write( " 37<BR>\n" );
document.write( " 59<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "a)     Develop an estimated regression equation that can be used to relate the risk of a stroke to the person’s age.\r<BR>\n" );
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document.write( "b)     Is the relationship between risk and age significant at the 95% confidence level?\r<BR>\n" );
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document.write( "c)      Compute the correlation coefficient and interpret the result.\r<BR>\n" );
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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 #105513 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=105513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A 10-year study conducted by the American Heart Association provided data on how age related to the risk of strokes.  Suppose that the following data was obtained in a follow-up study. Risk is interpreted as the probability that the patient will have a stroke over the next 10-year,\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Patient Risk       Age<BR>\n" );
document.write( " <BR>\n" );
document.write( "1       <BR>\n" );
document.write( " 12<BR>\n" );
document.write( " 57<BR>\n" );
document.write( " <BR>\n" );
document.write( "2<BR>\n" );
document.write( " 24<BR>\n" );
document.write( " 67<BR>\n" );
document.write( " <BR>\n" );
document.write( "3<BR>\n" );
document.write( " 13<BR>\n" );
document.write( " 58<BR>\n" );
document.write( " <BR>\n" );
document.write( "4<BR>\n" );
document.write( " 56<BR>\n" );
document.write( " 86<BR>\n" );
document.write( " <BR>\n" );
document.write( "5<BR>\n" );
document.write( " 28<BR>\n" );
document.write( " 59<BR>\n" );
document.write( " <BR>\n" );
document.write( "6<BR>\n" );
document.write( " 51<BR>\n" );
document.write( " 76<BR>\n" );
document.write( " <BR>\n" );
document.write( "7<BR>\n" );
document.write( " 31<BR>\n" );
document.write( " 78<BR>\n" );
document.write( " <BR>\n" );
document.write( "8<BR>\n" );
document.write( " 18<BR>\n" );
document.write( " 56<BR>\n" );
document.write( " <BR>\n" );
document.write( "9<BR>\n" );
document.write( " 37<BR>\n" );
document.write( " 80<BR>\n" );
document.write( " <BR>\n" );
document.write( "10<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 78<BR>\n" );
document.write( " <BR>\n" );
document.write( "11<BR>\n" );
document.write( " 22<BR>\n" );
document.write( " 71<BR>\n" );
document.write( " <BR>\n" );
document.write( "12<BR>\n" );
document.write( " 36<BR>\n" );
document.write( " 70<BR>\n" );
document.write( " <BR>\n" );
document.write( "13<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 67<BR>\n" );
document.write( " <BR>\n" );
document.write( "14<BR>\n" );
document.write( " 48<BR>\n" );
document.write( " 77<BR>\n" );
document.write( " <BR>\n" );
document.write( "15<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 60<BR>\n" );
document.write( " <BR>\n" );
document.write( "16<BR>\n" );
document.write( " 36<BR>\n" );
document.write( " 82<BR>\n" );
document.write( " <BR>\n" );
document.write( "17<BR>\n" );
document.write( " 8<BR>\n" );
document.write( " 66<BR>\n" );
document.write( " <BR>\n" );
document.write( "18<BR>\n" );
document.write( " 34<BR>\n" );
document.write( " 80<BR>\n" );
document.write( " <BR>\n" );
document.write( "19<BR>\n" );
document.write( " 3<BR>\n" );
document.write( " 62<BR>\n" );
document.write( " <BR>\n" );
document.write( "20<BR>\n" );
document.write( " 37<BR>\n" );
document.write( " 59<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "I ran a Linear Regression function on a TI calculator to find<BR>\n" );
document.write( "the following: \r<BR>\n" );
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document.write( "a)     Develop an estimated regression equation that can be used to relate the risk of a stroke to the person’s age.<BR>\n" );
document.write( "Ans: age = 58.103 + (0.4210)(risk)\r<BR>\n" );
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document.write( "b)     Is the relationship between risk and age significant at the 95% confidence level?<BR>\n" );
document.write( "Critical value for n=20 and alpha = 5% is 0.444<BR>\n" );
document.write( "Since r=0.65.. > 0.444, reject Ho, which claimed there was no linear<BR>\n" );
document.write( "relation, and conclude there is a significant linear relation between<BR>\n" );
document.write( "age and risk.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "c)      Compute the correlation coefficient and interpret the result.<BR>\n" );
document.write( "r = 0.6502...<BR>\n" );
document.write( "r is a measure of the linear correlation between age and risk.<BR>\n" );
document.write( "r^2 is the proportion of the variation in age that is explained<BR>\n" );
document.write( "by the linear relationship between risk and age.<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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