document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206836>Question 1206836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The owner of Maumee Motors wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at Maumee Motors during the last year:\r<BR>\n" );
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document.write( "Car	Age (years)	Selling Price ($ thousands)	Car	Age (years)	Selling Price ($ thousands)<BR>\n" );
document.write( "1	8	 	$9.5	 	7	 	6	 	$10.0	 <BR>\n" );
document.write( "2	13	 	5.5	 	8	 	2	 	5.5	 <BR>\n" );
document.write( "3	7	 	9.7	 	9	 	1	 	9.6	 <BR>\n" );
document.write( "4	15	 	3.6	 	10	 	4	 	3.1	 <BR>\n" );
document.write( "5	9	 	3.2	 	11	 	9	 	7.0	 <BR>\n" );
document.write( "6	8	 	4.8	 	12	 	1	 	3.7	 <BR>\n" );
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document.write( "a. Determine the correlation coefficient. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)      \r<BR>\n" );
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document.write( "r =  \r<BR>\n" );
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document.write( "b. Determine the coefficient of determination. (Round the final answer to 3 decimal places.)\r<BR>\n" );
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document.write( "c. Interpret these statistical measures. Does it surprise you that an inverse relationship exists? (Round the final answer to the nearest whole number.)\r<BR>\n" );
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document.write( "Weak negative (inverse) correlation between age of car and selling price. So, <BR>\n" );
document.write( "  percent of the variation in the selling price is explained by the variation in the age of the car.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844531 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=844531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i put this through the linear regression calculator at <a  rel=nofollow HREF= \"\" target = \"_blank\"></a>\r<BR>\n" );
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document.write( "these are the results.\r<BR>\n" );
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document.write( "wnasers to your questions are shown below.\r<BR>\n" );
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document.write( "a. Determine the correlation coefficient. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)\r<BR>\n" );
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document.write( "r = -.1763\r<BR>\n" );
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document.write( "b. Determine the coefficient of determination. (Round the final answer to 3 decimal places.)\r<BR>\n" );
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document.write( "r^2 = .03107\r<BR>\n" );
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document.write( "c. Interpret these statistical measures. Does it surprise you that an inverse relationship exists? (Round the final answer to the nearest whole number.)\r<BR>\n" );
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document.write( "r^2 is very small, indicating very little of the data is explained by the relationship between x and y.\r<BR>\n" );
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document.write( "r is very weak in a negative direction, indicating very little to no correlation between the values of x and y in a negative direction, i.e. as value of x goes up, value of y goes down.\r<BR>\n" );
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document.write( "you would expect that, as the age of the care gets higher, that the value of the car will go down.\r<BR>\n" );
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document.write( "this is supported by the correlation, but very weakly.\r<BR>\n" );
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document.write( "a very large part of the reason is that the data is insufficiently narrowed down to the point where the data will make sense.\r<BR>\n" );
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document.write( "one glaring problem is that the make and model of the car is not considered.<BR>\n" );
document.write( "different makes and models of cars start at different cost points.<BR>\n" );
document.write( "you can't just grab a car at random without taking this into consideration.<BR>\n" );
document.write( "a cheap car's starting value can easily be lower than an expensive car's value after 5 or even 10 years.<BR>\n" );
document.write( "the data can be all over the place, as is evident with this sample.\r<BR>\n" );
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document.write( "the lack of any discernible correlation is definitely caused by a poor selection of data to be analyzed.\r<BR>\n" );
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document.write( "a look at the graph shows that the data is spread far and wide from the regression line.\r<BR>\n" );
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document.write( "this indicates very poor correlation between the x and y coordinates.\r<BR>\n" );
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document.write( "the high p-value supports this conclusion.\r<BR>\n" );
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document.write( "if you just go with the r-value and the r^2-value, there is very strong evidence that there's no real good correlation to be derived from this data.\r<BR>\n" );
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