The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between t
ID: 3158716 • Letter: T
Question
The owner of Maumee Ford-Mercury-Volvo 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 the dealership during the last year.
Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?(Round your answer to nearest whole number.)
The owner of Maumee Ford-Mercury-Volvo 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 the dealership during the last year.
Explanation / Answer
Correlation
r( X,Y) = Co V ( X,Y) / S.D (X) * S.D (y)
r( X,Y) = Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )
Co v ( X, Y ) = 1 /12 (712.9) - [ 1/12 *107 ] [ 1/12 *82.9] = -2.191
S. D ( X ) = Sqrt( 1/12*1009-(1/12*107)^2) 2.139
S .D (Y) = Sqrt( 1/12*615.29-(1/12*82.9)^2) 1.884
r(x,y) = -2.191 / 2.139*1.884 = -0.5437
If r = -0.5437< 0, Perfect Nagative Correlation
Coeffcient of determination = r^2 = 0.2956
[ANSWERS]
a. r = -0.5437
b. r^2 = 0.2956
( X) ( Y) X^2 Y^2 X*Y 9 8.1 81 65.61 72.9 7 6 49 36 42 11 3.6 121 12.96 39.6 12 4 144 16 48 8 5 64 25 40 7 10 49 100 70 8 7.6 64 57.76 60.8 11 8 121 64 88 10 8 100 64 80 12 6 144 36 72 6 8.6 36 73.96 51.6 6 8 36 64 48 107 82.9 1009 615.29 712.9 TotalsRelated Questions
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