The following data on sale price, size, and land-to-building ratio for 10 large
ID: 3127630 • Letter: T
Question
The following data on sale price, size, and land-to-building ratio for 10 large industrial properties appeared in a paper.
(a) Calculate the value of the correlation coefficient between sale price and size. (Give the answer to three decimal places.)
r = ________
(b) Calculate the value of the correlation coefficient between sale price and land-to-building ratio. (Give the answer to three decimal places.)
r = _______
(c) If you wanted to predict sale price and you could use either size or land-to-building ratio as the basis for making predictions, which would you use?
A) Size
B)Land-to-building ratio
Sale Price Size (millions (thousands Building Land-to- Property of dollars) of sq. ft.)Ratio 10.5 2.5 30.4 1.7 20.0 8.0 10.1 6.8 5.9 4.4 2166 751 2423 225 3916 2866 1698 1047 1107 406 1.9 2 3 4 6 7 8 9 10 3.5 4.8 1.7 2.4 3.1 4.8 7.7 17.1Explanation / Answer
a. Calculate the value of the correlation coefficient between sale price and size
a.
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 /10 (232497.3) - [ 1/10 *100.3 ] [ 1/10 *16605] = 6594.915
S. D ( X ) = Sqrt( 1/10*1709.97-(1/10*100.3)^2) 8.39
S .D (Y) = Sqrt( 1/10*40095821-(1/10*16605)^2) 1119.072
r(x,y) = 6594.915 / 8.39*1119.072 = 0.7024
b.
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 /10 (381.33) - [ 1/10 *100.3 ] [ 1/10 *50.6] = -12.619
S. D ( X ) = Sqrt( 1/10*1709.97-(1/10*100.3)^2) 8.39
S .D (Y) = Sqrt( 1/10*444.86-(1/10*50.6)^2) 4.345
r(x,y) = -12.619 / 8.39*4.345 = -0.3462
c.
A) Size, because it is positively skewwed
d.
Line of Regression Y on X i.e Y = bo + b1 X
Mean of X = X / n = 1660.5
Mean of Y = Y / n = 10.03
(Xi - Mean)^2 = 12523218.5
(Yi - Mean)^2 = 703.96
(Xi-Mean)*(Yi-Mean) = 65949.19
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 65949.19 / 12523218.5 = 0.0053
bo = Y / n - b1 * X / n
bo = 10.03 - 0.0053*1660.5 = 1.2856
Y = bo + b1 X
Y'=1.2856+0.0053*X