The following data on sale price, size, and land-to-building ratio for 10 large

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 17.1

Explanation / 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  

( X) ( Y) X^2 Y^2 X*Y 10.5 2166 110.25 4691556 22743 2.5 751 6.25 564001 1877.5 30.4 2423 924.16 5870929 73659.2 1.7 225 2.89 50625 382.5 20 3916 400 15335056 78320 8 2866 64 8213956 22928 10.1 1698 102.01 2883204 17149.8 6.8 1047 46.24 1096209 7119.6 5.9 1107 34.81 1225449 6531.3 4.4 406 19.36 164836 1786.4 100.3 16605 1709.97 40095821 232497.3 Totals

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.