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.)

Property Sale Price
(millions
of dollars) Size
(thousands
of sq. ft.) Land-to-
Building
Ratio 1 10.5 2166 1.9 2   2.7   752 3.4 3 30.5 2422 3.7 4   1.7   223 4.8 5 19.9 3917 1.7 6   7.9 2866 2.4 7 10.0 1698 3.2 8   6.6 1045 4.7 9   5.7 1108 7.5 10   4.4   405 17.1  

Explanation / Answer

here we have given that

X1= sale prize

X2= size

X3 = land building ratio

(a)

Now we want to calculate

correlation coefficient between sale prize and size

that is Corr ( X1,X2)

By using EXCEL we find it

put the data into EXCEL

command is = corr(all x1 values, x2 values )

we get

corr(x1,x2) =0.69853

(b)

Now we find the

correlation coefficient between sale prize and land to building ratio

command is

= corr(all values of x1, all values of x2)

we get

Corr(x1,x3) = -0.32846

(c)

Now ,

we want to find the least square regression line

DATA < DATA ANALYSIS < REGRESSION

We get the following output

here

the least sqare regresion line is

Yhat=2.076+(-0.111) X1 +0.0011(x2) +0.5365 (x3)

Coefficients Standard Error t Stat P-value Intercept 2.076 2.465935579 0.841975732 0.432075 SALE -0.111 0.135687311 -0.819834992 0.443651 SIZE 0.001102786 0.001175548 0.938103944 0.3844 LAND 0.536546975 0.230252859 2.330251086 0.058621

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