A realtor studies the relationship between the size of a house (in square feet)

Question

A realtor studies the relationship between the size of a house (in square feet) and the property taxes owed by the owner. He collects the following data on six homes in an affluent suburb 60 miles outside of New York City. Use Table 2.

a. Calculate sxy and rxy. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. Calculate the value of the test statistic.

Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

A realtor studies the relationship between the size of a house (in square feet) and the property taxes owed by the owner. He collects the following data on six homes in an affluent suburb 60 miles outside of New York City. Use Table 2.

Square Feet Property Taxes ($)   Home 1 4,182 12,540             Home 2 2,844 9,363             Home 3 5,293 22,717             Home 4 2,284 6,508             Home 5 1,586 5,355             Home 6 3,394 7,901            

a. Calculate sxy and rxy. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. Calculate the value of the test statistic.

d-1.

Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Explanation / Answer

Sxy=Covariance= 6557730.611

Correlation rxy= 0.9229

Test statistic t=r*sqrt(n-2)/sqrt(1-r2)

=0.9229*sqrt(6-2)/sqrt(1-0.92292)

= 4.7947

Degree of freedom =n-2=6-2=4

p-value=0.0087 using excel function =TDIST(4.7947,4,2)

As p-value<0.05, we conclude correlation is significant

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