Question

2. Purchasing a Home in Upstate New York A quantitatively savvy, young couple is interested in

purchasing a home in northern New York. They collected data on 26 houses that had recently sold in

the area. They want to predict the selling price of homes (in thousands of dollars) based on the size

of the home (in square feet).

The regression equation is: Price ̂ = -86.097 + 0.248*Size

Regression Statistics

Multiple R 0.745865819

R Square 0.55631582

Adjusted R Square 0.537828979

Standard Error 162.8663093

Observations 26

              Coefficients StandardError    t Stat              P-value

Intercept -86.097322 82.2443144       -1.0468483      0.30559862

Size      0.24792500 0.04519506       5.48566590     1.22193E-05

a. What is the correlation of the data set? Use the correlation value to help describe the association

shown in the data.

b. Write down the regression equation and then use it to predict the selling price of a home that is

1,742 square feet in size.

c. One home in the data set is 1,400 square feet and costs $187,000, calculate the residual for this

home.

d. What is the slope of the regression line? Interpret the slope in context.

e. If it would make sense, provide a clear interpretation of the intercept of the regression line, in

context. Otherwise, explain why the interpretation does not make sense.

f. What are the degrees of freedom for constructing a confidence interval for, or performing a test

for the effectiveness of the model using slope or correlation?

g. Construct and interpret a 95% confidence interval for the population slope.

h. Use the computer output to do a slope test to determine whether size is an effective linear

predictor of the selling price of recently sold homes. Use a significance level of 5%. Include and

label all six steps of a formal test of hypothesis for regression using slope.

i. We could also use the value of the sample correlation to find a test statistic and p-value to test the

effectiveness of the model. Use the sample correlation, r, to find the test statistic and p-value.

Compare these to the results of part h).

j. What is the R2

for this model? Interpret it in context.

Answer 1