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 on26 houses that had recently sold in

the area. They want to predict the selling price of homes (inthousands 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    tStat             P-value

Intercept -86.09732282.2443144      -1.0468483      0.30559862

Size      0.247925000.04519506      5.48566590     1.22193E-05

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

shown in the data.

b. Write down the regression equation and then use it to predictthe 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 slopein context.

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

context. Otherwise, explain why the interpretation does not makesense.

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

for the effectiveness of the model using slope orcorrelation?

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

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

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

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

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

effectiveness of the model. Use the sample correlation, r, tofind 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.