# St. Paul, Minnesota home sample

A sample of 12 homes sold last week in St. Paul, Minnesota, is selected. Can we conclude that as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $ thousands) also increases?

Home Size Selling

(thousands Price

of square feet) ($ thousands)

X Y X Y XY

1.4 100 1.96 10000 140

1.3 110 3.9 12100 143

1.2 105 1.44 11025 126

1.1 120 1.21 14400 132

1.4 80 1.96 6400 112

1.0 105 1 11025 105

1.3 110 3.9 12100 143

0.8 85 .64 7225 68

1.2 105 1.44 11025 126

0.9 75 .81 5625 67.5

1.1 70 1.21 4900 77

1.1 95 1.21 9025 104.5

Total 13.8 1160 20.68 114850 1344

a. Compute the coefficient of correlation.

b. Determine the coefficient of determination.

c. Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.

a. r = .087

b. r = (.087) = 0.0076

c. H : p 0; p>0. Reject H if t >

t = = .275

We cannot conclude that there is a positive correlation between the size of the home and the selling price.

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#### Solution Summary

The solution outlines:

A sample of 12 homes sold last week in St. Paul, Minnesota, is selected. Can we conclude that as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $ thousands) also increases?

Home Size Selling

(thousands Price

of square feet) ($ thousands)

X Y X Y XY

1.4 100 1.96 10000 140

1.3 110 3.9 12100 143

1.2 105 1.44 11025 126

1.1 120 1.21 14400 132

1.4 80 1.96 6400 112

1.0 105 1 11025 105

1.3 110 3.9 12100 143

0.8 85 .64 7225 68

1.2 105 1.44 11025 126

0.9 75 .81 5625 67.5

1.1 70 1.21 4900 77

1.1 95 1.21 9025 104.5

Total 13.8 1160 20.68 114850 1344

a. Compute the coefficient of correlation.

b. Determine the coefficient of determination.

c. Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.

a. r = .087

b. r = (.087) = 0.0076

c. H : p 0; p>0. Reject H if t >

t = = .275

We cannot conclude that there is a positive correlation between the size of the home and the selling price.

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