The data in the table give the square footages and sales prices of n = 12 houses

Question

The data in the table give the square footages and sales prices of n = 12 houses randomly selected from those sold in a small city.

(b) A real estate salesperson needs to estimate the average sales price of houses with a total of 1900 square feet of heated space. Use a 95% confidence interval. (Round your answers to the nearest whole number.)
$  to $  

(d) Suppose that a house with 1720 square feet of heated floor space is offered for sale. Construct a 95% prediction interval for the price at which the house will sell. (Round your answers to the nearest whole number.)
$  to $

Square Feet, x     Price, y     Square Feet, x     Price, y 1462 $288,600   1976 $305,400 2109 309,300 1611 296,900 1745 301,400 1530 292,600 1499 291,200 1759 298,400 1865 302,200 1820 304,100 2389 315,000 2218 311,500

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 251249.79 + 27.366715 x
Sample size: 12
R (correlation coefficient) = 0.97981337
R-sq = 0.96003424
Estimate of error standard deviation: 1728.8568

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

b) 95% confidence interval: ($302103, $304390)

d) 95% prediction interval: ($299228, $307265)

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 251249.79 3272.9382 0 10 76.765823 <0.0001 Slope 27.366715 1.7657261 0 10 15.498845 <0.0001

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