A land developer wanted a model to estimate the selling pric

A land developer wanted a model to estimate the selling price of beach lots. To do so she recorded for each of 20 beach lots recently sold:

Y = Sale price of the beach lot in $10,000 units

X1 = Area of the lot (in hundreds of square feet)

X2 = elevation of the lot (in feet above sea level)

X3 = Slope of the lot toward the ocean (in degrees)

A statistical regression program generated the following output:

Multiple R:          0.8854

R Squared:          0.7838

Std. Error of Est.: 0.6075

Analysis of variance

Source

D of F

Sum of Squares

Mean Square

F-Ratio

Regression

3

21.409

7.136

19.345

Error

16

5.903

0.369

Individual Analysis of Variables

Variable

Coefficient

Std. Error

t-Value

Constant

-2.491

Area

0.099

0.058

1.713

Elevation

0.029

0.006

4.830

Slope

0.086

0.031

2.800

f) Find a 90% Confidence Interval for the regression parameter relating area to selling price using the model which also includes elevation and slope.

Solution

90% CI for regression parameter of area is given by :

(beta^ - t_16,0.05* (S.E (beta^)), beta^ + t_16,0.05 * (S.E(beta^)))

= (0.099 - (1.713 * 0.058) , 0.099 + (1.713 * 0.058)) = (-0.000354, 0.1984) .

This is the requires CI for regression parameter relating