Question

Let x be the size of a house (sq ft) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values.

ß = slope of population regression line = 0.019
a = y intercept of population regression line = -7
(a) What is the equation of the population regression line?
y = 1
b) What is the mean value of gas usage for houses with 2100 sq ft of space?
(c) What is the average change in usage associated with a 1 square foot increase in size?
(d) What is the average change in usage associated with a 100 square feet increase in size?

Answer 1

y = 0.019x - 7

32.9 therms

0.019 therms

1.9 therms

Explanation:

Given the following :

X =size of house (sq ft)

Y = Amount of natural gas used

The general form of a some linear regression model :

y = ßx + a

Where ;

ß = slope or gradient

x = independent variable

y = predicted value

a = y- intercept value

(A)

If ß = slope of population regression line = 0.019

a = y intercept of population regression line = -7

The regression model could be expressed as :

y = 0.019x + (-7)

y = 0.019x - 7

(B)What is the mean value of gas usage for houses with 2100 sq ft of space?

Here x = 2100 sq ft ; Inputting the value of x into the regression equation:

y = 0.019x - 7

y = 0.019(2100) - 7

y = 39.9 - 7

y = 32.9 therms

C) What is the average change in usage associated with a 1 square foot increase in size?

Change in usage associated with change in size can be gotten from :

ßx, where, ß change in y with respect to x ;

x = 1 square foot

ß = 0.019

Change = 0.019*(1) = 0.019 therms

(d) What is the average change in usage associated with a 100 square feet increase in size?

ßx, where, ß change in y with respect to x ;

x = 100 square feet

ß = 0.019

Change = 0.019*(100) = 1.9 therms