Let x be the size of a house (in square feet) and y be the amount of natural gas
ID: 3200304 • Letter: L
Question
Let x be the size of a house (in square feet) 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.
= slope of population regression line = 0.011
= y intercept of population regression line
= 7
(a) What is the equation of the population regression line?
y =
(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 sq. ft. increase in size?
(d) What is the average change in usage associated with a 100 sq. ft. increase in size?
Explanation / Answer
a.) A typical equation of line if y = mx + c.
Where, m is the slope of the line and c is the y-intercept. In the given situtation where, slope is 0.011 and y intercept is -7 the equation of regression line will be:
y = 0.011x - 7
b.) x = 2100 sq.ft.
y = 0.011*2100 - 7 = 16.1 therms
c.) The average change in usage associated with a 1 sq. ft. increase in size will be equal to the slope of the regression line, that is, in this case is 0.011 therms
d.) Building upon the previous answer we can say that the average change in usage associated with a 100 sq. ft. increase in size will be equal to 100 times the slope of the regression line = 100*0.011 = 1.1 therms
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