1.) 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 = −4 Houses in this community range in size from 1,000 to 3,000 square feet. (a) What is the mean value of gas usage (in therms) for houses with 2,100 sq. ft. of space? __ therms (b) What is the average change in usage (in therms) associated with a 1 sq. ft. increase in size? therms (c) What is the average change in usage (in therms) associated with a 100 sq. ft. increase in size? therms (d) Should the model be used to predict mean usage for a 500 sq. ft. house? Why or why not? -No. The size of this house is too small and lies outside the range of the sample that the model is based on. -No. The model predicts a negative mean usage for this size of house. -Yes. The size of this house lies inside the range of the sample that the model is based on. -No. The size of this house is too big and lies outside the range of the sample that the model is based on. -Yes. The model can be used to predict mean usage for any sized house regardless of the sample the model is based on.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...

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Question

1.) 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
= −4

Houses in this community range in size from 1,000 to 3,000 square feet.

(a)

What is the mean value of gas usage (in therms) for houses with 2,100 sq. ft. of space?

____________ therms

(b)

What is the average change in usage (in therms) associated with a 1 sq. ft. increase in size?

therms

(c)

What is the average change in usage (in therms) associated with a 100 sq. ft. increase in size?

__________ therms

(d)

Should the model be used to predict mean usage for a 500 sq. ft. house? Why or why not?

-No. The size of this house is too small and lies outside the range of the sample that the model is based on.

-No. The model predicts a negative mean usage for this size of house.

-Yes. The size of this house lies inside the range of the sample that the model is based on.

-No. The size of this house is too big and lies outside the range of the sample that the model is based on.

-Yes. The model can be used to predict mean usage for any sized house regardless of the sample the model is based on.

2.)

A paper suggests that the simple linear regression model is reasonable for describing the relationship between

y = eggshell

thickness (in micrometers, µm) and

x = egg

length (mm) for quail eggs. Suppose that the population regression line is

y = 0.125 + 0.007x

and that ?_e = 0.005. Then, for a fixed x value, y has a normal distribution with mean

0.125 + 0.007x

and standard deviation 0.005.

(a)

What is the mean eggshell thickness for quail eggs that are 15 mm in length?

_____µm

What is the mean eggshell thickness for quail eggs that are 17 mm in length?

_____µm

(b)

What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.23 µm?

_______

(c)

Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.222? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.)

_______

Approximately what proportion of quail eggs of length 14 mm have a shell thickness of less than 0.224? (Round your answer to four decimal places.)

_______

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