Find the equation of the population regression line.

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Answer 1

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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 13.1, Problem 1E

a.

To determine

Find the equation of the population regression line.

b.

To determine

Graph the population regression line.

c.

To determine

Find the mean value of gas usage for houses with 2,100 square feet of space.

d.

To determine

Find the average change in usage associated with 1 square feet increase in size.

e.

To determine

Find the average change in usage associated with a 100 square feet increase in size.

f.

To determine

Explain whether the model can be used to predict mean usage for a 500 square feet house.

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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. B = slope of population regression line = 0.018 a = 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? O Yes. The size of this house lies inside the range of the sample that the model is based on. O Yes. The model can be used to predict mean usage for any sized house…

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 = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.

The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water) across the device's filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y = -0.11 + 0.097x. (a.1) What is the true average flow rate for a pressure drop of 10 in.?(a.2) A drop of 15 in.?(b) What is the true average change in flow rate associated with a 1 inch increase in pressure drop?(c) What is the average change in flow rate when pressure drop decreases by 5 in.?

Answer 2

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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 13.1, Problem 1E

a.

To determine

Find the equation of the population regression line.

b.

To determine

Graph the population regression line.

c.

To determine

Find the mean value of gas usage for houses with 2,100 square feet of space.

d.

To determine

Find the average change in usage associated with 1 square feet increase in size.

e.

To determine

Find the average change in usage associated with a 100 square feet increase in size.

f.

To determine

Explain whether the model can be used to predict mean usage for a 500 square feet house.

Expert Solution & Answer

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Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 13.1, Problem 1E

a.

To determine

Find the equation of the population regression line.

b.

To determine

Graph the population regression line.

c.

To determine

Find the mean value of gas usage for houses with 2,100 square feet of space.

d.

To determine

Find the average change in usage associated with 1 square feet increase in size.

e.

To determine

Find the average change in usage associated with a 100 square feet increase in size.

f.

To determine

Explain whether the model can be used to predict mean usage for a 500 square feet house.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 13.1, Problem 1E

a.

To determine

Find the equation of the population regression line.

b.

To determine

Graph the population regression line.

c.

To determine

Find the mean value of gas usage for houses with 2,100 square feet of space.

d.

To determine

Find the average change in usage associated with 1 square feet increase in size.

e.

To determine

Find the average change in usage associated with a 100 square feet increase in size.

f.

To determine

Explain whether the model can be used to predict mean usage for a 500 square feet house.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 13.1, Problem 1E

a.

To determine

Find the equation of the population regression line.

b.

To determine

Graph the population regression line.

c.

To determine

Find the mean value of gas usage for houses with 2,100 square feet of space.

d.

To determine

Find the average change in usage associated with 1 square feet increase in size.

e.

To determine

Find the average change in usage associated with a 100 square feet increase in size.

f.

To determine

Explain whether the model can be used to predict mean usage for a 500 square feet house.

Answer 6

Chapter 13.1, Problem 1E

a.

To determine

Find the equation of the population regression line.

Answer 7

Chapter 13.1, Problem 1E

a.

To determine

Find the equation of the population regression line.

Answer 8

b.

To determine

Graph the population regression line.

Answer 9

b.

To determine

Graph the population regression line.

Answer 10

c.

To determine

Find the mean value of gas usage for houses with 2,100 square feet of space.

Answer 11

c.

To determine

Find the mean value of gas usage for houses with 2,100 square feet of space.

Answer 12

d.

To determine

Find the average change in usage associated with 1 square feet increase in size.

Answer 13

d.

To determine

Find the average change in usage associated with 1 square feet increase in size.

Answer 14

e.

To determine

Find the average change in usage associated with a 100 square feet increase in size.

Answer 15

e.

To determine

Find the average change in usage associated with a 100 square feet increase in size.

Answer 16

f.

To determine

Explain whether the model can be used to predict mean usage for a 500 square feet house.

Answer 17

f.

To determine

Explain whether the model can be used to predict mean usage for a 500 square feet house.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 13.1 - Prob. 1E Ch. 13.1 - The flow rate in a device used for air quality...Ch. 13.1 - The paper Predicting Yolk Height, Yolk Width,...Ch. 13.1 - Prob. 4E Ch. 13.1 - Suppose that a simple linear regression model is...Ch. 13.1 - a. Explain the difference between the line y x...Ch. 13.1 - Prob. 7E Ch. 13.1 - Hormone replacement therapy (HRT) is thought to...Ch. 13.1 - Prob. 9E Ch. 13.1 - A simple linear regression model was used to...

Find the equation of the population regression line.

Solution Summary: The author explains the equation of the population regression line, which is y=-5.0+0.017x.

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Find the equation of the population regression line.

Graph the population regression line.

Find the mean value of gas usage for houses with 2,100 square feet of space.

Find the average change in usage associated with 1 square feet increase in size.

Find the average change in usage associated with a 100 square feet increase in size.

Explain whether the model can be used to predict mean usage for a 500 square feet house.

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Chapter 13 Solutions