Explain why it is more sensible to let α + β x represent the means of the conditional distributions rather than individual observations.

Question

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Answer 1

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 12, Problem 62CP

a.

To determine

Explain why it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

a.

Expert Solution

Explanation of Solution

In this case, it is observed that there is variability in the values of y at fixed values of x. Therefore, one cannot specify the individual values of y using x values, but can specify the mean of the individual values and the way mean changes when x changes.

Therefore, it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

b.

To determine

Explain why the model allows variation around the mean with its parameter σ.

b.

Expert Solution

Explanation of Solution

In this case, it is observed that the values of y differs at a fixed value of x and the parameter of the model σ explains the variability of the conditional distribution of the values of y at each fixed value x. Therefore, the model allows variation around the mean with its parameter σ.

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Answer 2

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 12, Problem 62CP

a.

To determine

Explain why it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

a.

Expert Solution

Explanation of Solution

In this case, it is observed that there is variability in the values of y at fixed values of x. Therefore, one cannot specify the individual values of y using x values, but can specify the mean of the individual values and the way mean changes when x changes.

Therefore, it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

b.

To determine

Explain why the model allows variation around the mean with its parameter σ.

b.

Expert Solution

Explanation of Solution

In this case, it is observed that the values of y differs at a fixed value of x and the parameter of the model σ explains the variability of the conditional distribution of the values of y at each fixed value x. Therefore, the model allows variation around the mean with its parameter σ.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 12, Problem 62CP

a.

To determine

Explain why it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

a.

Expert Solution

Explanation of Solution

In this case, it is observed that there is variability in the values of y at fixed values of x. Therefore, one cannot specify the individual values of y using x values, but can specify the mean of the individual values and the way mean changes when x changes.

Therefore, it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

b.

To determine

Explain why the model allows variation around the mean with its parameter σ.

b.

Expert Solution

Explanation of Solution

In this case, it is observed that the values of y differs at a fixed value of x and the parameter of the model σ explains the variability of the conditional distribution of the values of y at each fixed value x. Therefore, the model allows variation around the mean with its parameter σ.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 12, Problem 62CP

a.

To determine

Explain why it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

a.

Expert Solution

Explanation of Solution

In this case, it is observed that there is variability in the values of y at fixed values of x. Therefore, one cannot specify the individual values of y using x values, but can specify the mean of the individual values and the way mean changes when x changes.

Therefore, it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

b.

To determine

Explain why the model allows variation around the mean with its parameter σ.

b.

Expert Solution

Explanation of Solution

In this case, it is observed that the values of y differs at a fixed value of x and the parameter of the model σ explains the variability of the conditional distribution of the values of y at each fixed value x. Therefore, the model allows variation around the mean with its parameter σ.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 12, Problem 62CP

a.

To determine

Explain why it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

a.

Expert Solution

Explanation of Solution

In this case, it is observed that there is variability in the values of y at fixed values of x. Therefore, one cannot specify the individual values of y using x values, but can specify the mean of the individual values and the way mean changes when x changes.

Therefore, it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

b.

To determine

Explain why the model allows variation around the mean with its parameter σ.

b.

Expert Solution

Explanation of Solution

In this case, it is observed that the values of y differs at a fixed value of x and the parameter of the model σ explains the variability of the conditional distribution of the values of y at each fixed value x. Therefore, the model allows variation around the mean with its parameter σ.

Answer 6

Chapter 12, Problem 62CP

a.

To determine

Explain why it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

a.

Expert Solution

Explanation of Solution

In this case, it is observed that there is variability in the values of y at fixed values of x. Therefore, one cannot specify the individual values of y using x values, but can specify the mean of the individual values and the way mean changes when x changes.

Therefore, it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

Answer 7

Chapter 12, Problem 62CP

a.

To determine

Explain why it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

Answer 8

a.

Expert Solution

Explanation of Solution

In this case, it is observed that there is variability in the values of y at fixed values of x. Therefore, one cannot specify the individual values of y using x values, but can specify the mean of the individual values and the way mean changes when x changes.

Therefore, it is more sensible to let α+βx represent the means of the conditional distributions rather than individual observations.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

b.

To determine

Explain why the model allows variation around the mean with its parameter σ.

b.

Expert Solution

Explanation of Solution

In this case, it is observed that the values of y differs at a fixed value of x and the parameter of the model σ explains the variability of the conditional distribution of the values of y at each fixed value x. Therefore, the model allows variation around the mean with its parameter σ.

Answer 13

b.

To determine

Explain why the model allows variation around the mean with its parameter σ.

Answer 14

b.

Expert Solution

Explanation of Solution

In this case, it is observed that the values of y differs at a fixed value of x and the parameter of the model σ explains the variability of the conditional distribution of the values of y at each fixed value x. Therefore, the model allows variation around the mean with its parameter σ.