Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x .

Question

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Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 15, Problem 1RP

a.

To determine

Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x.

a.

Expert Solution

Answer to Problem 1RP

The distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Explanation of Solution

Given info:

The random variable x is a predictor variable and the random variable y is a response variable of a population.

Justification:

According to assumption of regression inferences, the conditional distribution of the response variable is normal distribution for each value of the predictor variable.

Thus, the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Statistics Concept Introduction

Assumption for regression inferences:

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

b.

To determine

State the four assumptions for regression inferences.

b.

Expert Solution

Explanation of Solution

Justification:

The four assumptions of regression inferences are given as,

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

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Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 15, Problem 1RP

a.

To determine

Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x.

a.

Expert Solution

Answer to Problem 1RP

The distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Explanation of Solution

Given info:

The random variable x is a predictor variable and the random variable y is a response variable of a population.

Justification:

According to assumption of regression inferences, the conditional distribution of the response variable is normal distribution for each value of the predictor variable.

Thus, the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Statistics Concept Introduction

Assumption for regression inferences:

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

b.

To determine

State the four assumptions for regression inferences.

b.

Expert Solution

Explanation of Solution

Justification:

The four assumptions of regression inferences are given as,

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 15, Problem 1RP

a.

To determine

Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x.

a.

Expert Solution

Answer to Problem 1RP

The distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Explanation of Solution

Given info:

The random variable x is a predictor variable and the random variable y is a response variable of a population.

Justification:

According to assumption of regression inferences, the conditional distribution of the response variable is normal distribution for each value of the predictor variable.

Thus, the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Statistics Concept Introduction

Assumption for regression inferences:

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

b.

To determine

State the four assumptions for regression inferences.

b.

Expert Solution

Explanation of Solution

Justification:

The four assumptions of regression inferences are given as,

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 15, Problem 1RP

a.

To determine

Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x.

a.

Expert Solution

Answer to Problem 1RP

The distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Explanation of Solution

Given info:

The random variable x is a predictor variable and the random variable y is a response variable of a population.

Justification:

According to assumption of regression inferences, the conditional distribution of the response variable is normal distribution for each value of the predictor variable.

Thus, the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Statistics Concept Introduction

Assumption for regression inferences:

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

b.

To determine

State the four assumptions for regression inferences.

b.

Expert Solution

Explanation of Solution

Justification:

The four assumptions of regression inferences are given as,

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

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Answer 5

Chapter 15, Problem 1RP

a.

To determine

Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x.

a.

Expert Solution

Answer to Problem 1RP

The distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Explanation of Solution

Given info:

The random variable x is a predictor variable and the random variable y is a response variable of a population.

Justification:

According to assumption of regression inferences, the conditional distribution of the response variable is normal distribution for each value of the predictor variable.

Thus, the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Statistics Concept Introduction

Assumption for regression inferences:

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

b.

To determine

State the four assumptions for regression inferences.

b.

Expert Solution

Explanation of Solution

Justification:

The four assumptions of regression inferences are given as,

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

Answer 6

Chapter 15, Problem 1RP

a.

To determine

Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x.

a.

Expert Solution

Answer to Problem 1RP

The distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Explanation of Solution

Given info:

The random variable x is a predictor variable and the random variable y is a response variable of a population.

Justification:

According to assumption of regression inferences, the conditional distribution of the response variable is normal distribution for each value of the predictor variable.

Thus, the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Statistics Concept Introduction

Assumption for regression inferences:

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

Answer 7

Chapter 15, Problem 1RP

a.

To determine

Find the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x.

Answer 8

a.

Expert Solution

Answer to Problem 1RP

The distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given info:

The random variable x is a predictor variable and the random variable y is a response variable of a population.

Justification:

According to assumption of regression inferences, the conditional distribution of the response variable is normal distribution for each value of the predictor variable.

Thus, the distribution of all possible values of the response variable y corresponding to a particular value of the predictor variable x is called a conditional distribution of the response variable.

Answer 13

Statistics Concept Introduction

Assumption for regression inferences:

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

Answer 14

b.

To determine

State the four assumptions for regression inferences.

b.

Expert Solution

Explanation of Solution

Justification:

The four assumptions of regression inferences are given as,

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.

Answer 15

b.

To determine

State the four assumptions for regression inferences.

Answer 16

b.

Expert Solution

Explanation of Solution

Justification:

The four assumptions of regression inferences are given as,

Population regression line: There exists constants β0 and β1, such that for each value of the predictor variable (x), the conditional mean of the response variable (y) is β0+β1x.
Equal standard deviation: For all values of the predictor variable (x), response variable (y) has same conditional standard deviation (σ).
Normal populations: The conditional distribution of the response variable (y) is normal distribution for each value of the predictor variable (x).
Independent observations: The observations of the response variable are independent on each other.