For this problem, use the following multiple regression equation: Y ^ i = 10 + 5 X 1 i + 3 X 2 i a. Interpret the meaning of the slopes. b. Interpret the meaning of the Y intercept.

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Answer 1

Textbook Question

Chapter 14, Problem 1PS

For this problem, use the following multiple regression equation:

Y ^ i = 10 + 5 X 1 i + 3 X 2 i

a. Interpret the meaning of the slopes.

b. Interpret the meaning of the Y intercept.

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 + ...

a.

Expert Solution

To determine

Interpret the meaning of slopes.

Explanation of Solution

The given multiple regression is:

Yi^=10+5X1i+3X2i

The coefficients of X1i and X2i represent the slope of the equation. The coefficient of X1i is 5 . It means that holding the independent variable X2i constant , one unit increase in X1i leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of X2i represents the 3 unit increase in the response variable Y for a unit increase in X2i while keeping other independent variable constant.

b.

Expert Solution

To determine

Interpret the meaning of the Y intercept.

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables X1 and X2 are zero.

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Answer 2

Textbook Question

Chapter 14, Problem 1PS

For this problem, use the following multiple regression equation:

Y ^ i = 10 + 5 X 1 i + 3 X 2 i

a. Interpret the meaning of the slopes.

b. Interpret the meaning of the Y intercept.

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 + ...

a.

Expert Solution

To determine

Interpret the meaning of slopes.

Explanation of Solution

The given multiple regression is:

Yi^=10+5X1i+3X2i

The coefficients of X1i and X2i represent the slope of the equation. The coefficient of X1i is 5 . It means that holding the independent variable X2i constant , one unit increase in X1i leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of X2i represents the 3 unit increase in the response variable Y for a unit increase in X2i while keeping other independent variable constant.

b.

Expert Solution

To determine

Interpret the meaning of the Y intercept.

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables X1 and X2 are zero.

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Answer 3

Textbook Question

Chapter 14, Problem 1PS

For this problem, use the following multiple regression equation:

Y ^ i = 10 + 5 X 1 i + 3 X 2 i

a. Interpret the meaning of the slopes.

b. Interpret the meaning of the Y intercept.

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 + ...

a.

Expert Solution

To determine

Interpret the meaning of slopes.

Explanation of Solution

The given multiple regression is:

Yi^=10+5X1i+3X2i

The coefficients of X1i and X2i represent the slope of the equation. The coefficient of X1i is 5 . It means that holding the independent variable X2i constant , one unit increase in X1i leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of X2i represents the 3 unit increase in the response variable Y for a unit increase in X2i while keeping other independent variable constant.

b.

Expert Solution

To determine

Interpret the meaning of the Y intercept.

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables X1 and X2 are zero.

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Answer 4

Textbook Question

Chapter 14, Problem 1PS

For this problem, use the following multiple regression equation:

Y ^ i = 10 + 5 X 1 i + 3 X 2 i

a. Interpret the meaning of the slopes.

b. Interpret the meaning of the Y intercept.

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 + ...

a.

Expert Solution

To determine

Interpret the meaning of slopes.

Explanation of Solution

The given multiple regression is:

Yi^=10+5X1i+3X2i

The coefficients of X1i and X2i represent the slope of the equation. The coefficient of X1i is 5 . It means that holding the independent variable X2i constant , one unit increase in X1i leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of X2i represents the 3 unit increase in the response variable Y for a unit increase in X2i while keeping other independent variable constant.

b.

Expert Solution

To determine

Interpret the meaning of the Y intercept.

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables X1 and X2 are zero.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Interpret the meaning of slopes.

Explanation of Solution

The given multiple regression is:

Yi^=10+5X1i+3X2i

The coefficients of X1i and X2i represent the slope of the equation. The coefficient of X1i is 5 . It means that holding the independent variable X2i constant , one unit increase in X1i leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of X2i represents the 3 unit increase in the response variable Y for a unit increase in X2i while keeping other independent variable constant.

b.

Expert Solution

To determine

Interpret the meaning of the Y intercept.

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables X1 and X2 are zero.

Answer 8

a.

Expert Solution

To determine

Interpret the meaning of slopes.

Explanation of Solution

The given multiple regression is:

Yi^=10+5X1i+3X2i

The coefficients of X1i and X2i represent the slope of the equation. The coefficient of X1i is 5 . It means that holding the independent variable X2i constant , one unit increase in X1i leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of X2i represents the 3 unit increase in the response variable Y for a unit increase in X2i while keeping other independent variable constant.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Interpret the meaning of slopes.

Answer 13

Explanation of Solution

The given multiple regression is:

Yi^=10+5X1i+3X2i

The coefficients of X1i and X2i represent the slope of the equation. The coefficient of X1i is 5 . It means that holding the independent variable X2i constant , one unit increase in X1i leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of X2i represents the 3 unit increase in the response variable Y for a unit increase in X2i while keeping other independent variable constant.

Answer 14

b.

Expert Solution

To determine

Interpret the meaning of the Y intercept.

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables X1 and X2 are zero.

Answer 15

b.

Expert Solution

Answer 16

b.

Expert Solution

Answer 17

Expert Solution

Answer 18

To determine

Interpret the meaning of the Y intercept.

Answer 19

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables X1 and X2 are zero.

Answer 20

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For this problem, use the following multiple regression equation: Y ^ i = 10 + 5 X 1 i + 3 X 2 i a. Interpret the meaning of the slopes. b. Interpret the meaning of the Y intercept.

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