To predict: The margin of win if the home team is favored by 3 points.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 4, Problem 1RE

(a)

To determine

To predict: The margin of win if the home team is favored by 3 points.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the home team is favored by 3 points is 3.009.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of winning can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of winning for the home team when the team is favored by 3 points can be calculated as follows:

y^=1.007x−0.012=1.007×3−0.012=3.009

(b)

To determine

To predict: The margin of win if the visiting team is favored by 7 points.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the visiting team is favored by 7 points is 7.037.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of win can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of win for the visiting team if the team is favored by 7 points can be calculated as follows:

y^=1.007x−0.012=1.007×7−0.012=7.037

(c)

To determine

To interpret: The slope.

(c)

Expert Solution

Answer to Problem 1RE

Solution: The slope can be interpreted as follows: if there is an increase of 1 unit of the variable x, then there is an increase of 1.007 units in the value of the variable y^.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The slope of the least-squares regression equation indicates the quantity of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of y^ is 1.007 due to the 1-unit increase in the value of x.

(d)

To determine

To interpret: The y-intercept.

(d)

Expert Solution

Answer to Problem 1RE

Solution: The y-intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. The value of the y-intercept is −0.012 when the value of the explanatory variable is zero.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The y-intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. In the provided data set, if the value of the explanatory variable is equal to zero, then the value of y^ response variable is −0.012.

(e)

To determine

To interpret: The value of the coefficient of determination.

(e)

Expert Solution

Answer to Problem 1RE

Solution: The variation in winning margin is 39%, which can be explained by the least-squares regression equation.

Explanation of Solution

Given: The value of the coefficient of determination is 0.39.

Explanation: The coefficient of determination indicates that 39% of the variation is explained by the regression equation involving independent variable and the rest of the 61% variation remains unexplained.

Conclusion: From coefficient of determination, it is concluded that 39% of the variation in the winning margin is explained by the regression line.

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!

Students have asked these similar questions

Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks

28. (a) Under what conditions do we say that two random variables X and Y are independent? (b) Demonstrate that if X and Y are independent, then it follows that E(XY) = E(X)E(Y); (e) Show by a counter example that the converse of (ii) is not necessarily true.

1. Let X and Y be random variables and suppose that A = F. Prove that Z XI(A)+YI(A) is a random variable.

Answer 2

Question

Chapter 4, Problem 1RE

(a)

To determine

To predict: The margin of win if the home team is favored by 3 points.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the home team is favored by 3 points is 3.009.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of winning can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of winning for the home team when the team is favored by 3 points can be calculated as follows:

y^=1.007x−0.012=1.007×3−0.012=3.009

(b)

To determine

To predict: The margin of win if the visiting team is favored by 7 points.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the visiting team is favored by 7 points is 7.037.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of win can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of win for the visiting team if the team is favored by 7 points can be calculated as follows:

y^=1.007x−0.012=1.007×7−0.012=7.037

(c)

To determine

To interpret: The slope.

(c)

Expert Solution

Answer to Problem 1RE

Solution: The slope can be interpreted as follows: if there is an increase of 1 unit of the variable x, then there is an increase of 1.007 units in the value of the variable y^.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The slope of the least-squares regression equation indicates the quantity of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of y^ is 1.007 due to the 1-unit increase in the value of x.

(d)

To determine

To interpret: The y-intercept.

(d)

Expert Solution

Answer to Problem 1RE

Solution: The y-intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. The value of the y-intercept is −0.012 when the value of the explanatory variable is zero.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The y-intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. In the provided data set, if the value of the explanatory variable is equal to zero, then the value of y^ response variable is −0.012.

(e)

To determine

To interpret: The value of the coefficient of determination.

(e)

Expert Solution

Answer to Problem 1RE

Solution: The variation in winning margin is 39%, which can be explained by the least-squares regression equation.

Explanation of Solution

Given: The value of the coefficient of determination is 0.39.

Explanation: The coefficient of determination indicates that 39% of the variation is explained by the regression equation involving independent variable and the rest of the 61% variation remains unexplained.

Conclusion: From coefficient of determination, it is concluded that 39% of the variation in the winning margin is explained by the regression line.

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 3

Question

Chapter 4, Problem 1RE

(a)

To determine

To predict: The margin of win if the home team is favored by 3 points.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the home team is favored by 3 points is 3.009.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of winning can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of winning for the home team when the team is favored by 3 points can be calculated as follows:

y^=1.007x−0.012=1.007×3−0.012=3.009

(b)

To determine

To predict: The margin of win if the visiting team is favored by 7 points.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the visiting team is favored by 7 points is 7.037.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of win can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of win for the visiting team if the team is favored by 7 points can be calculated as follows:

y^=1.007x−0.012=1.007×7−0.012=7.037

(c)

To determine

To interpret: The slope.

(c)

Expert Solution

Answer to Problem 1RE

Solution: The slope can be interpreted as follows: if there is an increase of 1 unit of the variable x, then there is an increase of 1.007 units in the value of the variable y^.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The slope of the least-squares regression equation indicates the quantity of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of y^ is 1.007 due to the 1-unit increase in the value of x.

(d)

To determine

To interpret: The y-intercept.

(d)

Expert Solution

Answer to Problem 1RE

Solution: The y-intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. The value of the y-intercept is −0.012 when the value of the explanatory variable is zero.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The y-intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. In the provided data set, if the value of the explanatory variable is equal to zero, then the value of y^ response variable is −0.012.

(e)

To determine

To interpret: The value of the coefficient of determination.

(e)

Expert Solution

Answer to Problem 1RE

Solution: The variation in winning margin is 39%, which can be explained by the least-squares regression equation.

Explanation of Solution

Given: The value of the coefficient of determination is 0.39.

Explanation: The coefficient of determination indicates that 39% of the variation is explained by the regression equation involving independent variable and the rest of the 61% variation remains unexplained.

Conclusion: From coefficient of determination, it is concluded that 39% of the variation in the winning margin is explained by the regression line.

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

Chapter 4, Problem 1RE

(a)

To determine

To predict: The margin of win if the home team is favored by 3 points.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the home team is favored by 3 points is 3.009.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of winning can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of winning for the home team when the team is favored by 3 points can be calculated as follows:

y^=1.007x−0.012=1.007×3−0.012=3.009

(b)

To determine

To predict: The margin of win if the visiting team is favored by 7 points.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the visiting team is favored by 7 points is 7.037.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of win can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of win for the visiting team if the team is favored by 7 points can be calculated as follows:

y^=1.007x−0.012=1.007×7−0.012=7.037

(c)

To determine

To interpret: The slope.

(c)

Expert Solution

Answer to Problem 1RE

Solution: The slope can be interpreted as follows: if there is an increase of 1 unit of the variable x, then there is an increase of 1.007 units in the value of the variable y^.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The slope of the least-squares regression equation indicates the quantity of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of y^ is 1.007 due to the 1-unit increase in the value of x.

(d)

To determine

To interpret: The y-intercept.

(d)

Expert Solution

Answer to Problem 1RE

Solution: The y-intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. The value of the y-intercept is −0.012 when the value of the explanatory variable is zero.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The y-intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. In the provided data set, if the value of the explanatory variable is equal to zero, then the value of y^ response variable is −0.012.

(e)

To determine

To interpret: The value of the coefficient of determination.

(e)

Expert Solution

Answer to Problem 1RE

Solution: The variation in winning margin is 39%, which can be explained by the least-squares regression equation.

Explanation of Solution

Given: The value of the coefficient of determination is 0.39.

Explanation: The coefficient of determination indicates that 39% of the variation is explained by the regression equation involving independent variable and the rest of the 61% variation remains unexplained.

Conclusion: From coefficient of determination, it is concluded that 39% of the variation in the winning margin is explained by the regression line.

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 5

Chapter 4, Problem 1RE

(a)

To determine

To predict: The margin of win if the home team is favored by 3 points.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the home team is favored by 3 points is 3.009.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of winning can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of winning for the home team when the team is favored by 3 points can be calculated as follows:

y^=1.007x−0.012=1.007×3−0.012=3.009

(b)

To determine

To predict: The margin of win if the visiting team is favored by 7 points.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the visiting team is favored by 7 points is 7.037.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of win can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of win for the visiting team if the team is favored by 7 points can be calculated as follows:

y^=1.007x−0.012=1.007×7−0.012=7.037

(c)

To determine

To interpret: The slope.

(c)

Expert Solution

Answer to Problem 1RE

Solution: The slope can be interpreted as follows: if there is an increase of 1 unit of the variable x, then there is an increase of 1.007 units in the value of the variable y^.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The slope of the least-squares regression equation indicates the quantity of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of y^ is 1.007 due to the 1-unit increase in the value of x.

(d)

To determine

To interpret: The y-intercept.

(d)

Expert Solution

Answer to Problem 1RE

Solution: The y-intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. The value of the y-intercept is −0.012 when the value of the explanatory variable is zero.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The y-intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. In the provided data set, if the value of the explanatory variable is equal to zero, then the value of y^ response variable is −0.012.

(e)

To determine

To interpret: The value of the coefficient of determination.

(e)

Expert Solution

Answer to Problem 1RE

Solution: The variation in winning margin is 39%, which can be explained by the least-squares regression equation.

Explanation of Solution

Given: The value of the coefficient of determination is 0.39.

Explanation: The coefficient of determination indicates that 39% of the variation is explained by the regression equation involving independent variable and the rest of the 61% variation remains unexplained.

Conclusion: From coefficient of determination, it is concluded that 39% of the variation in the winning margin is explained by the regression line.

Answer 6

Chapter 4, Problem 1RE

(a)

To determine

To predict: The margin of win if the home team is favored by 3 points.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the home team is favored by 3 points is 3.009.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of winning can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of winning for the home team when the team is favored by 3 points can be calculated as follows:

y^=1.007x−0.012=1.007×3−0.012=3.009

Answer 7

Chapter 4, Problem 1RE

(a)

To determine

To predict: The margin of win if the home team is favored by 3 points.

Answer 8

(a)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the home team is favored by 3 points is 3.009.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of winning can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of winning for the home team when the team is favored by 3 points can be calculated as follows:

y^=1.007x−0.012=1.007×3−0.012=3.009

Answer 13

(b)

To determine

To predict: The margin of win if the visiting team is favored by 7 points.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the visiting team is favored by 7 points is 7.037.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of win can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of win for the visiting team if the team is favored by 7 points can be calculated as follows:

y^=1.007x−0.012=1.007×7−0.012=7.037

Answer 14

(b)

To determine

To predict: The margin of win if the visiting team is favored by 7 points.

Answer 15

(b)

Expert Solution

Answer to Problem 1RE

Solution: The predicted value of the margin of win if the visiting team is favored by 7 points is 7.037.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The value of the margin of win can be obtained from the regression equation by substituting the value of the spread in the least-squares regression line. The predicted value of the margin of win for the visiting team if the team is favored by 7 points can be calculated as follows:

y^=1.007x−0.012=1.007×7−0.012=7.037

Answer 20

(c)

To determine

To interpret: The slope.

(c)

Expert Solution

Answer to Problem 1RE

Solution: The slope can be interpreted as follows: if there is an increase of 1 unit of the variable x, then there is an increase of 1.007 units in the value of the variable y^.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The slope of the least-squares regression equation indicates the quantity of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of y^ is 1.007 due to the 1-unit increase in the value of x.

Answer 21

(c)

To determine

To interpret: The slope.

Answer 22

(c)

Expert Solution

Answer to Problem 1RE

Solution: The slope can be interpreted as follows: if there is an increase of 1 unit of the variable x, then there is an increase of 1.007 units in the value of the variable y^.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The slope of the least-squares regression equation indicates the quantity of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of y^ is 1.007 due to the 1-unit increase in the value of x.

Answer 27

(d)

To determine

To interpret: The y-intercept.

(d)

Expert Solution

Answer to Problem 1RE

Solution: The y-intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. The value of the y-intercept is −0.012 when the value of the explanatory variable is zero.

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The y-intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. In the provided data set, if the value of the explanatory variable is equal to zero, then the value of y^ response variable is −0.012.

Answer 28

(d)

To determine

To interpret: The y-intercept.

Answer 29

(d)

Expert Solution

Answer to Problem 1RE

Solution: The y-intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. The value of the y-intercept is −0.012 when the value of the explanatory variable is zero.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given: The least-squares linear regression is provided in the question. The response variable is the winning margin and the explanatory variable is the spread.

Explanation: The y-intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. In the provided data set, if the value of the explanatory variable is equal to zero, then the value of y^ response variable is −0.012.

Answer 34

(e)

To determine

To interpret: The value of the coefficient of determination.

(e)

Expert Solution

Answer to Problem 1RE

Solution: The variation in winning margin is 39%, which can be explained by the least-squares regression equation.

Explanation of Solution

Given: The value of the coefficient of determination is 0.39.

Explanation: The coefficient of determination indicates that 39% of the variation is explained by the regression equation involving independent variable and the rest of the 61% variation remains unexplained.

Conclusion: From coefficient of determination, it is concluded that 39% of the variation in the winning margin is explained by the regression line.

Answer 35

(e)

To determine

To interpret: The value of the coefficient of determination.

Answer 36

(e)

Expert Solution

Answer to Problem 1RE

Solution: The variation in winning margin is 39%, which can be explained by the least-squares regression equation.

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given: The value of the coefficient of determination is 0.39.

Explanation: The coefficient of determination indicates that 39% of the variation is explained by the regression equation involving independent variable and the rest of the 61% variation remains unexplained.

Conclusion: From coefficient of determination, it is concluded that 39% of the variation in the winning margin is explained by the regression line.