Basketball Spreads In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points and wins the game by 7 points, then a bet on Team A is a winning bet. However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. For NCAA Division I basketball games, a least-squares regression with explanatory variable home team Las Vegas spread, x , and response variable home team winning margin, y , is y ^ = 1.007 x − 0.012 . Source: Justin wolfers. “Point Shaving: Corruption in NCAA Basketball” a. Predict the winning margin if the home team is favored by 3 points. b. Predict the winning margin (of the visiting team) if the visiting team is favored by 7 points (this is equivalent to the home team being favored by −7 points). c. Interpret the slope. d. Interpret the y -intercept. e. The coefficient of determination is 0.39. Interpret this value.

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Answer 1

Textbook Question

Chapter 4, Problem 1RE

Basketball Spreads In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points and wins the game by 7 points, then a bet on Team A is a winning bet. However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. For NCAA Division I basketball games, a least-squares regression with explanatory variable home team Las Vegas spread, x, and response variable home team winning margin, y, is y ^ = 1.007 x − 0.012 .

Source: Justin wolfers. “Point Shaving: Corruption in NCAA Basketball”

a. Predict the winning margin if the home team is favored by 3 points.
b. Predict the winning margin (of the visiting team) if the visiting team is favored by 7 points (this is equivalent to the home team being favored by −7 points).
c. Interpret the slope.
d. Interpret the y-intercept.
e. The coefficient of determination is 0.39. Interpret this value.

(a)

Expert Solution

To determine

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

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Given info:

The least square regression line relating the spread of the home team and winning point is given.

Calculation:

Substituting x=3 in the equation,

y^=1.007x−0.012=1.007×3−0.012=3.021−0.012=3.009

Thus, the predicted winning margin is 3.009.

(b)

Expert Solution

To determine

To predict: The winning margin if the visiting team has 7 points.

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Calculation:

The visiting team that is favored by 7 points is equivalent to the home team that is favored by –7 points. So substituting x=−7 in the equation,

y^=1.007x−0.012=1.007×(−7)−0.012=−7.049−0.012=−7.061

Thus, the predicted winning margin of visiting team is –7.061.

(c)

Expert Solution

To determine

To interpret: The slope parameter.

Answer to Problem 1RE

If 1 point increased in the spread, the winning margin will increase by 1.007 points.

Explanation of Solution

Interpretation:

Slope:

The coefficient value for “home team Las Vegas Spread” is 1.007.

The interpretation for slope is that, if 1 point increased in the spread, the winning margin will increase by 1.007 points.

(d)

Expert Solution

To determine

To interpret: The y-intercept.

Answer to Problem 1RE

If the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Explanation of Solution

Interpretation:

Intercept:

It is possible that home speed to have 0 spread. That is zero is reasonable for explanatory variable.

Thus, y-intercept is interpretable.

The interpretation for y-intercept is that if the spread is by 0 points, then the home team is expected to lose by 0.012 points.

(d)

Expert Solution

To determine

To interpret: The coefficient of determination of the data.

Answer to Problem 1RE

The interpretation for the coefficient of determination is that the 39% of the variation in the winning margin is explained by the least square regression line.

Explanation of Solution

Interpretation:

The value of R2 is 39%.

That is, the proportion of variability in winning margin is 39%.

Hence, it can be interpreted that the 39% of the variation in the winning margin is explained by the least square regression line.

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Answer 2

Textbook Question

Chapter 4, Problem 1RE

Basketball Spreads In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points and wins the game by 7 points, then a bet on Team A is a winning bet. However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. For NCAA Division I basketball games, a least-squares regression with explanatory variable home team Las Vegas spread, x, and response variable home team winning margin, y, is y ^ = 1.007 x − 0.012 .

Source: Justin wolfers. “Point Shaving: Corruption in NCAA Basketball”

a. Predict the winning margin if the home team is favored by 3 points.
b. Predict the winning margin (of the visiting team) if the visiting team is favored by 7 points (this is equivalent to the home team being favored by −7 points).
c. Interpret the slope.
d. Interpret the y-intercept.
e. The coefficient of determination is 0.39. Interpret this value.

(a)

Expert Solution

To determine

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

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Given info:

The least square regression line relating the spread of the home team and winning point is given.

Calculation:

Substituting x=3 in the equation,

y^=1.007x−0.012=1.007×3−0.012=3.021−0.012=3.009

Thus, the predicted winning margin is 3.009.

(b)

Expert Solution

To determine

To predict: The winning margin if the visiting team has 7 points.

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Calculation:

The visiting team that is favored by 7 points is equivalent to the home team that is favored by –7 points. So substituting x=−7 in the equation,

y^=1.007x−0.012=1.007×(−7)−0.012=−7.049−0.012=−7.061

Thus, the predicted winning margin of visiting team is –7.061.

(c)

Expert Solution

To determine

To interpret: The slope parameter.

Answer to Problem 1RE

If 1 point increased in the spread, the winning margin will increase by 1.007 points.

Explanation of Solution

Interpretation:

Slope:

The coefficient value for “home team Las Vegas Spread” is 1.007.

The interpretation for slope is that, if 1 point increased in the spread, the winning margin will increase by 1.007 points.

(d)

Expert Solution

To determine

To interpret: The y-intercept.

Answer to Problem 1RE

If the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Explanation of Solution

Interpretation:

Intercept:

It is possible that home speed to have 0 spread. That is zero is reasonable for explanatory variable.

Thus, y-intercept is interpretable.

The interpretation for y-intercept is that if the spread is by 0 points, then the home team is expected to lose by 0.012 points.

(d)

Expert Solution

To determine

To interpret: The coefficient of determination of the data.

Answer to Problem 1RE

The interpretation for the coefficient of determination is that the 39% of the variation in the winning margin is explained by the least square regression line.

Explanation of Solution

Interpretation:

The value of R2 is 39%.

That is, the proportion of variability in winning margin is 39%.

Hence, it can be interpreted that the 39% of the variation in the winning margin is explained by the least square regression line.

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Answer 3

Textbook Question

Chapter 4, Problem 1RE

Basketball Spreads In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points and wins the game by 7 points, then a bet on Team A is a winning bet. However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. For NCAA Division I basketball games, a least-squares regression with explanatory variable home team Las Vegas spread, x, and response variable home team winning margin, y, is y ^ = 1.007 x − 0.012 .

Source: Justin wolfers. “Point Shaving: Corruption in NCAA Basketball”

a. Predict the winning margin if the home team is favored by 3 points.
b. Predict the winning margin (of the visiting team) if the visiting team is favored by 7 points (this is equivalent to the home team being favored by −7 points).
c. Interpret the slope.
d. Interpret the y-intercept.
e. The coefficient of determination is 0.39. Interpret this value.

(a)

Expert Solution

To determine

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

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Given info:

The least square regression line relating the spread of the home team and winning point is given.

Calculation:

Substituting x=3 in the equation,

y^=1.007x−0.012=1.007×3−0.012=3.021−0.012=3.009

Thus, the predicted winning margin is 3.009.

(b)

Expert Solution

To determine

To predict: The winning margin if the visiting team has 7 points.

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Calculation:

The visiting team that is favored by 7 points is equivalent to the home team that is favored by –7 points. So substituting x=−7 in the equation,

y^=1.007x−0.012=1.007×(−7)−0.012=−7.049−0.012=−7.061

Thus, the predicted winning margin of visiting team is –7.061.

(c)

Expert Solution

To determine

To interpret: The slope parameter.

Answer to Problem 1RE

If 1 point increased in the spread, the winning margin will increase by 1.007 points.

Explanation of Solution

Interpretation:

Slope:

The coefficient value for “home team Las Vegas Spread” is 1.007.

The interpretation for slope is that, if 1 point increased in the spread, the winning margin will increase by 1.007 points.

(d)

Expert Solution

To determine

To interpret: The y-intercept.

Answer to Problem 1RE

If the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Explanation of Solution

Interpretation:

Intercept:

It is possible that home speed to have 0 spread. That is zero is reasonable for explanatory variable.

Thus, y-intercept is interpretable.

The interpretation for y-intercept is that if the spread is by 0 points, then the home team is expected to lose by 0.012 points.

(d)

Expert Solution

To determine

To interpret: The coefficient of determination of the data.

Answer to Problem 1RE

The interpretation for the coefficient of determination is that the 39% of the variation in the winning margin is explained by the least square regression line.

Explanation of Solution

Interpretation:

The value of R2 is 39%.

That is, the proportion of variability in winning margin is 39%.

Hence, it can be interpreted that the 39% of the variation in the winning margin is explained by the least square regression line.

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Answer 4

Textbook Question

Chapter 4, Problem 1RE

Basketball Spreads In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is favored by 5 points and wins the game by 7 points, then a bet on Team A is a winning bet. However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. For NCAA Division I basketball games, a least-squares regression with explanatory variable home team Las Vegas spread, x, and response variable home team winning margin, y, is y ^ = 1.007 x − 0.012 .

Source: Justin wolfers. “Point Shaving: Corruption in NCAA Basketball”

a. Predict the winning margin if the home team is favored by 3 points.
b. Predict the winning margin (of the visiting team) if the visiting team is favored by 7 points (this is equivalent to the home team being favored by −7 points).
c. Interpret the slope.
d. Interpret the y-intercept.
e. The coefficient of determination is 0.39. Interpret this value.

(a)

Expert Solution

To determine

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

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Given info:

The least square regression line relating the spread of the home team and winning point is given.

Calculation:

Substituting x=3 in the equation,

y^=1.007x−0.012=1.007×3−0.012=3.021−0.012=3.009

Thus, the predicted winning margin is 3.009.

(b)

Expert Solution

To determine

To predict: The winning margin if the visiting team has 7 points.

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Calculation:

The visiting team that is favored by 7 points is equivalent to the home team that is favored by –7 points. So substituting x=−7 in the equation,

y^=1.007x−0.012=1.007×(−7)−0.012=−7.049−0.012=−7.061

Thus, the predicted winning margin of visiting team is –7.061.

(c)

Expert Solution

To determine

To interpret: The slope parameter.

Answer to Problem 1RE

If 1 point increased in the spread, the winning margin will increase by 1.007 points.

Explanation of Solution

Interpretation:

Slope:

The coefficient value for “home team Las Vegas Spread” is 1.007.

The interpretation for slope is that, if 1 point increased in the spread, the winning margin will increase by 1.007 points.

(d)

Expert Solution

To determine

To interpret: The y-intercept.

Answer to Problem 1RE

If the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Explanation of Solution

Interpretation:

Intercept:

It is possible that home speed to have 0 spread. That is zero is reasonable for explanatory variable.

Thus, y-intercept is interpretable.

The interpretation for y-intercept is that if the spread is by 0 points, then the home team is expected to lose by 0.012 points.

(d)

Expert Solution

To determine

To interpret: The coefficient of determination of the data.

Answer to Problem 1RE

The interpretation for the coefficient of determination is that the 39% of the variation in the winning margin is explained by the least square regression line.

Explanation of Solution

Interpretation:

The value of R2 is 39%.

That is, the proportion of variability in winning margin is 39%.

Hence, it can be interpreted that the 39% of the variation in the winning margin is explained by the least square regression line.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

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

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Given info:

The least square regression line relating the spread of the home team and winning point is given.

Calculation:

Substituting x=3 in the equation,

y^=1.007x−0.012=1.007×3−0.012=3.021−0.012=3.009

Thus, the predicted winning margin is 3.009.

(b)

Expert Solution

To determine

To predict: The winning margin if the visiting team has 7 points.

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Calculation:

The visiting team that is favored by 7 points is equivalent to the home team that is favored by –7 points. So substituting x=−7 in the equation,

y^=1.007x−0.012=1.007×(−7)−0.012=−7.049−0.012=−7.061

Thus, the predicted winning margin of visiting team is –7.061.

(c)

Expert Solution

To determine

To interpret: The slope parameter.

Answer to Problem 1RE

If 1 point increased in the spread, the winning margin will increase by 1.007 points.

Explanation of Solution

Interpretation:

Slope:

The coefficient value for “home team Las Vegas Spread” is 1.007.

The interpretation for slope is that, if 1 point increased in the spread, the winning margin will increase by 1.007 points.

(d)

Expert Solution

To determine

To interpret: The y-intercept.

Answer to Problem 1RE

If the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Explanation of Solution

Interpretation:

Intercept:

It is possible that home speed to have 0 spread. That is zero is reasonable for explanatory variable.

Thus, y-intercept is interpretable.

The interpretation for y-intercept is that if the spread is by 0 points, then the home team is expected to lose by 0.012 points.

(d)

Expert Solution

To determine

To interpret: The coefficient of determination of the data.

Answer to Problem 1RE

The interpretation for the coefficient of determination is that the 39% of the variation in the winning margin is explained by the least square regression line.

Explanation of Solution

Interpretation:

The value of R2 is 39%.

That is, the proportion of variability in winning margin is 39%.

Hence, it can be interpreted that the 39% of the variation in the winning margin is explained by the least square regression line.

Answer 8

(a)

Expert Solution

To determine

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

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Given info:

The least square regression line relating the spread of the home team and winning point is given.

Calculation:

Substituting x=3 in the equation,

y^=1.007x−0.012=1.007×3−0.012=3.021−0.012=3.009

Thus, the predicted winning margin is 3.009.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

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

Answer 13

Answer to Problem 1RE

The predicted winning margin is 3.009.

Answer 14

Explanation of Solution

Given info:

The least square regression line relating the spread of the home team and winning point is given.

Calculation:

Substituting x=3 in the equation,

y^=1.007x−0.012=1.007×3−0.012=3.021−0.012=3.009

Thus, the predicted winning margin is 3.009.

Answer 15

(b)

Expert Solution

To determine

To predict: The winning margin if the visiting team has 7 points.

Answer to Problem 1RE

The predicted winning margin is 3.009.

Explanation of Solution

Calculation:

The visiting team that is favored by 7 points is equivalent to the home team that is favored by –7 points. So substituting x=−7 in the equation,

y^=1.007x−0.012=1.007×(−7)−0.012=−7.049−0.012=−7.061

Thus, the predicted winning margin of visiting team is –7.061.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To predict: The winning margin if the visiting team has 7 points.

Answer 20

Answer to Problem 1RE

The predicted winning margin is 3.009.

Answer 21

Explanation of Solution

Calculation:

The visiting team that is favored by 7 points is equivalent to the home team that is favored by –7 points. So substituting x=−7 in the equation,

y^=1.007x−0.012=1.007×(−7)−0.012=−7.049−0.012=−7.061

Thus, the predicted winning margin of visiting team is –7.061.

Answer 22

(c)

Expert Solution

To determine

To interpret: The slope parameter.

Answer to Problem 1RE

If 1 point increased in the spread, the winning margin will increase by 1.007 points.

Explanation of Solution

Interpretation:

Slope:

The coefficient value for “home team Las Vegas Spread” is 1.007.

The interpretation for slope is that, if 1 point increased in the spread, the winning margin will increase by 1.007 points.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

To interpret: The slope parameter.

Answer 27

Answer to Problem 1RE

If 1 point increased in the spread, the winning margin will increase by 1.007 points.

Answer 28

Explanation of Solution

Interpretation:

Slope:

The coefficient value for “home team Las Vegas Spread” is 1.007.

The interpretation for slope is that, if 1 point increased in the spread, the winning margin will increase by 1.007 points.

Answer 29

(d)

Expert Solution

To determine

To interpret: The y-intercept.

Answer to Problem 1RE

If the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Explanation of Solution

Interpretation:

Intercept:

It is possible that home speed to have 0 spread. That is zero is reasonable for explanatory variable.

Thus, y-intercept is interpretable.

The interpretation for y-intercept is that if the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

To interpret: The y-intercept.

Answer 34

Answer to Problem 1RE

If the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Answer 35

Explanation of Solution

Interpretation:

Intercept:

It is possible that home speed to have 0 spread. That is zero is reasonable for explanatory variable.

Thus, y-intercept is interpretable.

The interpretation for y-intercept is that if the spread is by 0 points, then the home team is expected to lose by 0.012 points.

Answer 36

(d)

Expert Solution

To determine

To interpret: The coefficient of determination of the data.

Answer to Problem 1RE

The interpretation for the coefficient of determination is that the 39% of the variation in the winning margin is explained by the least square regression line.

Explanation of Solution

Interpretation:

The value of R2 is 39%.

That is, the proportion of variability in winning margin is 39%.

Hence, it can be interpreted that the 39% of the variation in the winning margin is explained by the least square regression line.

Answer 37

(d)

Expert Solution

Answer 38

(d)

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

To interpret: The coefficient of determination of the data.

Answer 41

Answer to Problem 1RE

The interpretation for the coefficient of determination is that the 39% of the variation in the winning margin is explained by the least square regression line.