Concept explainers
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
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)
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
Thus, the predicted winning margin is 3.009.
(b)
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
Thus, the predicted winning margin of visiting team is –7.061.
(c)
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)
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)
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
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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Chapter 4 Solutions
Fundamentals of Statistics (5th Edition)
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