What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 9 randomly selected games are shown below. Attendance 45 38 55 56 58 58 35 17 56 Runs 7 5 11 7 12 9 8 1 9 Use the model to predict the runs scored at a game that has an attendance of 40,000 people. Runs scored = (Please round your answer to the nearest whole number.) Interpret the slope of the regression line in the context of the question: As x goes up, y goes up. For every additional thousand people who attend a game, there tends to be an average increase of 0.20 runs scored. The slope has no practical meaning since the total number runs scored in a game must be positive. Interpret the y-intercept in the context of the question: The best prediction for a game with 0 attendance is that there will be -2 runs scored. The average runs scored is predicted to be -2. If the attendance of a baseball game is 0, then -2 runs will be scored. The y-intercept has no practical meaning for this study.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 9 randomly selected games are shown below.
| Attendance | 45 | 38 | 55 | 56 | 58 | 58 | 35 | 17 | 56 |
|---|---|---|---|---|---|---|---|---|---|
| Runs | 7 | 5 | 11 | 7 | 12 | 9 | 8 | 1 | 9 |
- Use the model to predict the runs scored at a game that has an attendance of 40,000 people.
Runs scored = (Please round your answer to the nearest whole number.) - Interpret the slope of the regression line in the context of the question:
- As x goes up, y goes up.
- For every additional thousand people who attend a game, there tends to be an average increase of 0.20 runs scored.
- The slope has no practical meaning since the total number runs scored in a game must be positive.
- Interpret the y-intercept in the context of the question:
- The best prediction for a game with 0 attendance is that there will be -2 runs scored.
- The average runs scored is predicted to be -2.
- If the attendance of a baseball game is 0, then -2 runs will be scored.
- The y-intercept has no practical meaning for this study.
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