Suppose the regression line for the number of runs scored in a season, y, is given by 790 + 5700x, where x is the team's batting average. a. For a team with a batting average of 0.235, find the expected number of runs scored in a season. Round your answer to the nearest whole number. b. If we can expect the number of runs scored in a season is 440, then what is the assumed team's batting average? Round your answer to three decimal places.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![### Baseball Regression Line Prediction:
Suppose the regression line for the number of runs scored in a season, \( y \), is given by
\[
\hat{y} = -790 + 5700x,
\]
where \( x \) is the team's batting average.
**a.** For a team with a batting average of 0.235, find the expected number of runs scored in a season. **Round your answer to the nearest whole number.**
\[ \_\_\_\_\_\_ \]
**b.** If we can expect the number of runs scored in a season is 440, then what is the assumed team's batting average? **Round your answer to three decimal places.**
\[ \_\_\_\_\_\_ \]
### Explanation:
In the formula \( \hat{y} = -790 + 5700x \):
- \( \hat{y} \) represents the predicted number of runs scored.
- \( x \) represents the batting average.
To solve part **a**, substitute \( x = 0.235 \) into the equation to find \( \hat{y} \). To solve part **b**, set \( \hat{y} = 440 \) and solve for \( x \).
This exercises helps in understanding how to use a regression line for prediction purposes in the context of baseball statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcebbde0b-56df-456f-b45f-057baf1d3a0f%2Fefb276d9-7140-424d-b6d9-fe1b6afd0b99%2Fkcne0qr_processed.png&w=3840&q=75)
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