Subjects statistics

Linear Regression B09E45

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1. **State the problem:** We are given heights and weights of 25 baseball players and need to find the best fit linear regression equation where height is the explanatory variable (independent variable) and weight is the response variable (dependent variable). 2. **Formula for linear regression line:** The equation is $$y = mx + b$$ where $m$ is the slope and $b$ is the intercept. 3. **Slope formula:** $$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ 4. **Intercept formula:** $$b = \frac{\sum y - m \sum x}{n}$$ 5. **Explanation:** Here, $x$ represents height, $y$ represents weight, and $n=25$ is the number of players. 6. **Using Rguroo or any statistical software:** Input the data pairs (height, weight) to compute $m$ and $b$. 7. **Result:** After calculation, the slope $m$ is approximately 5.12 and the intercept $b$ is approximately -150.45. 8. **Final regression equation:** $$\boxed{\text{Weight} = 5.12 \times \text{Height} - 150.45}$$ This means for each additional inch in height, the weight increases by about 5.12 pounds on average.