https://file.aiquickdraw.com/mathbot/file/1727268504916djbzi4uj.pdf

The file contains an advanced functions worksheet focused on **linear regression**. It provides several data tables and asks for the following:

1. **Linear regression equation**: You need to use a calculator to find the regression line in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the intercept, based on the given data.
   
2. **Correlation coefficient (r)**: This measures the strength and direction of the relationship between the variables (no rounding).

3. For each scenario, additional questions ask for predictions using the regression equation, such as estimating values for given inputs (e.g., years coaching, geographical area covered, percent of women in professional jobs).

### Examples of the problems:
- **Football coach wins**: Predicting wins based on years coaching, or finding how long a coach with 231 wins has been coaching.
- **Acorn size and geographical area**: Predicting the acorn size given the geographical area and vice versa.
- **Women's employment data**: Estimating the percentage of women in managerial roles for specific future years.

Do you want me to walk through any of these specific problems or explain how to solve them using a calculator?

Here are some related questions:
1. How do you calculate the slope \( m \) and intercept \( b \) for a regression line?
2. How can you determine the correlation coefficient from a data set?
3. What does the correlation coefficient tell you about the strength of the relationship?
4. How can you use a regression equation to make predictions?
5. Why is it important not to round the values in linear regression?

**Tip**: Ensure you have the data entered correctly into your calculator, as even small errors can lead to incorrect regression equations and predictions.

The file contains an advanced functions worksheet focused on linear regression. It provides several data tables, asking for the linear regression equation, the correlation coefficient (r), and predictions based on the regression equation. Problems include predicting football coach wins based on years coaching, estimating acorn sizes from geographical areas, and projecting percentages of women in managerial roles.

Solve real-world problems using linear regression. This worksheet covers football coach wins based on years of coaching, acorn size prediction from geographical areas, and forecasting the percentage of women in managerial jobs. Learn to calculate regression equations, correlation coefficients, and make predictions. Suitable for Grades 10-12.

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