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It appears you've uploaded an image containing a table with data for heating times and their corresponding maximum heart rates for two different gas burners. You're looking for a linear function that best models this data, and you've also asked about the correlation coefficient \( r \).

To start, let's analyze the data from your image:

### Data for Burner A
- Heating Time (s): [60, 90, 120, 150]
- Maximum Heart Rate (beats per minute): [70, 75, 80, 82]

### Data for Burner B
- Heating Time (s): [60, 90, 120, 150]
- Maximum Heart Rate (beats per minute): [76, 79, 85, 88]

Now, I'll calculate the linear regression model for both datasets to find the best-fitting line for each burner. I'll also compute the correlation coefficient \( r \) for each dataset to assess the strength and direction of a linear relationship between heating time and heart rate.

Let's compute this now.The linear functions that best model the data for each gas burner and their respective correlation coefficients are as follows:

### Burner A
- **Linear Equation:** \( y = 0.14x + 62.40 \)
- **Correlation Coefficient \( r \):** 0.984

### Burner B
- **Linear Equation:** \( y = 0.14x + 67.30 \)
- **Correlation Coefficient \( r \):** 0.990

These equations suggest that for every second increase in heating time, the maximum heart rate increases by 0.14 beats per minute. The correlation coefficients are very high, indicating a strong positive linear relationship between the heating time and the heart rate for both burners.

If you have any questions or need further details, please let me know! Here are some additional topics you might consider:

1. Would you like to know how these equations can be used to predict heart rate at different times?
2. Are you interested in understanding why the intercepts of the equations for Burner A and Burner B are different?
3. Do you want to explore how the strength of correlation affects the prediction accuracy?
4. Would you like a visual graph of the data alongside the regression line?
5. Are there any other types of regression (e.g., polynomial) that you'd like to consider for this data?

**Tip:** When interpreting the correlation coefficient, a value close to 1 or -1 indicates a strong linear relationship, while a value close to 0 suggests little to no linear relationship.

A person who is exercising should not exceed his or her maximum heart rate, which is determined on the basis of that person's gender, age, and resting heart rate. The table relates heating heart rate and maximum heart rate for a 60-year-old man. Find the linear function that best models the data.

Explore how to calculate the linear regression model for heating time and maximum heart rate data. Learn about the strong linear relationship, represented by the equations y = 0.14x + 62.40 for Burner A and y = 0.14x + 67.30 for Burner B, and how the correlation coefficient helps assess this relationship.

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