During the first three years of their life, the age of a koala bear has a linear association with the koala bear's weight.  The ages and weights of six koala bears were recorded. 

Calculate the slope of the linear regression equation that can be used to predict a koala bear's age using their weight.   Use technology to find the answer.

Round answer to two decimal places  (e.g.  5.1764 would round to 5.18)

Age in months                    26.0           28.2         32.8        22.5            30.6           30.3

Weight in pounds               6.5             6.8           9.4         7.8            8.5           9.0 

Don't forget to round your answer to two decimal places.

Your Answer:

To calculate the slope of the linear regression equation, we can use the formula for the slope \( m \) of a regression line:

\[
m = \frac{n \sum (x_i y_i) - \sum x_i \sum y_i}{n \sum x_i^2 - (\sum x_i)^2}
\]

Where:
- \( x_i \) represents the ages (in months),
- \( y_i \) represents the weights (in pounds),
- \( n \) is the number of data points.

We are given the following dataTo calculate the slope of the linear regression equation, we can use the formula for the slope \( m \) of a regression line:

\[
m = \frac{n \sum (x_i y_i) - \sum x_i \sum y_i}{n \sum x_i^2 - (\sum x_i)^2}
\]

Where:
- \( x_i \) represents the ages (in months),
- \( y_i \) represents the weights (in pounds),
- \( n \) is the number of data points.

We are given the following 

- Ages (in months): \( 26.0, 28.2, 32.8, 22.5, 30.6, 30.3 \)
- Weights (in pounds): \( 6.5, 6.8, 9.4, 7.8, 8.5, 9.0 \)

Let's compute the slope using the formula. I will calculate it step by step.The slope of the linear regression equation that can be used to predict a koala bear's age based on their weight is \( 0.21 \).

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How can we calculate the intercept of the regression line?
2. How would we interpret the slope in this context?
3. What is the full linear regression equation for this data?
4. How can we use the linear regression model to predict the age of a koala bear weighing 10 pounds?
5. How does the correlation coefficient relate to the strength of this linear relationship?

**Tip:** In linear regression, the slope represents how much the dependent variable changes for a one-unit increase in the independent variable.

During the first three years of their life, the age of a koala bear has a linear association with the koala bear's weight. The ages and weights of six koala bears were recorded. Calculate the slope of the linear regression equation that can be used to predict a koala bear's age using their weight. Use technology to find the answer. Round answer to two decimal places. Age in months: 26.0, 28.2, 32.8, 22.5, 30.6, 30.3. Weight in pounds: 6.5, 6.8, 9.4, 7.8, 8.5, 9.0.

Learn how to calculate the slope of a linear regression equation to predict a koala bear's age based on their weight. This problem uses real data with koala bears' ages and weights, covering linear regression concepts and slope calculation. Suitable for high school students in Grades 10-12.

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