The data extracted from the image includes the height (in cm) and weight (in kg) of 10 students. Now, let's proceed to address your questions:

1. Find the value of $r$ (correlation coefficient) and interpret it.

We'll calculate Pearson's correlation coefficient between height and weight.

2. Determine the regression line.

We will calculate the linear regression equation in the form $y = mx + b$, where $y$ is weight, $x$ is height, $m$ is the slope, and $b$ is the y-intercept.

3. Predict the weight of a student whose height is:

• $a.$ 130 cm
• $b.$ 205 cm

Let's start by computing the correlation coefficient $r$, the regression line, and predictions.### 1. Correlation Coefficient ($r$):

The value of the correlation coefficient $r$ is 0.948. This indicates a strong positive correlation between height and weight, meaning as height increases, weight tends to increase as well.

2. Regression Line:

The equation of the regression line is:

$y = 0.912x - 83.001$

Where:

• $y$ represents the predicted weight (kg),
• $x$ represents the height (cm).

3. Predictions:

Using the regression line, the predicted weights are:

• For a height of 130 cm: 35.54 kg
• For a height of 205 cm: 103.93 kg

4. Two Real-Life Situations for Predicting Weight from Height:

1. Healthcare and Nutrition: Doctors can use this relationship to estimate healthy weight ranges for individuals of different heights to assess risks related to underweight or overweight.
2. Sports and Fitness: Coaches may predict the ideal weight for athletes based on their height to optimize performance in certain sports where body mass is a critical factor.

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. How is the strength of correlation measured, and what is considered a "strong" correlation?
2. How can we interpret the slope and intercept of the regression line in context?
3. What factors might affect the reliability of predictions based solely on height?
4. Can we use this same model to predict weight for individuals significantly outside this data range?
5. What other variables could be considered to improve predictions of weight?

Tip: Always check the assumptions of linear regression, such as linearity, before trusting the model's predictions.