Let's go through the problem step by step to determine the regression equation.

Given Data:

• Age ($x$) and Hours ($y$) jogged per week:

  • $x = [34, 22, 48, 56, 62]$
  • $y = [3.5, 7, 2.5, 2, 1]$

• Correlation coefficient, $r = -0.951$, is also provided.

Step 1: Compute the Regression Line Equation

The equation of a linear regression line is given by: $y = b_0 + b_1 x$ Where:

• $b_1 = r \cdot \frac{s_y}{s_x}$ is the slope of the line.
• $b_0 = \bar{y} - b_1 \cdot \bar{x}$ is the y-intercept.
• $\bar{x}$ and $\bar{y}$ are the means of $x$ and $y$.
• $s_x$ and $s_y$ are the standard deviations of $x$ and $y$, respectively.

Step 2: Compute the necessary values

• Means of $x$ and $y$: $\bar{x}$ and $\bar{y}$
• Standard deviations of $x$ and $y$: $s_x$ and $s_y$
• Calculate slope $b_1$ and intercept $b_0$.

Let me calculate those values for you.The equation of the regression line is:

$y = 9.1653 - 0.1344x$

Both values are rounded to four decimal places as requested.

Interpretation:

• The slope ($b_1 = -0.1344$) indicates that for every additional year in age, the number of hours jogged per week decreases by approximately 0.1344 hours.
• The intercept ($b_0 = 9.1653$) represents the estimated number of hours jogged when the age is 0, which is more of a theoretical value for this context.

Would you like further details or explanations on any part of the calculation?

Here are 5 related questions you might explore:

1. How would you interpret the correlation coefficient $r = -0.951$?
2. How do we determine if $r$ is significant at the 5% level?
3. Can we use this regression equation for ages outside the provided data range?
4. How would a positive correlation affect the slope of the line?
5. What assumptions underlie the linear regression model?

Tip: Always check the residuals of your regression model to verify how well the model fits the data.