To solve this, we'll go step by step:

Step 1: Check if the correlation coefficient $r$ is significant at the 5% level.

Given:

• $r \approx -0.951$
• Significance level = 5%

To check the significance of $r$, we compare the calculated value of $r$ with the critical value of $r$ from a table (based on sample size and significance level). The sample size $n$ is 5 (since we have 5 data points).

Degrees of Freedom (df)

$\text{df} = n - 2 = 5 - 2 = 3$

For $df = 3$ and a significance level of 0.05, the critical value of $r$ is approximately 0.878.

Since the absolute value of $r$, i.e., $|r| = 0.951$, is greater than the critical value of 0.878, $r$ is significant at the 5% level.

Step 2: Calculate the equation of the regression line.

The regression line equation is of the form: $y = b_1 x + b_0$ Where:

• $b_1$ is the slope
• $b_0$ is the y-intercept

Formula for slope $b_1$:

$b_1 = r \left( \frac{s_y}{s_x} \right)$ Where:

• $s_y$ is the standard deviation of the hours jogged (y-values)
• $s_x$ is the standard deviation of the ages (x-values)

Formula for intercept $b_0$:

$b_0 = \bar{y} - b_1 \bar{x}$ Where $\bar{x}$ and $\bar{y}$ are the means of the x-values and y-values, respectively.

Now, let's calculate these values.

• $\bar{x}$ (mean of ages) = $\frac{34 + 22 + 48 + 56 + 62}{5}$
• $\bar{y}$ (mean of hours jogged) = $\frac{3.5 + 7 + 2.5 + 2 + 1}{5}$

Let's compute the slope $b_1$ and intercept $b_0$.The calculations give us the following results:

• Mean of ages ($\bar{x}$) = 44.4
• Mean of hours jogged ($\bar{y}$) = 3.2
• Standard deviation of ages ($s_x$) = 16.3340
• Standard deviation of hours jogged ($s_y$) = 2.3076
• Slope ($b_1$) ≈ -0.1344
• Intercept ($b_0$) ≈ 9.1653

Equation of the regression line:

$y = -0.1344x + 9.1653$

This is the equation of the regression line.

Since $r$ is significant, we can proceed to plot the scatter plot and regression line.

Would you like me to plot the regression line along with the scatter plot? If yes, I can generate that for you.

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Here are 5 related questions to expand the discussion:

1. What is the interpretation of the slope in this regression line?
2. How would the regression line change if the correlation were closer to 0?
3. Can we predict the number of hours jogged for someone aged 40 using this regression equation?
4. How does the standard deviation of the data affect the slope of the regression line?
5. What would the effect of removing an outlier (like a 22-year-old jogging 7 hours) have on the line?

Tip:

Always check the significance of the correlation coefficient before interpreting a regression line.