Let's break down the problem step-by-step.

Given Data:

• Sample size $n = 104$
• Mean total length of possum $\bar{y} = 87.1 \, \text{cm}$
• Standard deviation of total length $s_y = 4.3 \, \text{cm}$
• Mean foot length $\bar{x} = 6.8 \, \text{cm}$
• Standard deviation of foot length $s_x = 0.4 \, \text{cm}$
• Correlation between total length and foot length $r = 0.445$

(a) Identify the mean and standard deviation of $x$ and $y$

From the provided table:

• $\bar{x} = 6.8$
• $s_x = 0.4$
• $\bar{y} = 87.1$
• $s_y = 4.3$

(b) Calculate the slope of the regression line, $b$

The formula for the slope $b$ of the regression line is: $b = r \times \frac{s_y}{s_x}$

Substituting the values: $b = 0.445 \times \frac{4.3}{0.4}$

Let me calculate that.

(c) Calculate the y-intercept of the regression line, $a$

The formula for the y-intercept $a$ is: $a = \bar{y} - b \times \bar{x}$ We will compute this after finding $b$.

(d) The least-squares regression line

Once we have both $b$ and $a$, the equation of the regression line will be: $y = a + b \times x$

Let me first calculate the slope $b$.The slope of the regression line, $b$, is approximately 4.784.

Now, let's calculate the y-intercept $a$ using the formula:

$a = \bar{y} - b \times \bar{x}$ Substituting the values: $a = 87.1 - 4.784 \times 6.8$

Let me calculate that next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the calculation:

To find the y-intercept $a$: $a = 87.1 - 4.784 \times 6.8$ You can manually compute this value by multiplying 4.784 by 6.8 and then subtracting the result from 87.1.

Would you like further help with this, or any other part of the question?

Here are 5 related questions for practice:

1. How does the correlation $r$ affect the slope of the regression line?
2. What does the slope $b$ represent in terms of foot length and total length?
3. How would you interpret a negative correlation in a similar problem?
4. How can you predict the total length if you only know the foot length?
5. How would outliers in the data affect the regression line?

Tip: When interpreting regression results, always keep in mind the units of both the independent and dependent variables to give meaningful context.