Let's address Part 3 of 3 where we predict the price when the prime interest rate is 4.5%.

We use the given least-squares regression line equation:

$\hat{y} = a + b \cdot x$ Where:

• $a = 1.84227408$ (y-intercept)
• $b = 0.36006575$ (slope)
• $x = 4.5$ (interest rate)

Now, substitute $x = 4.5$ into the equation:

$\hat{y} = 1.84227408 + 0.36006575 \cdot 4.5$

Calculation:

$\hat{y} = 1.84227408 + (0.36006575 \times 4.5)$

$\hat{y} = 1.84227408 + 1.620295875$

$\hat{y} = 3.46256996$

Final Answer:

The predicted price when the prime interest rate is 4.5% is approximately:

$\hat{y} = 3.4626$

Let me know if you want a step-by-step explanation or further clarification. Here are 5 related questions to expand your understanding:

1. What does the slope $b$ represent in the context of this regression equation?
2. How does the correlation coefficient $r$ indicate the strength and direction of the relationship?
3. If the interest rate increases to 6%, how would you predict the price?
4. What is the significance of the $r^2$-value in a regression model?
5. How would you interpret the y-intercept $a$ of the equation?

Tip: In regression, the closer $r$ is to $1$ or $-1$, the stronger the linear relationship between the variables.