Let's analyze the questions step by step:

Question 24: Correlation Coefficient

The correlation coefficient ($r$) quantifies the linear relationship between two variables $x$ and $y$. Using the given data, we calculate $r$. Based on the question, the options are:

• $a. -0.923$
• $b. -0.852$
• $c. -1.820$ (invalid since $r$ cannot exceed $-1$ or $1$)
• $d. -0.077$

Question 25: Least-Squares Regression Line

The least-squares regression equation is given as: $y = a + b x$ where:

• $b$ (slope) = $r \cdot \frac{s_y}{s_x}$
• $a$ (intercept) = $\bar{y} - b \cdot \bar{x}$

From the solution provided, the equation in question was chosen as $y = 481.4 - 1.8x$. However, the teacher notes an error, indicating a miscalculation for $a$ or $b$.

Question 26: Prediction

Using the regression equation $y = 481.4 - 1.8x$ and $x = 112.3$, the predicted $y$ is: $y = 481.4 - 1.8(112.3)$

When recalculated with accurate values of $a$ and $b$, the outcome should align with one of the provided options. In this case, the teacher explains that the prediction is invalid due to an earlier error.

If you'd like, I can help verify the exact calculations for each step (correlation coefficient, regression equation, and prediction). Would you like me to do that?

Expanded Questions:

1. Would you like a detailed breakdown of the correlation coefficient calculation?
2. Do you want me to recalculate the regression equation with the given data?
3. Should I verify the prediction using the corrected regression equation?
4. Would you like help understanding the significance of $r$ and regression equations in this context?
5. Do you want an explanation on how errors in regression parameters affect predictions?

Tip:

Always recheck regression equation parameters ($a$ and $b$) by substituting them back into the original formula to confirm accuracy.