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The question asks to find the correlation between verbal and math scores, based on the given regression equation \(\hat{y} = 188 + 0.6x\).

### Key information:
- **Verbal Scores** (\(x\)): mean = 420, standard deviation = 80
- **Math Scores** (\(y\)): mean = 440, standard deviation = 60
- **Regression Equation**: \(\hat{y} = 188 + 0.6x\)

### Step-by-step reasoning:
The formula for the least-squares regression line is given by:

\[
\hat{y} = b_0 + b_1 x
\]

Here, \(b_1\) (the slope) is 0.6, which represents the change in the math score (y) for each 1-point increase in the verbal score (x).

The correlation \(r\) between the two variables can be calculated using the following relationship between the slope of the regression line and the correlation coefficient:

\[
r = \frac{b_1 \cdot \sigma_x}{\sigma_y}
\]

Where:
- \(b_1 = 0.6\)
- \(\sigma_x = 80\) (standard deviation of verbal scores)
- \(\sigma_y = 60\) (standard deviation of math scores)

Substituting the values:

\[
r = \frac{0.6 \cdot 80}{60}
\]

\[
r = \frac{48}{60} = 0.8
\]

Thus, the correlation between verbal and math scores is **0.8**.

### Correct answer: **0.8**

Would you like further explanation or details? Here are some related questions:

1. How does the slope of a regression line relate to the correlation coefficient?
2. What is the significance of a correlation coefficient of 0.8?
3. How do standard deviations influence the correlation in regression?
4. Can you explain how the least-squares regression minimizes errors?
5. How would the correlation change if the standard deviations of the variables changed?

**Tip:** In regression, the closer the correlation is to 1 or -1, the stronger the linear relationship between two variables.

Scores on the 1995 SAT verbal aptitude test x among Kentucky high school seniors were normally distributed with mean 420 and standard deviation 80. Scores on the 1995 SAT quantitative aptitude test y among Kentucky high school seniors were normally distributed with mean 440 and standard deviation 60. The least-squares regression line has the equation ŷ = 188 + 0.6x. What is the correlation between verbal scores and math scores?

This problem explores the correlation between verbal and math scores for Kentucky high school seniors in the 1995 SAT. It covers regression analysis and statistical concepts, including the formula for calculating correlation using standard deviations and the slope of the regression line. Suitable for high school students in Grades 10-12.

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