Math Snap

STEP 1

What is this asking?
Given a regression equation, correlation coefficient, critical value, and centroid, predict the y-value for a specific x-value.
Watch out!
Don't forget to consider the critical value when deciding whether to use the regression equation or the mean y-value from the centroid for prediction!

STEP 2

1. Compare the correlation coefficient and the critical value.
2. Predict the y-value.

STEP 3

The absolute value of the correlation coefficient is $|0.325| = 0.325$.
This tells us the strength of the linear relationship between x and y.

STEP 4

We're given a critical value of $0.632$.
Since $0.325$ is less than $0.632$, the correlation is not statistically significant.
This means we shouldn't use the regression equation for prediction!

STEP 5

Since the correlation isn't significant, the best prediction for any x-value is simply the average y-value, which is given by the y-coordinate of the centroid.
Our centroid is $(5.9, 24.8)$, so the mean y-value is **$24.8$‌.

STEP 6

Therefore, when $x = 3.9$, our predicted y-value is $\hat{y} = 24.8$.

The predicted y-value when $x = 3.9$ is $24.8$.