To predict $y$ using the given regression equation:

$\hat{y} = 21.1870 + 0.5701x_1 + 0.4960x_2$

Substitute $x_1 = 160$ and $x_2 = 330$:

$\hat{y} = 21.1870 + 0.5701(160) + 0.4960(330)$

Step-by-step calculation:

1. $0.5701 \times 160 = 91.216$
2. $0.4960 \times 330 = 163.68$
3. Add these results to 21.1870:

$\hat{y} = 21.1870 + 91.216 + 163.68 = 276.083$

Final Prediction:

$\hat{y} = 276.083$

Would you like further explanation or assistance with regression analysis?

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Related Questions:

1. How does changing $x_1$ or $x_2$ influence $\hat{y}$?
2. What do the coefficients $0.5701$ and $0.4960$ represent in this regression?
3. How would we assess the accuracy of this regression model?
4. What statistical tests could be used to evaluate the significance of $x_1$ and $x_2$?
5. How would predictions change if $x_1$ or $x_2$ are highly correlated?

Tip: Always check for multicollinearity and ensure assumptions of linear regression are met before relying on predictions.