To predict the monthly precipitation using the regression equation:

$\hat{y} = 0.24x + 13.98$

Where:

• $x$ is the temperature in degrees Fahrenheit,
• $\hat{y}$ is the predicted monthly precipitation in inches.

Step 1: Substitute $x = 87$ into the equation.

$\hat{y} = 0.24(87) + 13.98$

Step 2: Perform the multiplication.

$0.24 \times 87 = 20.88$

Step 3: Add 13.98 to the result.

$\hat{y} = 20.88 + 13.98 = 34.86$

Final Answer:

The predicted monthly precipitation when the temperature is 87 degrees is 34.86 inches.

Would you like to go over the calculation steps in more detail or ask any further questions?

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Related Questions:

1. How is the slope of a regression line interpreted in this context?
2. What does the y-intercept ($13.98$) represent in this regression model?
3. Why does the regression line apply only to the range 75–90 degrees?
4. What are the limitations of using this linear model for predictions?
5. How can we assess whether this regression line fits the data well?

Tip:

Always verify that the prediction lies within the intended range of the model to avoid extrapolation errors.