The given multiple regression equation is:

$\hat{y} = -3.2 + 0.012x_1 + 0.23x_2$

where:

• $\hat{y}$ represents the predicted number of accidents per year.
• $x_1$ is the person's age.
• $x_2$ is the number of hours the person works per week.

We need to predict the number of accidents per year for a person who is 49 years old and works 54 hours per week. Plug the values $x_1 = 49$ and $x_2 = 54$ into the equation:

$\hat{y} = -3.2 + 0.012(49) + 0.23(54)$

Let's calculate this step by step:

1. Calculate $0.012 \times 49$: $0.012 \times 49 = 0.588$

2. Calculate $0.23 \times 54$: $0.23 \times 54 = 12.42$

3. Now, sum these values along with $-3.2$: $\hat{y} = -3.2 + 0.588 + 12.42 = 9.808$

Since the problem asks for the number of accidents per year to the nearest whole number:

$\hat{y} \approx 10$

So, the predicted number of accidents per year is 10.

Would you like more details on how the calculation works or have any other questions? Here are some related questions:

1. How would the prediction change if the age were increased to 60 years?
2. What happens to the prediction if the person works fewer hours, say 40 hours per week?
3. Can you explain what each coefficient in the regression equation represents?
4. How can this model be used to assess risk in different work environments?
5. What is the impact of multicollinearity on multiple regression models?
6. How would you calculate the residual for a person with a known number of accidents?
7. Can this regression equation be used to make predictions for extreme values of age or work hours?
8. How does one determine if a regression model is a good fit for the data?

Tip: Always check the range of your input variables to ensure they fall within the scope of the data used to create the regression model. This ensures more accurate predictions.