To estimate the profit in 1967, we calculate $X$ first:

Step 1: Determine $X$

Since $X$ represents the number of years after 1960: $X = 1967 - 1960 = 7$

Step 2: Use the linear model

The given model is: $Y = 0.38X + 14.81$ Substitute $X = 7$ into the equation: $Y = 0.38(7) + 14.81$

Step 3: Calculate $Y$

$Y = 2.66 + 14.81 = 17.47$

Final Answer:

The estimated profit in 1967 is: $Y = 17.47$

Would you like a detailed explanation or assistance with related calculations?

Related Questions:

1. How is the slope $0.38$ interpreted in the context of this problem?
2. What would be the estimated profit in 1970 using this model?
3. How does the actual profit for $X = 7$ (from the table) compare to the estimated value?
4. Can this linear model predict accurately beyond 1967? Why or why not?
5. What is the intercept $14.81$, and what does it represent in this scenario?

Tip:

Always check if the given data points closely align with the model for better reliability of predictions!