The year of origin of the following trend line equation of profit (in millions rupees) is 2017. y=22.5+ 1.5x Estimate the profit for the year 2023.

To estimate the profit for the year 2023 using the given trend line equation \( y = 22.5 + 1.5x \), we need to determine the value of \( x \) for the year 2023. 

Given that the year of origin is 2017, the value of \( x \) represents the number of years since 2017. Therefore, for the year 2023:

\[ x = 2023 - 2017 = 6 \]

Now, substitute \( x = 6 \) into the trend line equation:

\[ y = 22.5 + 1.5(6) \]

Calculate the profit:

\[ y = 22.5 + 9 \]
\[ y = 31.5 \]

Therefore, the estimated profit for the year 2023 is 31.5 million rupees.

Would you like any further details or have any questions?

Here are 5 questions you can ask:
1. How would the profit trend change if the rate of increase was different?
2. Can you explain how to interpret the slope in a trend line equation?
3. How do you calculate profit for other years using the given trend line?
4. What are the limitations of using a trend line for profit estimation?
5. Can you provide an example of a trend line equation in a different context?

Tip: When using a trend line equation, always ensure you correctly identify the base year and the corresponding value of \( x \) for accurate predictions.

Learn how to estimate profit for the year 2023 using the linear regression equation y = 22.5 + 1.5x. This problem involves applying the equation of a line in a real-world context, specifically estimating profit trends over time. Suitable for advanced high school students or anyone interested in linear regression analysis.

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