To solve this, we first need to determine the linear regression equation, typically written as:

$y = mx + b$

where:

• $m$ is the slope of the line, representing the rate of change in profit over time.
• $b$ is the y-intercept, representing the profit at $x = 0$ (the year 1995).

Step 1: Organize the data

Let's assume the table of profits looks something like this:

Year (Calendar)	$x$ (Years since 1995)	$y$ (Profit in 1000s of dollars)
1995	0	$y_1$
1996	1	$y_2$
1997	2	$y_3$
...	...	...

If you provide the actual data, I can calculate the exact equation. If no data is given, I can guide you on how to compute it manually or generate a fictional example.

---

Step 2: Calculate the slope ($m$) and y-intercept ($b$)

The formulas are:

1. Slope ($m$): $m = \frac{n\sum(xy) - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$
2. Intercept ($b$): $b = \frac{\sum y - m \sum x}{n}$

Where:

• $n$ = number of data points
• $\sum x$, $\sum y$, $\sum xy$, and $\sum x^2$ are summations based on the data.

---

Step 3: Solve for the year when profit reaches 207

Once the equation $y = mx + b$ is found:

1. Substitute $y = 207$ (profit in thousands of dollars) into the equation.
2. Solve for $x$, then add this $x$ to 1995 to find the calendar year.

---

Please share the specific values for the table, or I can create an example to illustrate the steps! Would you like me to calculate an example or proceed further?

---

Related Questions

1. How do you calculate the slope ($m$) and intercept ($b$) manually using specific data?
2. What is the significance of linear regression in predicting trends in profits?
3. How can the coefficient of determination ($R^2$) be used to measure the accuracy of this regression?
4. How does rounding coefficients affect the precision of predictions?
5. What other regression models might be used for more complex profit data?

Tip: Linear regression assumes a straight-line relationship. If your data shows a non-linear trend, consider higher-degree polynomial regression for better accuracy!