To find the linear regression equation, you need to determine the relationship between the size of the house (in square feet) and the price of the house (in thousands of dollars). The equation of a line is given by:

$y = mx + c$

where $y$ is the dependent variable (price), $x$ is the independent variable (size), $m$ is the slope, and $c$ is the y-intercept.

Here's a step-by-step approach using the given data:

1. Calculate the Means:

   • Mean of $x$ (size): $(1200 + 1339 + 1382 + 2351 + 2369 + 3600) / 6$
   • Mean of $y$ (price): $(320 + 430 + 389 + 635 + 689 + 750) / 6$

2. Calculate the Slope $m$: $m = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}}$

3. Calculate the Intercept $c$: $c = \bar{y} - m\bar{x}$

Let's plug in the values:

1. Means:

   • Mean of $x$: $\bar{x} = 2040.17$
   • Mean of $y$: $\bar{y} = 535.5$

2. Slope $m$: $m = \frac{(1200-2040.17)(320-535.5) + (1339-2040.17)(430-535.5) + \ldots + (3600-2040.17)(750-535.5)}{(1200-2040.17)^2 + (1339-2040.17)^2 + \ldots + (3600-2040.17)^2}$

   After calculation:

   $m \approx 0.216$

3. Intercept $c$: $c = 535.5 - 0.216 \times 2040.17 \approx 94.92$

Thus, the linear regression equation is approximately:

$y = 0.216x + 94.92$