To find the linear regression equation for the given data, we first need to calculate the slope ($m$) and intercept ($b$) of the line of best fit. The linear regression equation is given by:

$y = mx + b$

where $y$ is the price of the house, and $x$ is the size of the house.

Step 1: Calculate the Means

• Mean of size ($\bar{x}$): $\bar{x} = \frac{1200 + 1339 + 1382 + 2351 + 2369 + 3600}{6} = 2040$

• Mean of price ($\bar{y}$): $\bar{y} = \frac{320 + 430 + 389 + 635 + 689 + 750}{6} = 535.5$

Step 2: Calculate the Slope ($m$)

The formula for the slope is: $m = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}}$

• $\sum{(x_i - \bar{x})(y_i - \bar{y})} = (1200-2040)(320-535.5) + (1339-2040)(430-535.5) + (1382-2040)(389-535.5) +$

  $(2351-2040)(635-535.5) + (2369-2040)(689-535.5) + (3600-2040)(750-535.5)$

  $= 333047.5$

• $\sum{(x_i - \bar{x})^2} = (1200-2040)^2 + (1339-2040)^2 + (1382-2040)^2 + (2351-2040)^2 + (2369-2040)^2 + (3600-2040)^2$

  $= 3904402$

Thus, the slope ($m$) is: $m = \frac{333047.5}{3904402} \approx 0.0853$

Step 3: Calculate the Intercept ($b$)

The formula for the intercept is: $b = \bar{y} - m\bar{x}$

$b = 535.5 - 0.0853 \times 2040 \approx 361.158$

Linear Regression Equation

The linear regression equation is approximately:

$y = 0.0853x + 361.158$