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A real estate agent records the living area (\(x\)) in square meters (\(m^2\)) and the selling price (\(y\)) in thousands of dollars of 6 recently sold apartments in a neighborhood.
Area (\(x\)) 60 75 90 110 130 150
Price (\(y\)) 180 220 250 310 350 410
  1. Write down the equation of the regression line of \(y\) on \(x\) in the form \(y = ax + b\) using a calculator.
  2. Interpret the value of \(a\) in the context of the problem.
  3. Calculate the coefficient of determination, \(r^2\), and explain what it indicates.
  4. Estimate the selling price of an apartment with an area of \(100 \text{ m}^2\).
  5. Comment on the validity of using this model to estimate the price of a castle with an area of \(1000 \text{ m}^2\).

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