Consider the following data: Year20082009201020112012 Production (in…

The correct answer is Option (2) → \(y=74+4.5x\)

There are 5 years, an odd number, so the usual choice is to take the middle year 2010 as the origin: x = year − 2010, giving x = −2, −1, 0, 1, 2. Then \(\Sigma x = 0\), and the normal equations of y = a + bx give

    \( \displaystyle a = \frac{\Sigma y}{n}, \quad b = \frac{\Sigma xy}{\Sigma x^2} \)

The sums:

    \(\Sigma y = 60 + 75 + 80 + 70 + 85 = 370\)
    \(\Sigma xy = -120 - 75 + 0 + 70 + 170 = 45\)
    \(\Sigma x^2 = 4 + 1 + 0 + 1 + 4 = 10\)

So

    \( \displaystyle a = \frac{370}{5} = 74, \quad b = \frac{45}{10} = 4.5 \)

The trend line is y = 74 + 4.5x, with origin 2010 and x measured in years.