Sangeetha Pulapaka

The equation of the least squares line is given by y \approx a + bx where b is the slope of the line and a is the a is the y-intercept or the value of y when x = 0.

Below is the table created by the given data. The number of faculty owned personal computers is the dependent variable, y, which depends on the number of years, x. So, considering 2010 to be year 0 and 2015 to be year 5 we prepare the table shown below.

The slope, b, and the y-intercept, a, can be found by the formula.

a = \frac{n\sum x y - \sum x \sum y}{ n\sum x^{2} - (\sum x)^{2}}

b = \frac{1}{n}(\sum y-a \sum x)

Plugging in the values in the table in the above formulae we get

a = \frac{6 (30380) - (15)(7245)}{ 6(55) - (15)^{2}}

= \frac{73605}{105} = 701

Similarly b = \frac{1}{6}(7245- 701(15)) = -545

Plugging these in the equation of the regression line we get

y \approx 701 x - 545