LEAST SQUARES REGRESSION LINE?

Question

The graph and accompanying table shown here display 12 observations of a pair of variables (x, y).

The variables x and y are positively correlated, with a correlation coefficient of r = 0.96.

You estimate the slope of the least squares regression line, y = a + bx, for these data values to be b = 1.7. What is the y-intercept, a, of the least squares regression line? Round your answer to the nearest tenth.

x 3 6 8 9 9 13 15 18 20 21 23 23

y 9 17 15 15 18 24 29 36 43 39 46 35

Answer 1

It can be shown that the point (xbar, ybar) lies on the regression line (where xbar is the sum of the x-values divided by the number of values, and similarly for ybar). If the slope b is 1.7, then

a = ybar - b*xbar

I leave the arithmetic to you.