If , , n = 12, and the slope equals 0.5, then the y-intercept of the least squares line is b₀ = 276.08.

Question

Quizplus · Accepted Answer

Using the formula for the least squares line (y = mx + b), where m is the slope and b is the y-intercept, and plugging in the given slope of 0.5 and the three data points (n=12 is not used in this calculation), we can solve for b:

For the first data point: 
276.08 = 0.5(11) + b
b = 270.58

For the second data point:
579.34 = 0.5(11) + b
b = 573.84

For the third data point:
328.91 = 0.5(11) + b
b = 323.41

Taking the average of these three values for b, we get:

b = (270.58 + 573.84 + 323.41)/3 = 389.277

Therefore, the statement is false; the y-intercept of the least squares line is approximately 389.277, not 276.08.

If , , N = 12, and the Slope