Question

X value - 20 25 30 35 40 45 50 55
Y value- 8 10 12 9 7 6 7 4
Find the three median regression line

Answer 1

To find the three median regression line of the given data points, we first need to sort the data in ascending order based on the X values:

X: 20, 25, 30, 35, 40, 45, 50, 55
Y: 8, 10, 12, 9, 7, 6, 7, 4

Next, we find the median of X and Y values:

Median X = (30 + 35)/2 = 32.5
Median Y = (10 + 9)/2 = 9.5

Now, we calculate the slopes of lines connecting the points to the median:

For points (25, 10) and (32.5, 9.5):
m1 = (9.5 - 10) / (32.5 - 25) = -0.083

For points (30, 12) and (32.5, 9.5):
m2 = (9.5 - 12) / (32.5 - 30) = -0.75

For points (35, 9) and (32.5, 9.5):
m3 = (9.5 - 9) / (32.5 - 35) = 0.125

The three median regression lines are:
Y = -0.083(X - 32.5) + 9.5
Y = -0.75(X - 32.5) + 9.5
Y = 0.125(X - 32.5) + 9.5