Question

If x = 3u + 1 and y = 4v + 2 and the regression coefficient between u and v is 1.2, then find regression coefficient between x and y?
1. 0.8
2. 1
3. 0.9
4. 1.5

Answer 1

Correct Answer - Option 3 : 0.9

1 - Given

X = 3u + 1

Y = 4v + 2

Regression coefficient between x and y = (b_uv) = 1.2

Formula

Regression coefficient are independent of origin but depend on scale

If u = ax + b and v = cy + d

Then b_uv = (a/c) × b_xy

Calculation

According to the question

x = 3u + 1

⇒ u = x/3 – 1/3

Similarly

v = y/4 – 1/2

By using b_uv = (a/c) × b_xy

⇒ 1.2 = (1/3)/(1/4)b_xy

⇒ 1.2 = (4/3)b_xy

⇒ b_xy = 3 × 1.2/4

∴ Regression coefficient between x and y is 0.9