Question

The regression coefficients remain unchanged due to a shift of ______ but change due to a shift of _______

• A. scale, origin
• B. origin, scale
• C. rank, origin
• D. scale, rank

Answer 1

Answer: (B)

origin, scale

By properties of regression line we have,

The regression coefficients remain unchanged due to a shift of origin but change due to a shift of scale.

That is, if the original pair of variables is $(x,y)$ and if they are changed to the pair $(u,v)$ where $u=\frac{x-a}{p},v=\frac{y-c}{q}$ then $b_{yx}=\frac{q}{p}\times b_{uv}$ and $b_{xy}=\frac{p}{q}\times b_{uv}$

Hence option $\left(B\right)$ is correct.