A data set consists of 20 pairs of observations $\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) , \ldots \ldots \left( x _ { 20 } , y _ { 20 } \right)$ If each $x _ { i }$ is replaced by $x _ { i } - 1$ and if each $y _ { i }$ is replaced by $y _ { i } - 2$ then the sample correlation coefficient r
A) decreases by .05
B) decreases by .10
C) increases by.05
D) increases by .10
E) remains unchanged

Question

Quizplus · Accepted Answer

The sample correlation coefficient $r$ is not affected by linear transformations of the form $x_i' = x_i + a$ and $y_i' = y_i + b$, where $a$ and $b$ are constants. Therefore, subtracting 1 from each $x_i$ and 2 from each $y_i$ does not change the value of $r$.

A Data Set Consists of 20 Pairs of Observations (x1,y1),(x2,y2),……(x20,y20)\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) , \ldots \ldots \left( x _ { 20 } , y _ { 20 } \right)(x1​,y1​),(x2​,y2​),……(x20​,y20​)

A Data Set Consists of 20 Pairs of Observations $\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) , \ldots \ldots \left( x _ { 20 } , y _ { 20 } \right)$