LINEAR CORRELATION — Statistics STD 12 Commerce — Question
Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsLINEAR CORRELATION3 Marks
Question
Interpret $r = 1, r = -1$ and $r = 0.$
✓
Answer
$(1)\ r = 1 :$
If correlation coefficient between two correlated variables $X$ and $Y, r = 1$ then we can say that there is a perfect positive correlation between two variables.
That means values of both the variables change proportionally in the same direction.
Coefficient between two variables $X$ and $Y$ can be expressed by the equation $y = a + bx,$ where $b > 0.$
In such cases all the points on the scatter diagram lie on the line which is going in the upward direction from left to right.
$(2)\ r = -1 :$
If correlation coefficient between two correlated variables $X$ and $Y, r = -1$ then we can say that there is a perfect negative correlation between two variables.
That means values of both the variables change proportionally in the opposite direction.
Coefficient between two variables $X$ and $Y$ can be expressed by the equation $y = a + bx,$ where $b < 0.$
In such cases all the points on the scatter diagram lie on the line which is going in the downward direction from left to right.
$(3)\ r = 0 :$
If correlation coefficient between two correlated variables $X$ and $Y, r = 0$ the we can say that there is no linear correlation between two variables.
That means there are random changes in the values of both the variables and changes in the values one variable due to the changes in the values of other variables cannot be estimated.
In such cases all the points of the scatter diagram lie randomly without forming any specific pattern.
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