Tag: correlation coefficients

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Questions Related to correlation coefficients

Multiple choice statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

Write True/False in the following statement:
If regression coefficient are $0.8$ and $0.2$ then the value of corelation coefficient is $+0.4$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given:-

Coefficient of regression are $0.8$ and $0.2$.
Therefore,
Coefficient of correlation $= \sqrt{0.8 \cdot 0.2} = \sqrt{0.16} = 0.4$
Hence the given statement is true.

Multiple choice statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

The coefficient of correlation is always between

  1. $0\ and \ 1$
  2. $-1\ and \ 1$
  3. $-\infty \ and \ \infty$
  4. $-10\ and \ 10$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Correlation coefficients are expressed as values between $-1$ and $+1$. 

$\Rightarrow$  A coefficient of $+1$ indicates a perfect positive correlation: A change in the value of one variable will predict a change in the same direction in the second variable. 
$\Rightarrow$  A coefficient of $-1$ indicates a perfect negative correlation: A change in the value of one variable predicts a change in the opposite direction in the second variable. 

Multiple choice statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

The formula for correlation coeficient $r$ of two variables $x$ and $y$ is 

  1. $u _i=\dfrac{x _i-a}{h}$,
  2. $\dfrac{1}{n}\sum(x-\overline x)(y-\overline y)$
  3. $\dfrac{d _xd _y}{\sqrt{{\sum d _x}^2.{\sum d _y}^2}}$
  4. $\dfrac{\sum xy}{\sigma _x \sigma _y}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The formula provided in option C is a standard representation of the correlation coefficient using deviations from the mean or assumed mean (d_x and d_y).

Multiple choice statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

State the following statement is true or false

The value of coefficient of correlation is greater than $1$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Value of coeff. of correlation lies between $-1$ and $+1$.
Depending on the strength & direction of linear relationship between two variable. 
Coeff. of correlation $\ngtr   1$
$\therefore $ Given statement is false.
Multiple choice statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

State the following statement is True or False
The value of correlation coefficient is always $2$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Correlation coefficient is the measure of the degree of linear relationship between two variables, usually labelled X and Y. While in regression the emphasis is on predicting one variable from the other, in correlation the emphasis is on the degree to which a linear model may describe the relationship between two variables. In regression the interest is directional, one variable is predicted and the other is the predictor; in correlation the interest is non-directional, the relationship is the critical aspect.

$-1\le r\le 1$

Hence statement is false

Multiple choice statistics linear correlation coefficient of correlation correlation coefficient correlation coefficients

Consider the following statements :
1. Two independent variables are always uncorrelated.
2. The coefficient of correlation between two variables X and Y is positive. When X decreases then Y decreases.
Which of the above statements is/are correct ?

  1. 1 only

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Two independent variables have coefficient of correlation $0$, So they are always uncorrelated.

Positive coefficient means they both move in same direction, so if $X$ decreases then $Y$ also decreases.
So, both the statements are correct.
Hence, C is correct.