Statistical Co-relation and Regression

Last Updated on: 11th June 2025, 02:46 pm

Statistical Co-Relation and Regression – MCQ

Now a days, most of the Competitive Exams, Entrance Exams are conducted on MCQ. Click HERE to understand the Forms, Structure, Rules of MCQ, techniques of understanding, analysing and selection correct answer of MCQ,

Play the Video explaining some interesting aspects of selection of correct answer of MCQ.

Click for Complete Resources on Statistical Co-relation & Regression

1. The square root of the multiplication of both the regression coefficients is called
(a) Quartile deviation
(b) Correlation
(c) Mean deviation
(d) Range
Regression coefficients are b_yx & b_xy
r (correlation) = $\displaystyle \sqrt{{}}$ b_yx X $\displaystyle \sqrt{{}}$ b_xy
So, the correct option is (b)

2. If variable Y tends to decrease as variable X decreases, is called
(a) Negative correlation
(b) Inverse correlation
(c) No correlation
(d) Positive correlation
Because trend of both variables in same direction.
So, the correct option is (d)

3. If the coefficient of correlation between X and Y is 0.65, then the coefficient of determination is:
(a) 0.48
(b) 0.52
(c) 0.42
(d) 0.32
r = .65
Co-efficient of determination
= r²= (.65)² = .4225
So, the correct option is (c)

4. If r =0.6, then coefficient of non determination is:
(a) 0.4
(b) -0.6
(c) 0.36
(d) 0.64
Co-efficient of determination = r²
Co-efficient of non-determination = 1 – r²
Here r = .6
$\displaystyle \therefore$ Co-efficient of non – determination
= 1 – (.6)²
= 1 – .36 = .64
So, the correct option is (d)

5. If P.E. is 0.22 and r = + 0.28 the correlation is called
(a) Not useful
(b) Meaningful
(c) Useless
(d) Significant
Co-efficient of correlation is significant if r> 6 P.E.
(P.E. = probable error), r = Coefficient of correlation.
Here
P.E. = .22
r = + .28
6 x P.E. = 1.32
r = .28
$\displaystyle \therefore$ .28 ≯ 1.32
So, correlation is useless.
So, the correct option is (c)

6. The sum of the difference of rank is
(a) 1
(b) -1
(c) 0
(d) None.

Sum of the differences of ranks refers to the sum of the squared differences between the ranks of two variables. None is the correct answer. So, correct option is (d)

7. If two variables have perfectly positively correlation, r =
(a) – 1
(b) 1
(c) 0
(d) Between 0 to 1.
For perfectly positive correlation. Correlation co-efficient is 1
So, the correct option is (b)

8. If two variables are negatively correlated, r =
(a) – 1
(b) + 1
(c) Between 0 and 1
(d) Between -1 and 0.
For negative correlation, r lies between – 1 & 0
So, the correct option is (d)

9. What are the limits of the correlation coefficient?
(a) Non limit
(b) – 1 and 1
(c) 0 and 1, both inclusive
(d) – 1 and 1, both inclusive

So, the correct option is (c)

10. In rank correlation if $\displaystyle \sum{{{{d}^{2}}}}$ = 0 then r =
(a) – 1
(b) +1
(c) 0
(d) None.
$\displaystyle \text{Rank correlation}=1-\frac{{6\sum{{{{d}^{2}}}}}}{{n\left( {{{n}^{2}}-1} \right)}}$

$\displaystyle \sum{{{{d}^{2}}}}$ =0

$\displaystyle r=1-\frac{{6\times 0}}{{n\left( {{{n}^{2}}-1} \right)}}=1-\frac{0}{{n\left( {{{n}^{2}}-1} \right)}}$

=1-0 =1
So, the correct option is (b)

11. r < 0 implies if X increases Y______________.
(a) increase
(b) decrease
(c) perfect
(d) Imperfect
r < 0 means correlation is negative that means increase of one will result in decrease of other,
So. If x increases y will decrease.
So, the correct option is (b)

12. The limits of rank correlation coefficient are____________.
(a) $\displaystyle \pm$ 1
(b) $\displaystyle \pm$ 2
(c) $\displaystyle \pm$ 3
(d) None

The limits of spearman rank correlation coefficient are -1 to +1 .
So, the correct option is (a)

13. When r = 0 Correlation is_____________.
(a) positive
(b) perfect positive
(c) perfect negative
(d) Absent
r = 0 implies that there is no correlation between two variables.
So, the correct option is (d)

14. If $\displaystyle \sum{{}}$ xy = 140, $\displaystyle {{\sigma }^{x}}$ = 5, $\displaystyle {{\sigma }_{y}}$ = 4 and x = 10, the coefficient of correlation shall be
(a) + 0.77
(b) + 0.07
(c) – 0.7
(d) + 0.7
$\displaystyle \sum{{xy=140\text{ }}}{{\sigma }^{x}}=5\text{ }{{\sigma }_{y}}=4$
x=10
r= $\displaystyle \sum{{}}$ xy/X $\displaystyle \sigma$ _x $\displaystyle \sigma$ _y

$\displaystyle =\frac{{140}}{{10.5.4}}=\frac{{140}}{{200}}=+0.7$

So, the correct option is (d)

15. Find co. of correlation with the given data $\displaystyle \sum{{}}$ xy = 123, $\displaystyle \sum{{}}$ x² = 138, $\displaystyle \sum{{}}$ y² = 164, N = 0.10
(a) 0.18
(b) 0.82
(c) 0.81
(d) 0.19
$\displaystyle \sum{{}}$ xy = 123, $\displaystyle \sum{{}}$ x² = 138
$\displaystyle \sum{{}}$ y² = 164, N = 10
r= $\displaystyle \sum{{}}$ xy/ $\displaystyle \sqrt{{}}$ x² $\displaystyle \times$ y²

$\displaystyle =\frac{{123}}{{\sqrt{{138\times 164}}}}=\frac{{123}}{{\sqrt{{22632}}}}=\frac{{123}}{{168.83}}=.82$

So, the correct option is (b)

16. Given r = .5, $\displaystyle \sum{{}}$ xy = 60, & $\displaystyle \sigma$ y = 4 and $\displaystyle \sum{{}}$ x² = 90, then N = ?
(a) 100
(b) 110
(c) 10
(d) 12
r= $\displaystyle \sum{{}}$ xy/N $\displaystyle \sigma$ _x $\displaystyle \sigma$ _y
$\displaystyle r=.5\text{ }\sum{{xy=60\text{ }{{\sigma }_{y}}=4\text{ }\sum{{{{x}^{2}}=90}}}}$

$\displaystyle {{\sigma }_{x}}=\sqrt{{\frac{{\sum{{{{x}^{2}}}}}}{N}}}=\frac{{\sqrt{{90}}}}{{\sqrt{N}}}$

$\displaystyle \therefore .5=\frac{{60}}{{N.\frac{{\sqrt{{90}}}}{{\sqrt{N}}}.4}}$

$\displaystyle or\text{ }.5=\frac{{60}}{{\sqrt{N}.\sqrt{{90}}.4}}$

$\displaystyle Or,\text{ }2\times \sqrt{{90}}\times \sqrt{N}=60$

$\displaystyle or,\text{ }\sqrt{{90}}\times \sqrt{N}=30$

$\displaystyle or,\text{ }\sqrt{N}=\frac{{30}}{{90}}=\frac{{30}}{{3\sqrt{{10}}}}=\frac{{10}}{{\sqrt{{10}}}}$

$\displaystyle or,\text{ N=}\frac{{100}}{{10}}=10$

So, the correct option is (c)

17. Find the sum of the squares of differences in ranks when Spearman’s rank co-efficient is .143 and N is 7.
(a) 42
(b) 45
(c) 48
(d) 52
$\displaystyle r=1-\frac{{6\sum{{{{d}^{2}}}}}}{{{{n}^{3}}-n}}$
$\displaystyle \sum{{}}$ d² = the sum of the squares of differences in ranks
r = .143, N = 7

$\displaystyle \therefore .143=1-\frac{{6\sum{{{{d}^{2}}}}}}{{{{7}^{3}}-7}}$

$\displaystyle or,\text{ }.143=1-\frac{{6\sum{{{{d}^{2}}}}}}{{343-7}}$

$\displaystyle or,\text{ }.143=1-\frac{{6\sum{{{{d}^{2}}}}}}{{336}}$

$\displaystyle or,\text{ }.143-1=-\frac{{6\sum{{{{d}^{2}}}}}}{{336}}$

$\displaystyle or,\text{ }-.857=-\frac{{6\sum{{{{d}^{2}}}}}}{{336}}$

$\displaystyle or,\text{ }-287.952=-6\sum{{{{d}^{2}}}}$

$\displaystyle 6\sum{{{{d}^{2}}}}=287.957$

$\displaystyle or,\text{ }\sum{{{{d}^{2}}}}=48$

So, the correct option is (c)

18. If the value of correlation coefficient is Zero, the regression lines
(a) Cover each other
(b) Make an angle of 450
(c) Are parallel to each other
(d) Are perpendicular to each other.

So, the correct option is (d)

19. The value of correlation coefficient is equal to_______________of regression c0-efficients.
(a) total
(b) multiplication
(c) arithmetic mean
(d) Geometric mean.
Co-efficient of correlation is geometric mean of regression co-efficients.
R=√b_xy⋅b_yx. which represents the geometric mean of b_xy and b_yx .
So, the correct option is (d)

20. The formula for the rank correlation coefficient is
(a) $\displaystyle 1+\frac{{6\sum{{{{d}^{2}}}}}}{{n\left( {{{n}^{2}}-1} \right)}}$
(b) $\displaystyle 1-\frac{{6\sum{{{{d}^{2}}}}}}{{n\left( {{{n}^{2}}-1} \right)}}$
(c) $\displaystyle 1+\frac{{6\sum{{{{d}^{2}}}}}}{{n\left( {{{n}^{3}}-1} \right)}}$
(d) $\displaystyle \frac{{1-6\sum{{{{d}^{2}}}}}}{{n\left( {{{n}^{2}}-1} \right)}}$
So, the correct option is (b)

21. Probable Error is
(a) 0.6745 x S.E.
(b) 0.6753 x S.E.
(c) 0.6741 x S.E.
(d) 0.6457 x S.E.

Probable error is a less common measure, often used in the context of correlation coefficients, and is approximately equal to 0.6745 times the standard deviation.

So, the correct option is (a)

22. When r = 0 then cov (x,y)
(a) + 1
(b) – 1
(c) 0
(d) None.

Covariance represented by cov(), is a measure of how two variables change together.
Correlation (often represented by “r”) provides a standardized measure of the strength and direction of the relationship. Correlation coefficients range from -1 to +1, with +1 indicating a strong positive relationship, -1 indicating a strong negative relationship, and 0 indicating no linear relationship.
So, when r=0, cov (x,y)
So, the correct option is (c)

Statistical Co-relation and Regression – MCQ

Like this:

Work from Home. Earn Money

Thank you for your response. ✨