Correlation Test

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Correlation Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

If $$n=10, \sum x=4,\sum y=3, \sum x^2=8,\sum y^2=9$$ and $$\sum xy=3,$$ then the coefficient of $$r_{x,y}$$ is

A
$$\frac{3}{4}$$

B
$$\frac{1}{5}$$

C
$$\frac{1}{6}$$

D
$$\frac{1}{4}$$

Solution

Correlation coefficient
$${ r }_{ x,y }=\dfrac { n\sum { xy } -\sum { x } \sum { y } }{ \sqrt { \left[ n\sum { { x }^{ 2 }-{ \left( \sum { x } \right) }^{ 2 } } \right] \left[ n\sum { { y }^{ 2 }-{ \left( \sum { y } \right) }^{ 2 } } \right] } } $$

$$=\displaystyle\frac { 30-12 }{ \sqrt { 64\times 81 } } $$
$$\Rightarrow r_{x,y}=\dfrac{1}{4}$$
Question 2
1 / -0

Choose the statement which consists of two positively correlated variables.

A
Increase in temperature leads to increase in sales of air conditioners.

B
Increase in temperature leads to decrease in traffic on road.

C
Decrease in temperature is accompanied by increase in sales of ice creams

D
None of the above

Solution

A positive correlation is a relationship between two variables where if one variable increases, the other one also increases. A positive correlation also exists in one decreases and the other also decreases.
In the given options only option (A) has both positive variables.
Question 3
1 / -0

Directions For Questions

Correlation is a statistical method or statistical technique that measures quantitative relationship between different variables like price & demand. Correlation between different variables may either be positive or negative. When two variable move in the same direction i.e. when one increases other also increases & vice versa & when two variable change in different directions are the cause of positive & negative correlation.
In case of linear correlation, the two sets of data's show some fixed proportion to each other & therefore form a straight line on a graph paper. In case of non linear correlation, on the other hand the two sets of data's do not show any fixed proportion to each other, and therefore their graphs are different from the graphs of linear correlation. The degree of correlation refers to the coefficient of correlation. There are several degree of correlation like perfect positive, perfect negative high positive,high negative. Sometime variables are uncorrelated & degree of correlation in such cases is O.
Consider the Scattered diagrams
On the basis of above information answer the following questions

...view full instructions

If the value of correlation $$ \displaystyle r=\frac{1}{2} $$ or $$ \displaystyle r= - \frac{1}{2} $$, then correlation is called

A
High negative

B
High positive

C
Low positive

D
Moderate.

Solution

When correlation between two series or variables is neither large nor
small, then it is called moderate degree correlation. It may be positive
moderate or negative moderate. For positive moderate, correlation the
value of $$\displaystyle r=\frac{1}{2}$$ & for negative moderate
correlation the value of $$\displaystyle r=-\frac{1}{2}$$
so choice (d) is correct
Question 4
1 / -0

A strong positive association between x and y is depicted by which of the following graphs?

A

B

C

D

Solution

A strong association implies that there must be seen a concentrated set of points in the $$x-y$$ plane.
Also, a positive association implies that the points must be going upwards, meaning that as $$x$$ increases, correspondingly $$y$$ increases too.
This kind of set is visible in option D.

Question 5

1 / -0

The marks obtained by nine students in physics and Mathematics are given below:

Physics	48	60	72	62	56	40	39	52	30
Mathematics	62	78	65	70	38	54	60	32	31

calculate spearman's coefficient.

$$r=0.66$$

$$r=0.32$$

$$r=0.53$$

$$r =0.28$$

Solution

Descending order arranged data will be as follows:

Physics: $$72,62,60,56,52,48,40,39,30$$

MAthematics: $$78,70,65,62,60,54,38,32,31$$

Thus data will be

Physics$$(P)$$

Mathematics $$(M)$$

Rank $$(P)$$

$$|d|$$

$$d^2$$

$$n=9,\quad \sum d^2=40$$

$$r=1-\cfrac{6\sum d^2}{n(n^2-1)}=1-\cfrac{40\times 6}{9(9^2-1)}=1-\cfrac{240}{720}=0.66$$

Question 6
1 / -0

The coefficient of correlation is always between

A
$$0\ and \ 1$$

B
$$-1\ and \ 1$$

C
$$-\infty \ and \ \infty$$

D
$$-10\ and \ 10$$

Solution

$$\Rightarrow$$ 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.

Question 7

1 / -0

FInd the rank correlation from the following data:

S. No.	1	2	3	4	5	6	7	8	9	10
Rank Differences	-2	-4	-1	3	2	0	-2	3	3	-2

0.64

0.50

0.45

0.34 Solution

Sl.No

Rank Difference $$(d)$$

$$d^2$$

10.

-2

-4

-1

-2

$$\sum d^2=60,\quad n=10$$

$$r=1-\cfrac{6\sum d^2}{n(n^2-1)}$$

$$r=1-\cfrac{6(60)}{10(10^2-1)}$$

$$r=1-\cfrac{360}{990}$$

$$r=0.6363....\approx 0.64$$

Question 8

1 / -0

The marks in history and mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.

Student	A	B	C	D	E	F	G	H	I	J	K	L
History	69	36	39	71	67	76	40	20	85	65	55	34
Mathematics	33	52	71	25	79	22	83	81	24	35	46	64

-0.77

-0.92

0.77

0.92 Solution

Students

History $$(H)$$

Mathematics$$(M)$$

Rank $$(H)$$

Rank$$(M)$$

$$|d|$$

$$d^2$$

100

$$n=12,\quad \sum d^2=508$$

$$r=1-\cfrac{6\sum d^2}{n(n^2-1)}=1-\cfrac{6\times 508}{12(12^2-1)}=1-\cfrac{3048}{1716}=-0.77$$

Question 9
1 / -0

If increase in value of one variable is not accompnied by the proportional decrease in second variable, then corrrelation between two variables is

A
perfect positive

B
perfect negative

C
imperfect positive

D
imperfect negative

Solution

In general ,
1) Increase in the value of one is followed by a decrease in the value of the other, and a decrease in the value of one is followed by a decrease in the value of the other, and a decrease in the value of one is followed by an increase in the value of the other is called as negative corrrelation
2) when the values of the variables under study change at different ratios, it is a case of imperfect correlation.

hence in the given statement which satisfies these two statement and hence here the corrrelation is called as imperfect negative.

Question 10

1 / -0

The marks in History and Mathematics of twelve students in a public examination are given below. Calculate a coefficient of correlation by ranks.

Student	$$A$$	$$B$$	$$C$$	$$D$$	$$E$$	$$F$$	$$G$$	$$H$$	$$I$$	$$J$$	$$K$$	$$L$$
History	$$69$$	$$36$$	$$39$$	$$71$$	$$67$$	$$76$$	$$40$$	$$20$$	$$85$$	$$65$$	$$55$$	$$34$$
Mathematics	$$33$$	$$52$$	$$71$$	$$25$$	$$79$$	$$22$$	$$83$$	$$81$$	$$24$$	$$35$$	$$46$$	$$64$$

Interpret the result.

A very good student of history is a very bad student in mathematics.

A bad student of history is even bad student in mathematics.

This is positive correlation

None of the above

Solution

Students

History $$(H)$$

Mathematics$$(M)$$

Rank $$(H)$$

Rank$$(M)$$

$$|d|$$

$$d^2$$

100

$$n=12,\quad \sum d^2=508$$

$$r=1-\cfrac{6\sum d^2}{n(n^2-1)}=1-\cfrac{6\times 508}{12(12^2-1)}=1-\cfrac{3048}{1716}=-0.77$$

Since $$r<0,$$ we can say that a very good student of history is a very bad student in mathematics.

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Correlation Test - 12

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Correlation Test - 12

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SHARING IS CARING

Question 1

$$\frac{3}{4}$$

$$\frac{1}{5}$$

$$\frac{1}{6}$$

$$\frac{1}{4}$$

Solution

Question 2

Increase in temperature leads to increase in sales of air conditioners.

Increase in temperature leads to decrease in traffic on road.

Decrease in temperature is accompanied by increase in sales of ice creams

None of the above

Solution

Question 3

High negative

High positive

Low positive

Moderate.

Solution

Question 4

Solution

Question 5

$$r=0.66$$

$$r=0.32$$

$$r=0.53$$

$$r =0.28$$

Solution

Question 6

$$0\ and \ 1$$

$$-1\ and \ 1$$

$$-\infty \ and \ \infty$$

$$-10\ and \ 10$$

Solution

Question 7

0.64

0.50

0.45

0.34

Solution

Question 8

-0.77

-0.92

0.77

0.92

Solution

Question 9

perfect positive

perfect negative

imperfect positive

imperfect negative

Solution

Question 10

A very good student of history is a very bad student in mathematics.

A bad student of history is even bad student in mathematics.

This is positive correlation

None of the above

Solution

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