Correlation Test

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Correlation Test - 10

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Weekly Quiz Competition

Question 1
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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 ?

A
1 only

B
2 only

C
Both 1 and 2

D
Neither 1 nor 2

Solution

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.
Question 2
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Regression coefficient is independent of:

A
Units of measurement

B
Scale and origin

C
Both are correct

D
None of them

Solution

The regression coefficient is the measure of the relationship between two or more variables.

The regression coefficient is denoted by 'b'

The regression coefficient is independent of the measurement units, scale and origin.
Question 3
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It is possible that two regression coefficients have:

A
Opposite signs

B
Same signs

C
No sign

D
Difficult to tell

Solution

Regression coefficient is the measure of the relationship between two or more variables.

The regression coefficient is denoted by 'b'

The regression coefficients must have the same sign. i.e., both must be positive or both must be negative.
Question 4
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In correlation, there is______________.

A
cause and effect relationship

B
no cause and effect relationship

C
relationship between the independent variable and dependent variable

D
functional relationship between two variables

Solution

A cause- effect is a relationship in which one event makes another event happen while, in correlation, there is no cause effect relationship, there is only a casual relationship between the variables.
Question 5
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The value of Spearman's rank coefficient lies between

A
$$2$$ and $$3$$

B
$$1$$ and $$2$$

C
$$0$$ and $$1$$

D
$$-1$$ and $$1$$

Solution

Spearman's rank cofficient : $$R=1-\dfrac { 6\sum { { d }_{ i }^{ 2 } } }{ n({ n }^{ 2 }-1) } $$
Its values lies between $$-1$$ and $$1$$
So option $$D$$ is correct.
Question 6
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If the value of any regression coefficient is zero, then two variables are:

A
Qualitative

B
Correlation

C
Dependent

D
Independent

Solution

$$\Rightarrow$$ If the correlation coefficient of two variables is zero, it signifies that there is no linear relationship between the variables. However, this is only for a linear relationship; it is possible that the variables have a strong curvilinear relationship.
$$\Rightarrow$$ When the value of r is close to zero, generally between $$-0.1$$ and $$+0.1,$$ the variables are said to have no linear relationship or a very weak linear relationship.
$$\Rightarrow$$ For example, suppose the prices of coffee and of computers are observed and found to have a correlation of $$+.0008;$$ this means that there is no correlation, or relationship, between the two variables.
$$\therefore$$ We can say that, if the value of any regression coefficient is zero, then two variables are $$Independent$$.
Question 7
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What is the correlation of this scatter diagram

A
Perfect negative correlation

B
Negative correlation with high degree

C
Negative correlation with low degree

D
Zero correlation

Solution

If the band is falling down from left to right then it indicates negative correlation.
If the width of the band is bigger, then the correlation is of low degree.
Question 8
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Regression is________________.

A
independent of origin and scale

B
independent of origin and not of scale

C
independent of origin

D
independent of scale

Solution

Regression is the statistical analysis that measure the degree of relationship between two variables i.e. dependent and independent variables. Regression is independent of origin and not of scale.
Question 9
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What is the correlation of this scatter diagram

A

Perfect positive correlation

B
Positive correlation with high degree

C
Positive correlation with low degree

D
Zero correlation

Solution

If the points are rising from left to right in a straight line then scatter diagram indicates a perfect positive correlation
Question 10
1 / -0

What is the correlation of this scatter diagram

A
Perfect negative correlation

B
Negative correlation with high degree

C
Negative correlation with low degree

D
Zero correlation

Solution

If the points are falling from left to right in a straight line then scatter diagram indicates a perfect negative correlation

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Re-Attempt Weekly Quiz Competition

Correlation Test - 10

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Correlation Test - 10

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SHARING IS CARING

Question 1

1 only

2 only

Both 1 and 2

Neither 1 nor 2

Solution

Question 2

Units of measurement

Scale and origin

Both are correct

None of them

Solution

Question 3

Opposite signs

Same signs

No sign

Difficult to tell

Solution

Question 4

cause and effect relationship

no cause and effect relationship

relationship between the independent variable and dependent variable

functional relationship between two variables

Solution

Question 5

$$2$$ and $$3$$

$$1$$ and $$2$$

$$0$$ and $$1$$

$$-1$$ and $$1$$

Solution

Question 6

Qualitative

Correlation

Dependent

Independent

Solution

Question 7

Perfect negative correlation

Negative correlation with high degree

Negative correlation with low degree

Zero correlation

Solution

Question 8

independent of origin and scale

independent of origin and not of scale

independent of origin

independent of scale

Solution

Question 9

Perfect positive correlation

Positive correlation with high degree

Positive correlation with low degree

Zero correlation

Solution

Question 10

Perfect negative correlation

Negative correlation with high degree

Negative correlation with low degree

Zero correlation

Solution

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