# Free Correlation 03 Practice Test - 11th Grade - Commerce

### Question 1

Correlation implies causation. State true or false.

True

False

#### SOLUTION

Solution :B

Correlation

does notimply causation. It only says the two factors are related somehow - not that change in one affects the others directly. For example, the sales of ice-cream and sales of air conditioners may both go up during the summer season. Hence, they are correlated but one is not the cause of the other. In certain cases, correlation may be because of a causal relationship (eg: poverty and malnutrition) but this is not always the case. It is very important to understand this distinction.

### Question 2

Which of the following scatter charts shows zero correlation?

#### SOLUTION

Solution :A

For option A, there is no positive or negative correlation. The points are randomly scattered.

### Question 3

While representing a bivariate frequency distribution using a scatter chart, which of the following is correct?

the x-axis represents variables and the y-axis represents their frequencies

the y-axis represents variables and the x-axis represents their frequencies

The axes represent the two variables of the frequency distribution

The axes represent the frequency of the two variables.

#### SOLUTION

Solution :C

In a bivariate frequency distribution, there are two variables. In a scatter chart, the x-axis and y-axis contain the two variables of the frequency distribution.

### Question 4

If the y value increases as the x value increases, the correlation is called

#### SOLUTION

Solution :If the y value increases as the x value increases, the correlation is called positive correlation.

### Question 5

Which of the following cannot be the value of a correlation coefficient?

-1

1

0.5

2

#### SOLUTION

Solution :D

The correlation coefficient can take any value between (and including) -1 and 1. Hence, 2 cannot be a value of the correlation coefficient.

### Question 6

For perfect positive correlation, the value of r =

#### SOLUTION

Solution :For perfect positive correlation, the value of r = 1.

### Question 7

If the value of the simple correlation coefficient is zero, it means that there no relation whatsoever between the variables. State true or false.

True

False

#### SOLUTION

Solution :B

Karl Pearson's coefficient is used to measure correlation when the relationship between the variables is linear. Hence, zero correlation need not mean the absence of any type of relationship between the two variables. For example, for a relation of the form Y=X2, the correlation coefficient will be zero. The given statement is false.

### Question 8

Identify the correct formula for calculating r using the step deviation method, where U and V are the step deviations of X and Y.

r=N∑(UiVi)–N(∑Ui)(∑Vi)√N∑U2i–(∑Ui)2√N∑V2i–(∑Vi)2

r=N∑(UiVi)–(∑Ui)(∑Vi)√N∑U2i–(∑Ui)2√N∑V2i–(∑Vi)2

r=N∑(UiVi)–(∑Ui)(∑Vi)(N∑U2i–(∑Ui)2)(N∑V2i–(∑Vi)2)

r=N∑(UiVi)–N(∑Ui)(∑Vi)(N∑U2i–(∑Ui)2)(N∑V2i–(∑Vi)2)

#### SOLUTION

Solution :B

The shortcut formula for calculating r is

r=N∑(UiVi)–(∑Ui)(∑Vi)√N∑U2i–(∑Ui)2√N∑V2i–(∑Vi)2

### Question 9

Which of the following values of correlation coefficient indicates the strongest correlation?

#### SOLUTION

Solution :A

The value of the correlation coefficient lies between -1 and 1. Values closer to 1, irrespective of sign, indicate a stronger relationship, while the sign indicates the direction. From the given numbers, 0.86 is the closest number to 1 and hence has the strongest correlation.

### Question 10

What is the value of r when there is no linear correlation between two variables?

#### SOLUTION

Solution :A

When there is no linear correlation between two variables, r is 0.