# Free Correlation 02 Practice Test - 11th Grade - Commerce

### Question 1

The price per/kg of chicken and the quantity of chicken purchased per month in a household is tabulated below. Determine the type of correlation.

Price/kg (Rs)Quantity (kg)406505.5603.5703307.5802

Positive correlation

Zero correlation

Negative correlation

Perfect correlation

#### SOLUTION

Solution :C

The given data can be represented on a scatter chart as shown below.

It can be seen that there is a negative correlation between quantity and price.

### Question 2

To find the line of best fit, which of the following is minimized?

∑ni=1(yi−^yi)2

∑ni=1|yi−^yi|

∑ni=1(xi−^xi)2

∑ni=1|xi−^xi|

#### SOLUTION

Solution :A

The line of best fit is obtained by minimizing the squared errors of the data values i.e. the square of the difference between the predicted and actual values of the dependent variable with respect to the independent variable.

### Question 3

The demand for a good at different price points is given in the below. Find the correlation coefficeint between price and quantity demanded.

Price (P)Quantity (Q)1012020105308540555040

0.9

-0.9

0.99

-0.99

#### SOLUTION

Solution :D

xyx−¯x(x−¯x)2(y−¯y)(x−¯x)2(x−¯x)(y−¯y)10120−20400391521−78020105−1010024576−2403085004160405510100−26676−260504020400−411681−820∑=1000∑=4470∑=−2100

¯x=∑xn=1505=30

¯y=∑yn=4055=81r=∑ni=1(xi−¯x)(yi−¯y)√∑ni=1(xi−¯x)2√∑ni=1(yi−¯y)2=−2100√1000×4470=−21002114.24=−0.99

### Question 4

If the slope of the line of best fit for two variables is negative, then the correlation between the variables is also negative. State true or false.

True

False

#### SOLUTION

Solution :A

A negative correlation indicates that one quantity decreases as the other increases. So, if the slope of the line of best fit is negative, the correlation is also negative. Hence, the given statement is true.

### Question 5

Which of the following is the correct formula for the correlation coefficient, r?

r=∑ni=1(xi−¯x)(yi−¯y)√∑ni=1(xi−¯x)2√∑ni=1(yi−¯y)2

r=∑ni=1(xi−¯x)(yi−¯y)√∑ni=1(xi−¯x)2(yi−¯y)2

r=∑ni=1[(xi−¯x)(yi−¯y)]2√∑ni=1(xi−¯x)2√∑ni=1(yi−¯y)2

r=∑ni=1[(xi−¯x)(yi−¯y)]2√∑ni=1(xi−¯x)2(yi−¯y)2

#### SOLUTION

Solution :A

r=∑ni=1(xi−¯x)(yi−¯y)√∑ni=1(xi−¯x)2√∑ni=1(yi−¯y)2

### Question 6

Find cov(X,Y) for the following data.

XY456981210141215

8

10

12

15

#### SOLUTION

Solution :B

XYX−¯XY−¯Y(X−¯X)(Y−¯Y)45−4−62469−2−24812010101423612154416∑=50

¯X=∑XN=405=8

¯Y=∑YN=555=11Cov(X,Y)=(X−¯X)(Y−¯Y)N=505=10

### Question 7

The following table contains the cost of 5 motorcycles and their corresponding mileages in (km/litre). Find the correlation coefficient using the shortcut method.

Cost (X)Mileage (Y)500004010000030150000252000001525000010

0.95

-0.95

0.99

-0.99

#### SOLUTION

Solution :D

Let Ax=150000 & hx=50000Let Ay=25 & hy=5

XiYiUi=Xi−AxhxVi=Yi−AyhyU2iV2iUiVi5000040−2349−610000030−1111−11500002500000200000151−214−2250000102−349−6∑=0∑=−1∑=10∑=23∑=−15

r=N∑(UiVi)–(∑Ui)(∑Vi)√N∑U2i–(∑Ui)2√N∑V2i–(∑Vi)2=−757.07×10.68=−0.993

### Question 8

Identify the correct statement(s) about the correlation between two variables.

Statement 1: Correlation does not show that there is a causal relationship between two variables

Statement 2: Correlation shows the degree to which variations in one variable explain the variation of the second variable

Statement 1

Statement 2

Neither Statement 1 nor Statement 2

Both Statement 1 and Statement 2

#### SOLUTION

Solution :A and B

Correlation shows the degree to which variations in one variable explain the variation of the second variable. It does not show that there is a causal relationship between two variables.

### Question 9

Spearman's rank coefficient helps to understand the type of correlation by looking at non-linear ranked data.

#### SOLUTION

Solution :A

Spearman's rank coefficient helps to understand the type of correlation by looking at non-linear ranked data.

### Question 10

Variables in a correlation are called

Dependent variables

Independent variables

Co-variables

Dependent and independent variables

#### SOLUTION

Solution :C

Variables in a correlation are called co-variables.