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.