Correlation Test

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Correlation Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

Distance(Km) 80 120 160 200 240
Time(Hr) 2 3 4 5 6
A train travelled between two stations and distance and time were recorded as above,

Draw the scatter diagram and identify the type of correlation.

A
Perfect positive correlation

B
Positive correlation with high degree

C
Positive correlation with low degree

D
Zero correlation

Solution

Here we take distance on X-axis and time on Y-axis and plot the points as above.

Since all the points lie on the straight line rising from left to right, there is perfect positive correlation between distance and time for the train.
Question 2
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 band is falling down from left to right then it indicates negative correlation.
If the width of the band is smaller, then the correlation is of high degree.
Question 3
1 / -0

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 band is rising from left to right then it indicates positive correlation.
If the width of the band is smaller, then the correlation is of high degree.
Question 4
1 / -0

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 band is rising from left to right then it indicates positive correlation.
If the width of the band is bigger, then the correlation is of low degree.
Question 5
1 / -0

Capital (in crores Rs.) 2 3 4 5 6 8 9
Profit (in Lakh Rs.) 6 5 7 7 8 9 10
Draw scatter diagram for the following data and
identify the type of correlation.

A
Perfect positive correlation

B
Positive correlation with high degree

C
Positive correlation with low degree

D
Zero correlation

Solution

Here we take capital on X-axis and profit on Y-axis

We get a band of points rising left to right.
This indicates the high degree positive correlation between capital and profit.
Question 6
1 / -0

Calculate the correlation coefficient between the corresponding values of X and Y in the following table:
X 2 4 5 6 8 11
Y 18 12 10 8 7 5

A
$$-0.65$$

B
$$-0.82$$

C
$$-0.92$$

D
$$-0.48$$

Solution

$$X\\ 2\\ 4\\ 5\\ 6\\ 8\\ 11\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \sum { x } =36$$ $$Y\\ 18\\ 12\\ 10\\ 08\\ 07\\ 05\\ \_ \_ \_ \_ \_ \_ \_ \\ \sum { y } =60$$ $$x=x-\overline { x } \\ -4\\ -2\\ -1\\ \quad 0\\ \quad 2\\ \quad 5\\ \_ \_ \_ \_ \_ \_ \\ \quad 0$$ $$Y=y-\overline { y } \\ \quad 8\\ \quad 2\\ \quad 0\\ -2\\ -3\\ -5\\ \_ \_ \_ \_ \_ \\ \quad 0$$ $$XY\\ -32\\ -4\\ \quad 0\\ \quad 0\\ -6\\ -25\\ \_ \_ \_ \_ \_ \_ \\ -67$$ $${ X }^{ 2 }\\ 16\\ 4\\ 1\\ 0\\ 4\\ 25\\ \_ \_ \_ \_ \_ \\ \quad 50$$ $${ Y }^{ 2 }\\ 64\\ 4\\ 0\\ 4\\ 9\\ 25\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \sum { { Y }^{ 2 }=106 } $$

Therefore, $$\overline { a } =\cfrac { 36 }{ 6 } \\ \quad =6$$
$$\overline { y } =\cfrac { 60 }{ 6 } \\ \quad =10$$

Therefore, $$=\quad \cfrac { \sum { XY } }{ \sqrt { \sum { { X }^{ 2 } } \sum { { Y }^{ 2 } } } } \\ =\cfrac { -67 }{ \sqrt { 50*106 } } \\ =-0.92$$
Question 7
1 / -0

Choose the statement which consists of two correlated variables.

A
Increase in the price of commodity results in a decrease in its demand.

B
Increase in weight of the children leads to increase in weight of their mother.

C
Increase in intake of healthy food leads to bad health

D
None of these

Solution

Since increase in price of commodity results in a decrease in its demand.
Question 8
1 / -0

The data in which of the following scatterplots would be best modeled by a quadratic function in which the $$x^2$$ term has a negative coefficient?

A

B

C

D

Solution

The option 1 is correct for the quadratic equation having negative coefficient of $$x^2$$ term.
Example: $$y = -x^2$$
So, the value is decreasing.
When you graph the points of x and y you will get the first graph as answer for quadratic equation having negative coefficient of $$x^2$$ term.
y: 1 2 3
$$x^2$$: -1 -4 -9
Question 9
1 / -0

Choose the statement which consists of two correlated variables.

A
Increase in the intensity of cold results in greater sale of woollen clothes

B
Increase in temperature of delhi has led to congestion

C
Increase in weight of children s accompanied by increase in weight of their mother

D
None of the above

Solution

Since increase in intensity of cold result in greater scale of woolen clothes,
Question 10
1 / -0

If $$\displaystyle cov\left( X,Y \right) =1,var\left( X \right) =1,var\left( Y \right) =4$$ then $$Cor(X,Y)=$$

A
$$1$$

B
$$2$$

C
$$\displaystyle \frac { 1 }{ 2 } $$

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

Solution

$$Cor(X,Y) = \dfrac{Cov(X,Y)}{Var(X) .Var(Y)}$$

$$\Rightarrow Cor(X,Y)=\dfrac{1}{\sqrt1. \sqrt4}=\dfrac12$$