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Correlation - class-XI

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In correlation, there is______________.

  1. cause and effect relationship

  2. no cause and effect relationship

  3. relationship between the independent variable and dependent variable

  4. functional relationship between two variables


Correct Option: B
Explanation:

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.

Regression is________________.

  1. independent of origin and scale

  2. independent of origin and not of scale

  3. independent of origin

  4. independent of scale


Correct Option: B
Explanation:

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.

When the number of items is small, the correlation co-efficient can be found out by _________.

  1. karl pearson's method

  2. spearman's method

  3. product moment correlation

  4. concurrent deviation method


Correct Option: C
Explanation:

The product moment correlation coefficient is a measure of the strength of linear relationship between two variables. It is referred to as Pearson's correlation or simply as the correlation coefficient.

Correlation measures____________.

  1. the degree of variability between the two variables

  2. the nature of the relationship between the two variables

  3. functional relationship between two variables

  4. all of the above


Correct Option: A
Explanation:

Correlation is the statistical measure that indicates the degree tow which two or more variables fluctuate or how strongly they are connected to each other. Value of coefficient ranges between -1 to +1.

Which of the following is advisable to use while interpreting the value of co-efficient correlation?

  1. Square of the co-efficient of correlation

  2. Probable error

  3. Scatter diagram

  4. Correlation graph


Correct Option: A
Explanation:

Square of the coefficient of correlation is advisable to use because it makes the data easy to be interpreted easily by the researcher. This value represents the variation in one variable that may be explained by another variable.

Co-variance between two variables is _____________.

  1. the average of the product of deviations taken from their averages

  2. a is further divided by the product of their standard deviations

  3. a is further divided by the product of their arithmetic averages

  4. none of the above


Correct Option: A

Correlation is concerned with the association of ___________.

  1. a single variable

  2. two variables

  3. three variables

  4. four variables


Correct Option: B

If the regression coefficient by $x$ is $0.5$, what is the value of $a$ in the given equation?
$2Y=aX-16.80$

  1. $4$

  2. $0.5$

  3. $1.0$

  4. $3.32$


Correct Option: C

Kandalls co-efficient of concordance is used to test the ______________.

  1. difference among two or more sets of data

  2. relationship between variables

  3. variations in the given data

  4. randomness of samples


Correct Option: B

Estimate the value of coefficient of correlation between $x$ and $y$ if the two coefficient of regression are $0.49$ and $1$____.

  1. $0.9$

  2. $0.7$

  3. $0.8$

  4. $1.0$


Correct Option: B

If the regression coefficient of x on y is -1/3 and that of y on x is -3/4. Find the value of correlation coefficient between x and y___.

  1. -0.5

  2. 0.57

  3. 0.8

  4. None


Correct Option: A

Correlation is______________.

  1. independent of change of origin

  2. independent of change of scale

  3. independent of origin and not of scale

  4. both (A) and (B)


Correct Option: D
Explanation:

Correlation is independent of change in both of scale and origin. Correlation simply measures the strength of association between two or more variables i.e. how strongly they are connected.

The angle between the two lines will be wider when the correlation between two variable is___________.

  1. less

  2. more

  3. equal

  4. very high


Correct Option: A
Explanation:

The larger the angle between the two regression lines, less the degree of correlation between the two variables and similarly, the small the angle between two lines, the larger would be the degree of correlation between them.

If the regression coefficient bxy is 2.0, what is the value of a in the given equation 2.9X = aY + 15?

  1. 5.8

  2. 2.9

  3. 6.18

  4. 4.32


Correct Option: A

When there is a linear relationship between two numerical variables it can be measured by.

  1. Mean

  2. Mode

  3. Scatter diagram

  4. Coefficient of correlation


Correct Option: D

What does correlation measure?

  1. Direction and intensity of relationship among variables

  2. It measures covariation, not causation

  3. Both A and B

  4. None of the above


Correct Option: C

If $bxy = 0.25$ and $byx = 0.64$, correlation coefficient is equal to ________.

  1. $0.16$

  2. $0.40$

  3. $0.89$

  4. $0.30$


Correct Option: B

Which one of the following is false statement ?

  1. The sign of the regression coefficients are always the same.

  2. Correlation coefficient is the geometric mean of the regression coefficients.

  3. The co-variance between two variables divided by the product of their standard deviations produces the value of coefficient of correlation.

  4. Coefficient of correlation is independent of origin but not of sale.


Correct Option: D

If the value of co-efficient of determination is $0.64$, what is the value of co-efficient of correlation?

  1. $0.40$

  2. $0.80$

  3. $0.08$

  4. $0.04$


Correct Option: B

Which of the following is not true?

  1. Correlation means when value of one variable changes, the other variable also changes in the same direction

  2. Correlation studies and measures the direction and intensity of relationship among variables

  3. A scatter diagram visually presents the nature of association without giving any specific numerical value

  4. None of these


Correct Option: A

Correlation is commonly classified into ___  and ____  correlation.

  1. primary, secondary

  2. negative, positive

  3. same, opposite

  4. none of the above


Correct Option: B

If the scatter points are widely dispersed around the line, the correlation is _______. 

  1. unity

  2. linear

  3. high

  4. low


Correct Option: D

Correlation is said to be ______ when the variables move together in the opposite direction.

  1. positive

  2. negative

  3. indirect

  4. opposite


Correct Option: B

Correlation is said to be ________ when the variables move together in the same direction.

  1. negative

  2. direct

  3. same

  4. positive


Correct Option: D

When the income rises, consumption also rises. This is an example of ________. 

  1. correlation

  2. negative correlation

  3. direct relationship

  4. positive correlation


Correct Option: D

A ________ visually presents the nature of association without giving any specific numerical value. 

  1. Karl Pearsons coefficient of correlation

  2. Scatter diagram

  3. Spearmans rank correlation

  4. All of these


Correct Option: B

Regression analysis was first used by ____________.

  1. Karl Pearson

  2. Spearman

  3. Sir Francis Golton

  4. Kafta


Correct Option: C
Explanation:

The term regression was coined by Sir Francis Golton in the nineteenth century but his work was later explored by Karl pearson.

From the following data find correlation coefficient between X and Y.

X Y
21 10
24 14
28 18
30 20
32 23
  1. (0.77)

  2. (-0.77)

  3. (0.99)

  4. (-0.99)


Correct Option: C

If all the points in a scatter diagram lie on a line, the correlation is perfect and is said to be _______.

  1. low

  2. unity

  3. linear

  4. none of the above


Correct Option: C

When r=0, the lines of regression will____________.

  1. intersect each other at $90^o$

  2. be positive slope

  3. be negative slope

  4. be convex to the origin


Correct Option: A

 The correlation is said to be _______ if the scatter points lie near a line or on a line.

  1. linear

  2. unity

  3. low

  4. none


Correct Option: A

Francis Galton used the regression analysis to study the relationship between the _______________.

  1. heights of fathers and sons

  2. weights of fathers and sons

  3. heights of mothers and daughters

  4. weights of mothers and daughters


Correct Option: A
Explanation:

Francis Golton used the regression analysis for a biological phenomenon to study the relationship between the heights of fathers and son i.e. how the heights of the descendants of the tall ancestors tends to regress down towards a normal average.

In positive correlation, _________________.

  1. when one variable increases, the other variable decreases and vice-versa

  2. when one variable increases, the other variable also increases and vice-versa

  3. the study is made on more than two variables

  4. the study is made on less than two variables


Correct Option: B
Explanation:

In positive correlation, increase in one variable leads to an increase in another variable or vice versa . It states both the variables move in the same direction.

If the ratio of change between the two variables is constant, it is said to be _____________.

  1. partial correlation

  2. total correlation

  3. linear correlation

  4. nonlinear correlation


Correct Option: C

If the ratio of change between the two variables are not constant, it is called ____________.

  1. multiple correlation

  2. negative correlation

  3. linear correlation

  4. non-linear correlation


Correct Option: D
Explanation:

If the ratio of change between two variable is not constant i.e. change in one variable leads to a change in another variable but by different amount or when all the points in the scatter diagram tends to lie around a smooth curve.

Example of negative correlation is________________.

  1. relationship between price and supply of a commodity

  2. relationship between price and demand for a commodity

  3. relationship between income and saving

  4. relationship between income and consumption


Correct Option: B
Explanation:

Relationship between price and commodity is an example of negative correlation as increase in the price of a commodity leads to a decrease in the quantity of a commodity i.e. both the variables move in an opposite direction.

Linear correlation can be represented by a ___________.

  1. horizontal line

  2. straight line

  3. backward bending curve

  4. 'u' shaped curve


Correct Option: B
Explanation:

Linear correlation is represented as a straight line as the ratio of change is constant , change in one variable leads to a constant change in another variable.

In ______ correlation, the study is made on more than two variables but assuming some variables are exchanged.

  1. simple

  2. multiple

  3. partial

  4. total


Correct Option: C

Which of the following methods of measuring correlation is the most popular method?

  1. Product Moment Correlation

  2. Spearman's Rank Correlation

  3. Concurrent Deviation Method

  4. Karl Pearson's Co-efficient of Correlation


Correct Option: D
Explanation:

Karl pearson's coefficient of correlation determines how strongly the two variables are related to each other i.e. measure the linear correlation between the variables.

Karl Pearson's method helps to__________.

  1. give direction and degree of relationship between the two variables.

  2. calculate the unknown value from a known value.

  3. both (A) and (B).

  4. calculate the known value from an unknown value.


Correct Option: C
Explanation:

Karl pearson's coefficient of correlation helps in measuring the degree of relationship between two variable i.e. how strongly they are connected and it also calculate the unknown value from the known values.

Rank correlation is used ________.

  1. only when the number of variables is smaller

  2. only when the rank is given

  3. to know the talent of the workers of two factories

  4. all of the above


Correct Option: D
Explanation:

Rank correlation is used when the ranks are provided to the items or individuals that makes the comparison or measuring the relation between them easy  and also when the number of variables is small.

Which of the following plays a great part in interpreting the value of the relationship?

  1. Square of the co-efficient of correlation

  2. Probable error

  3. Scatter diagram

  4. Correlation graph


Correct Option: B
Explanation:

The probable error of correlation coefficient helps in determining the accuracy and reliability of the value of the coefficient that so far depends on the random sampling.

The formula of product moment correlation is ______________.

  1. $r=\dfrac{S _{xy}}{\sqrt{S _xS _y}}$ ; S= Standard error

  2. $ r = \dfrac {{\sigma} _{xy}}{{N}{\sigma} _{x}{\sigma} _{y}}$ ; N=number of variables

  3. $ r = \dfrac {{-r}^2}{\sqrt{N}}$

  4. $ r = \dfrac {{6}{\sigma}^2 _{{d}}}{n({n}^2 - {1})}$


Correct Option: A
Explanation:

The formula for product moment correlation given in the option A is correct and measures the linear relationship between two variables. The formula basically tries to show how strongly are the two variables (x and y in this case) are related to each other. A correlation could be weakly or strongly correlated depending on the value of 'r'. 

The formula of Karl Pearson's co-efficient of correlation is ________.

  1. $r = 1 - \dfrac{6\Sigma{{D} _2}}{{{N} _{3}} - N}$

  2. $r = \dfrac{{\Sigma}{x}{y}}{{N}{\sigma}{x}{\sigma}{y}}$

  3. $ r = \dfrac {{\sigma}{x}}{{\sigma}{y}}$

  4. $ r = \dfrac {{\sigma}{y}}{{\sigma}{x}}$


Correct Option: B
Explanation:

The correct formula foe the karl pearson's coefficient if correlation is given in the option B. The value of coefficient always lies between -1 to +1 that measures the strength of linear relationship between two variables.

Defects of Karl Pearson's method is/are________.

  1. it consumes more time

  2. the value of correlation is affected by extreme values

  3. if the data are not homogeneous, the co-efficient of correlation will give a wrong picture

  4. all of the above


Correct Option: D
Explanation:

Disadvantages of using karl pearson's method is that it is avery time consuming and lengthy process and it gets affected by extreme values and it may give a wrong image if the variables are not of same nature or homogeneous.

The original formula that Pearson developed is commonly known as___________.

  1. Probable error

  2. the product moment method

  3. concurrent deviation method

  4. short-cut method


Correct Option: B

Karl Pearson's method is popularly known as ______________.

  1. concurrent deviation method

  2. correlation co-efficient

  3. technical co-efficient

  4. rank correlation


Correct Option: B
Explanation:

Karl Pearson's method is known as correlation coefficient as it measures the degree of relationship between two variables and its value ranges between +1 to -1.

The regression is linear when the curve of the regression is_____________.

  1. straight line

  2. not a straight line

  3. concave to the origin

  4. convex to the origin


Correct Option: A
Explanation:

Regression is said to be linear when the curve drawn from the data is a straight line. It measures the relationship between one dependent variable with one or more independent variables.

The problem of predicting the average value of one unknown variable from the known variable is called the problem of __________.

  1. correlation

  2. regression

  3. sampling distribution

  4. index number


Correct Option: B
Explanation:

In statistical modelling, regression analysis measures the degree of relationship among variables and here, the problem of predicting the average value of unknown variable from the known variable arise.

Regression establishes______________.

  1. the direction and degree of relationship between two variables

  2. the direction and degree of relationship between two or more variables

  3. the degree of variability between two and more variables

  4. the functional relationship between two variables


Correct Option: D
Explanation:

Regression measures the functional relationship between two variables in which one is a dependent variable while other variable is an independent. It measures the degree of association between the variables.

In statistics, 'regression' means _____________.

  1. act of returning back

  2. act of stepping back

  3. simply average relationship

  4. all of the above


Correct Option: C
Explanation:

Regression is a statistical measure that shows the relationship between two variables i.e. between dependent and independent variable. It also refers to as simply average relationships.

The Linear regression equation y = a + bx helps to estimate the _______.

  1. dependent variable

  2. independent variable

  3. both (A) and (B)

  4. none of the above


Correct Option: A
Explanation:

Regression equations are algebraic equations of regression lines. Regression equation of y on x can be stated as y=a+bx while regression equation of x on y will be stated as x=a+by.

When r = -1, the lines of regression will be_____________.

  1. negative slope

  2. positive slope

  3. running downwards from left to right

  4. both (A) and (C)


Correct Option: D
Explanation:

When coefficient of correlation is -1, then the two lines of regression coincides and have a negative slope and also run downwards from left to right.

When r = +1, the lines of regression will_____________.

  1. be positive slope

  2. move upwards from left to right

  3. be negative slope

  4. both (A) and (B)


Correct Option: A
Explanation:

When coefficient of correlation is +1, it is referred to as perfect positive correlation and the two lines of regression coincide and it has a positive slope.

The word 'Regression' was first used by___________.

  1. Karl Pearson

  2. Sir Francis Galton

  3. M. Blair

  4. Bowley


Correct Option: B
Explanation:

The term regression was first used by Sir Francis Galton to represent the biological phenomenon that the the heights of descendants of tall ancestors tend to regress down towards a normal average.

Under regression analysis, there is____________.

  1. relationship between the independent variable and dependent variable

  2. no relationship between the independent variable and dependent variable

  3. no cause and effect relationship

  4. none of the above


Correct Option: A
Explanation:

Under regression analysis, relationship between the independent variable and the dependent variable is considered and the degree of relationship between them is ascertained.

Regression analysis studies____________.

  1. the degree of variability between the two variables

  2. the direction of relationship between the two variables

  3. the nature of relationship between the two variables

  4. none of the above


Correct Option: C
Explanation:

Regression analysis studies the relationship between two variables (between dependent and independent variable) that is the strength of association between the variables

Regression means_________.

  1. act of returning back

  2. method of studying correlation between two variables

  3. the direction of change

  4. simply average relationship


Correct Option: B
Explanation:

Regression analysis is a set of statistical measure for estimating the relationship between two variables i.e. how the dependent variable changes when there is a change in an independent variable.

If bxy$=0.25$ and byx$=0.64$, correlation coefficient is _________.

  1. $0.16$

  2. $0.40$

  3. $0.89$

  4. $0.30$


Correct Option: B

The regression co-efficient of x on y is represented by__________.

  1. $\sqrt{byx \times bxy}$

  2. $ byx = \dfrac{r sy}{sx}$

  3. $bxy = \dfrac{r sx}{sy}$

  4. none of the above


Correct Option: C

If the dependent variable increases as the independent variable increases in an estimating equation, the coefficient of correlation will be in the range of _________.

  1. 0 to (-) 1

  2. 0 to (-) 0

  3. 0 to (-) 0.05

  4. 0 to 1


Correct Option: D

Karl Pearsons Coefficient of Correlation is also known as ______.

  1. simple correlation coefficient

  2. product moment correlation

  3. both A and B

  4. none of the above


Correct Option: C

If the two regression coefficients are 0.8 and 0.2,then the value of coefficient of correlation is __________.

  1. -0.16

  2. -0.50

  3. +0.40

  4. -0.40


Correct Option: C

Which of the following techniques are used for the study of correlation?

  1. Scatter diagrams

  2. Karl Pearsons coefficient of correlation

  3. Spearmans rank correlation

  4. All of these


Correct Option: D

If two polynomial of the degree 7 and 4 respectively are multiplied, find the degree of the resultant polynomial

  1. 11

  2. -11

  3. 12

  4. 10


Correct Option: A

Which of these is a Geometric series?

  1. 1,3,5,7,9........

  2. 2,4,8,16.........

  3. 3,2,4,5,1,3..........

  4. 1,3,4,7,6........


Correct Option: B

A leading MNC operating in India has decided to reduce the work force in the ratio of 15:12 and at the same time increased the workers salary in the ratio of 18:21, the total wages likely to be affected by this proposed plan will be_____.

  1. total wages will go down in the ratio of 90:84

  2. total wages will go up in the ratio of 84:90

  3. total wages will go up by 5%

  4. no changes in total wages will


Correct Option: A

If regression coefficient between x and y is -2/3, y on x is -1/6, the coefficient of correlation between x and y is_____.

  1. -3

  2. 1

  3. -1/2

  4. -1/3


Correct Option: D

Estimate the value of coefficient of correlation between x and y if the two coefficient of regression are 0.64 and 1 :___

  1. 0.9

  2. 0.7

  3. 0.8

  4. 1.0


Correct Option: C

The correlation coefficient is a measure of ________________.

  1. association

  2. location

  3. relative location

  4. variability


Correct Option: B

Match the following :
List I
1. Correlation in Bivariable Frequency table.
2. Probable error and co-efficient correlation.
3. Rank correlation.
4. Karl pearson's co-efficient of correlation.
List II
a) $\dfrac{{\Sigma}{f}{d}{x} {d}{y} - {\dfrac{{\Sigma}{f}{d}{x} {\Sigma}{f}{d}{y}}{N}}}{\sqrt{{\Sigma}{f}{d}{{x}^2} - {\dfrac{({\Sigma}{f}{d}{x})^2}{N}}}{\sqrt{{\Sigma}{f}{d}{{y}^2} - {\dfrac{({\Sigma}{f}{d}{y})^2}{N}}}}}$
b) $ r = 0.6745 \dfrac{{-r}^2}{\sqrt{N}}$
c) $ r = 1 - \dfrac{{6}{\Sigma}{{d}^2}}{n({{n}^2 - {1})}}$
d) $ r = \dfrac{{\Sigma}{x}{y}}{{N}{\sigma}{x}{\sigma}{y}}$
Codes :
1   2   3  4

  1. b $\space$ d $\space$ a $\space$ b

  2. b $\space$ a $\space$ c $\space$ d

  3. a $\space$ b $\space$ c $\space$ d

  4. d $\space$ b $\space$ c $\space$ a


Correct Option: D
Explanation:

The correct formula for the calculation of correlation through karl pearson is option d, for bivarial frequency table is c and also for rank correlation in option c, therefore the correct option is D.

Karl Pearson's co-efficient of correlation between two variables is _____________.

  1. the product of their standard deviations

  2. the square root of the product of their regression co-efficient

  3. the co-variance between the variables

  4. none of the above


Correct Option: B

F-test is used to test the significance of the differences between ______________.

  1. co-efficient of correlation between two sample groups

  2. co-efficient of correlation among more than two sample groups

  3. average between two sample groups

  4. averages of more than two sample groups


Correct Option: A

Match the following items in List - I with most suitable options in List - II:

List-I List-II
(a) Fisher 1. Inverse probability
(b) Karl Pearson 2. Normal Distribution
(c) Thomas Baye's 3. Correlation Coefficient
(d) Karl Gauss 4. Index Numbers
  1. $(a) - 4, (b) - 3, (c) - 2, (d) - 1$

  2. $(a) - 4, (b) - 3, (c) - 1, (d) - 2$

  3. $(a) - 4, (b) - 2, (c) - 3, (d) - 1$

  4. $(a) - 4, (b) - 2, (c) - 1, (d) - 3$


Correct Option: B

__________  gives a precise numerical value of the degree of linear relationship between two variables X and Y.

  1. Scatter diagram

  2. Spearmans coefficient of correlation

  3. Karl Pearsons Coefficient of Correlation

  4. None


Correct Option: C
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