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11th Business Maths Monthly Test - 2 ( Correlation and Regression Analysis )

MABS Institution

11th Business Maths Monthly Test - 2 ( Correlation and Regression Analysis )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The lines of regression of X on Y estimates

X for a given value of Y
Y for a given value of X
X from Y and Y from X
none of these

The variable which influences the values or is used for prediction is called

Dependent variable
Independent variable
Explained variable
Regressed

Correlation co-efficient lies between

0 to ∞
-1 to +1
-1 to 0
-1 to ∞

If the values of two variables move in opposite direction then the correlation is said to be

Negative
Positive
Perfect positive
No correlation

If r(X,Y) = 0 the variables X and Y are said to be

Positive correlation
Negative correlation
No correlation
Perfect positive correlation

From the following data, N=11, ΣX=117, ΣY=260, ΣX²=1313, ΣY²=6580,ΣXY=2827 the correlation coefficient is

0.3566
-0.3566
0
0.4566

The coefficient of correlation describes

the magnitude and direction
only magnitude
only direction
no magnitude and no direction

Scatter diagram of the variate values (X,Y) give the idea about

functional relationship
regression model
distribution of errors
no relation

The correlation coefficient is

r(X,Y)=\(\frac { { \sigma }_{ x }{ \sigma }_{ y } }{ cov(x,y) } \)
r(X,Y)=\(\frac { cov(x,y) }{ { \sigma }_{ x }{ \sigma }_{ y } } \)
r(X,Y)=\(\frac { cov(x,y) }{ { \sigma }_{ y } } \)
r(X,Y)=\(\frac { cov(x,y) }{ { \sigma }_{ x } } \)

Example for positive correlation is

Income and expenditure
Price and demand
Repayment period and EMI
Weight and Income

Part - B

Generic 2 - Answer All Question

Calculate the correlation coefficient from the following data
N=9, ΣX=45, ΣY=108, ΣX²=285, ΣY²=1356, ΣXY=597

The following information is given

X(in Rs.) Y(in Rs.)

Arithmetic Mean 6 8

Standard Deviation 5 \(\frac{40}{3}\)

Coefficient of correlation between X and Y is \(\frac{8}{15}\) . Find (i) The regression Coefficient of Y on X (ii) The most likely value of Y when X =Rs.100.

From the following data calculate the correlation coefficient Σxy=120, Σx²=90, Σy²=640

Part - C

Generic 3 - Answer All Question

An examination of 11 applicants for a accountant post was taken by a finance company. The marks obtained by the applicants in the reasoning and aptitude tests are given below.

Applicant A B C D E F G H I J K

Reasoning test 20 58 28 25 70 90 76 45 30 19 26

Aptitude test 30 60 50 40 85 90 56 82 42 31 49

Calculate Spearman’s rank correlation coefficient from the data given above.

prove that the correlation co-efficient is the geometric mean of regression co-efficients.

Calculate the correlation coefficient from the following data:
ΣX=125, ΣY=100, ΣX² =650, ΣY² =436, ΣXY=520, N=25

Calculate the co-efficient of correlation between x and y on the basis of the following observations. \(\sum\)x=125, \(\sum\)x²=1650, \(\sum\)y=100, \(\sum\)y²=1460, \(\sum\)xy=50, n=25.

X and Y are a pair of correlated variables. Ten observations of their values (X, Y) have the following results. ΣX=55, ΣXY=350, ΣX² =385, ΣY=55, Predict the value of y when the value of X is 6.

A random sample of recent repair jobs was selected and estimated cost, actual cost were recorded.

Estimated cost 30 45 80 25 50 97 47 40

Actual cost 27 48 73 29 63 87 39 45

Calculate the value of spearman’s correlation.

Calulate the co-efficient of correlation between x and y on the basis of the following observations. \(\sum\)\(\sum\)x=10, \(\sum\)x²=250, \(\sum\)y=70, \(\sum\)y²=300, \(\sum\)xy=75 and n =20

In a correlation study, the following values are obtained

X Y

Mean 50 50

S.D 3.5 4.5

The co-efficient of correlation is 0.5. Find the lines of regression.

Part - D

Generic 5 - Answer All Question

A computer while calculating the correlation co-efficient between two variables x and y from 25 pairs of observations, obtained the following results. \(\sum\)x=125, \(\sum\)x²=650, \(\sum\)y=100, \(\sum\)y²=460, xy=508. It was later found out that it had copied down two pairs as while the correct values are

x y

6 14

8 6

x y

8 12

6 8

Obtain the correlation co-efficient for the correct value.

Ten competitors in a beauty contest are ranked by three judges in the following order

First judge 1 4 6 3 2 9 7 8 10 5

Second judge 2 6 5 4 7 10 9 3 8 1

Third judge 3 7 4 5 10 8 9 2 6 1

Use the method of rank correlation coefficient to determine which pair of judges has the nearest approach to common taste in beauty?

Find coefficient of correlation for the following:

Cost(Rs) 14 19 24 21 26 22 15 20 19

Sales(Rs) 31 36 48 37 50 45 33 41 39

Obtain regression equation of Y on X and estimate Y when X=55 from the following.

X 40 50 38 60 65 50 35

Y 38 60 55 70 60 48 30

The following are the ranks obtained by 10 students in Statistics and Mathematics.

Statistics 1 2 3 4 5 6 7 8 9 10

Mathematics 1 4 2 5 3 9 7 10 6 8

Find the rank correlation coefficient.

Obtain the two regression lines from the following

X 6 2 10 4 8

Y 9 11 5 8 7

Using the following information you are requested to (i) obtain the linear regression of Y on X (ii) Estimate the level of defective parts delivered when inspection expenditure amounts to Rs.28,000 ΣX=424, ΣY=363, ΣX² =21926, ΣY² =15123, ΣXY=12815, N=10. Here X is the expenditure on inspection, Y is the defective parts delivered.

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