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11th Business Maths Monthly Test - 3 ( Correlation and Regression Analysis )

MABS Institution

11th Business Maths Monthly Test - 3 ( Correlation and Regression Analysis )-Aug 2020

Time : 2.00 Hours

Part - A

Multiple Choice Question - Answer All Question

The person suggested a mathematical method for measuring the magnitude of linear relationship between two variables say X and Y is

Karl Pearson
Spearman
Croxton and Cowden
Ya Lun Chou

The variable whose value is influenced or is to be predicted is called

dependent variable
independent variable
regressor
explanatory variable

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 lines of regression intersect at the point

(X,Y)
\(\left( \bar { X } ,\bar { Y } \right) \)
(0,0)
(σ_x, σ_y)

The correlation coefficient from the following data N=25, ΣX=125, ΣY=100, ΣX²=650, ΣY²=436, ΣXY=520
0.667

-0.006

-0.667

0.70
If the values of two variables move in opposite direction then the correlation is said to be
Negative

Positive

Perfect positive

No correlation

Example for positive correlation is

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

Correlation co-efficient lies between

0 to ∞
-1 to +1
-1 to 0
-1 to ∞

Cov(x,y)=–16.5, \({ \sigma }_{ x }^{ 2 }=2.89,{ \sigma }_{ y }^{ 2 }\)=100. Find correlation coefficient

-0.12
0.001
-1
-0.97

If r=–1, then correlation between the variables
perfect positive

perfect negative

negative

no correlation
If regression co-efficient of Y on X is 2, then the regression co-efficient of X on Y is
≤\(\frac{1}{2}\)

2

>\(\frac{1}{2}\)

1

The term regression was introduced by

R.A Fisher
Sir Francis Galton
Karl Pearson
Croxton and Cowden

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

Positive correlation
Negative correlation
No correlation
Perfect positive correlation

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

The coefficient of correlation describes

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

Part - B

Generic 2 - Answer All Question

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

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.

Part - C

Generic 3 - Answer All Question

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.

A survey was conducted to study the relationship between expenditure on accommodation (X) and expenditure on Food and Entertainment (Y) and the following results were obtained:

Mean SD

Expenditure on Accommodation Rs. 178 63.15

Expenditure on Food and Entertainment Rs 47.8 22.98

Coefficient of Correlation 0.43

Write down the regression equation and estimate the expenditure on Food and Entertainment, if the expenditure on accommodation is Rs. 200.

Calculate the regression equation of X on Y from the following data:

X 10 12 13 12 16 15

Y 40 38 43 45 37 43

For the following observations, find the regression co-efficients b_yx and b_xy and hence find the correlation co-efficient between x and y.(4,2) (2, 3)(3, 2)(4, 4)(2, 4)

Calculate the correlation coefficient from the data given below:

X 1 2 3 4 5 6 7 8 9

Y 9 8 10 12 11 13 14 16 15

Calculate Co-efficient of correlation for the following data:

X -3 -2 -2 0 1 2 3

Y 9 4 1 0 1 4 9

Part - D

Generic 5 - Answer All Question

The following data relate to advertisement expenditure(in lakh of rupees) and their corresponding sales( in crores of rupees)

Advertisement expenditure 40 50 38 60 65 50 35

Sales 38 60 55 70 60 48 30

Estimate the sales corresponding to advertising expenditure of Rs. 30 lakh.

For the following data, (i) the regression equation of X on Y regression equation of Y on X (iii) the correlation co-efficient between X and Y (iv) the value of x when y=5 (v) the value of y when x=6

The equations of two lines of regression obtained in a correlation analysis are the following 2X=8–3Y and 2Y=5–X. Obtain the value of the regression coefficients and correlation coefficient.

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.

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

For the data on price (in rupees) and demand (in tonnes) for a commodity, calculate the co-efficient of correlations.

Price(X) 22 24 26 28 30 3 34 36 38 40

Demand(Y) 60 58 58 50 48 48 48 42 36 32

For the following observations, find the regression co-efficient b_yx and b_xy and hence find the correlation co-efficient (4,2)(2,3)(3,2)(4,4)(2,4).

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