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

MABS Institution

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

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The coefficient of correlation describes

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

The regression coefficient of X on Y

b_xy=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)
b_yx=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)
b_xy=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)
b_xy=\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma y^{ 2 }-(\Sigma y)^{ 2 } } } } \)

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

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

functional relationship
regression model
distribution of errors
no relation

If two variables moves in decreasing direction then the correlation is

positive
negative
perfect negative
no correlation

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 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 which influences the values or is used for prediction is called

Dependent variable
Independent variable
Explained variable
Regressed

The regression coefficient of Y on X

b_xy=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)
b_yx=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)
b_yx=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)
b_xy=\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma { y }^{ 2 }-(\Sigma y)^{ 2 } } } } \)

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

Negative
positive
Perfect positive
No correlation

Part - B

Generic 5 - Answer All Question

Find out the coefficient of correlation in the following case and interpret.

Height of father (in inches) 65 66 67 67 68 69 71 73

Height of son (in inches) 67 68 64 68 72 70 69 70

Find the equation of the regression line of Y on X, if the observations ( Xt, Yi) are the following (1,4) (2,8) (3,2) ( 4,12) ( 5, 10) ( 6, 14) ( 7, 16) ( 8, 6) (9, 18)

Calculate coefficient of correlation for the ages of husbands and their respective wives:

Age of husbands 23 27 28 29 30 31 33 35 36 39

Age of wives 18 22 23 24 25 26 28 29 30 32

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.

The two regression lines are 3X+2Y=26 and 6X+3Y=3l. Find the correlation coefficient.

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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