11th Business Maths Weekly Test - 1 ( Correlation and Regression Analysis )

MABS Institution

11th Business Maths Weekly Test - 1 ( Correlation and Regression Analysis )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

If r=–1, then correlation between the variables

perfect positive
perfect negative
negative
no correlation

When one regression coefficient is negative, the other would be

Negative
Positive
Zero
None of them

Example for positive correlation is

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

The term regression was introduced by

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

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

Negative
Positive
Perfect positive
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

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

-0.12
0.001
-1
-0.97

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

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

Positive correlation
Negative correlation
No correlation
Perfect positive correlation

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

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

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

If two regression co-efficient are 2 and 0.45, what will be the co-efficient of correlation?

The following data pertains to the marks in subjects A and B in a certain examination. Mean marks in A = 39.5, Mean marks in B= 47.5 standard deviation of marks in A =10.8 and Standard deviation of marks in B= 16.8. coefficient of correlation between marks in A and marks in B is 0.42. Give the estimate of marks in B for candidate who secured 52 marks in A.
Marks in two subjects X and Y given below: Calculate the rank correlation:

X 46 54 56 57 58 60 62

Y 36 40 44 54 42 58 53

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

Part - D

Generic 5 - Answer All Question

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

Find the means of X and Y variables and the coefficient of correlation between them from the following two regression equations:
2Y–X–50 = 0
3Y–2X–10 = 0

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

The two regression lines were found to be 4X–5Y+33=0 and 20X–9Y–107=0. Find the mean values and coefficient of correlation between X and Y.

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

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	X(in Rs.)	Y(in Rs.)
Arithmetic Mean	6	8
Standard Deviation	5	\(\frac{40}{3}\)

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11th Business Maths Weekly Test - 1 ( Correlation and Regression Analysis )

MABS Institution

11th Business Maths Weekly Test - 1 ( Correlation and Regression Analysis )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

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

If r=–1, then correlation between the variables

When one regression coefficient is negative, the other would be

Example for positive correlation is

The term regression was introduced by

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

The lines of regression of X on Y estimates

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

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

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

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

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

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

If two regression co-efficient are 2 and 0.45, what will be the co-efficient of correlation?

Marks in two subjects X and Y given below: Calculate the rank correlation: X 46 54 56 57 58 60 62 Y 36 40 44 54 42 58 53

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

Part - D

Generic 5 - Answer All Question

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

Find the means of X and Y variables and the coefficient of correlation between them from the following two regression equations: 2Y–X–50 = 0 3Y–2X–10 = 0

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

The two regression lines were found to be 4X–5Y+33=0 and 20X–9Y–107=0. Find the mean values and coefficient of correlation between X and Y.

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

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

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

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

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.

Marks in two subjects X and Y given below: Calculate the rank correlation:

X 46 54 56 57 58 60 62

Y 36 40 44 54 42 58 53

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

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

Find the means of X and Y variables and the coefficient of correlation between them from the following two regression equations:
2Y–X–50 = 0
3Y–2X–10 = 0