#### Correlation and Regression Analysis Model Question Paper

11th Standard

Reg.No. :
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Time : 01:30:00 Hrs
Total Marks : 50
10 x 1 = 10
1. Example for positive correlation is

(a)

Income and expenditure

(b)

Price and demand

(c)

Repayment period and EMI

(d)

Weight and Income

2. Correlation co-efficient lies between

(a)

0 to ∞

(b)

-1 to +1

(c)

-1 to 0

(d)

-1 to ∞

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

(a)

0.667

(b)

-0.006

(c)

-0.667

(d)

0.70

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

(a)

0.3566

(b)

-0.3566

(c)

0

(d)

0.4566

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

(a)

Dependent variable

(b)

Independent variable

(c)

Explained variable

(d)

Regressed

6. When one regression coefficient is negative, the other would be

(a)

Negative

(b)

Positive

(c)

Zero

(d)

None of them

7. If regression co-efficient of Y on X is 2, then the regression co-efficient of X on Y is

(a)

$\frac{1}{2}$

(b)

2

(c)

>$\frac{1}{2}$

(d)

1

8. If two variables moves in decreasing direction then the correlation is

(a)

positive

(b)

negative

(c)

perfect negative

(d)

no correlation

9. The term regression was introduced by

(a)

R.A Fisher

(b)

Sir Francis Galton

(c)

Karl Pearson

(d)

Croxton and Cowden

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

(a)

-0.12

(b)

0.001

(c)

-1

(d)

-0.97

11. 2 x 2 = 4
12. From the following data calculate the correlation coefficient Σxy=120, Σx2=90, Σy2=640

13. 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.

14. 7 x 3 = 21
15. Calculate the correlation co-efficient for the following data.

 X 5 10 5 11 12 4 3 2 7 1 Y 1 6 2 8 5 1 4 6 5 2
16. The following are the ranks obtained by 10 students in commerce and accountancy are given below.

 Commerce 6 4 3 1 2 7 9 8 10 5 Accountancy 4 1 6 7 5 8 10 9 3 2

To what extent is the knowledge of students in the two subjects related?

17. The rank of 10 students of same batch in two subjects A and B are given below. Calculate the rank correlation coefficient.

 Rank of A 1 2 3 4 5 6 7 8 9 10 Rank of B 6 7 5 10 3 9 4 1 8 2
18. There are two series of index numbers P for price index and S for stock of the commodity. The mean and standard deviation of P are 100 and 8 and of S are 103 and 4 respectively. The correlation coefficient between the two series is 0.4. With these data obtain the regression lines of P on S and S on P.

19. 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
20. 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.

21. 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.

22. 3 x 5 = 15
23. 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
24. 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.

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