#### Correlation and Regression Analysis - Important Questions

11th Standard

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All questions are compulsory.
Time : 01:00:00 Hrs
Total Marks : 40

Part A

5 x 1 = 5
1. Correlation co-efficient lies between

(a)

0 to ∞

(b)

-1 to +1

(c)

-1 to 0

(d)

-1 to ∞

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

(a)

dependent variable

(b)

independent variable

(c)

regressor

(d)

explanatory variable

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

(a)

Negative

(b)

Positive

(c)

Zero

(d)

None of them

4. The lines of regression intersect at the point

(a)

(X,Y)

(b)

$\left( \bar { X } ,\bar { Y } \right)$

(c)

(0,0)

(d)

x, σy)

5. 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

6. Part B

5 x 3 = 15
7. 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.

8. 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.

9. 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.

10. Explain the concept of correlation and co-efficient of correlation.

11. If two lines of regression are 3X-2Y+1=0, 2X-Y-2=0, find $\bar {X}$and $\bar{Y}$.

12. Part C

4 x 5 = 20
13. Calculate correlation coefficient for the following data.

 X 25 18 21 24 27 30 36 39 42 48 Y 26 35 48 28 20 36 25 40 43 39
14. Obtain the two regression lines from the following data N=20, ΣX=80, ΣY=40, ΣX2=1680, ΣY2=320 and ΣXY=480

15. Obtain the two regression lines from the following

 X 6 2 10 4 8 Y 9 11 5 8 7
16. For the following observations, find the regression co-efficient byx and bxy and hence find the correlation co-efficient (4,2)(2,3)(3,2)(4,4)(2,4).