Regression equation

1. Calculate the regression equation of Y on X from the following data

X Y40 3038 3535 4042 3630 29

2. Out of the two regression equations given below which one is the regression of X on Y and which one the regression of Y on X

2 X + 4 Y = 104 X + 6 Y = 9

3. For 100 students of a class, the regression equation of marks in Statistics (X) on the marks in Commerce (Y) is 3 Y – 5X + 180 = 0. The mean marks in commerce are 50 and variance of marks in statistics is 4/9the to the variance of marks in commerce. Find the mean marks in statistics and the coefficient of correlation between marks in the two subjects.

4. The lines of regression of Y on X and X on Y are respectivelyY = X + 5 and 16 X – 9 Y =94Find the variance of X if the variance of Y is 16. Also find the covariance of X and Y.

5. A survey was conducted to study the relationship between expenditure on a accommodation (s) and expenditure on entertainment (y) and the following results were obtained:

Expenditure on Mean S.DAccommodation 173 66Entertainment 47.8 22Coefficient of correlation : 0.57

Write down the equation of regression of y on x and estimate the expenditure on entertainment if the expenditure on accommodation is 200.

6. (a) Given

X Series Y seriesMean 18 100SD 14 20

Coefficient of correlation between X and Y series = +0.8Find the most probable value of Y if X is 70 and most Probable value of X if Y is 90.

(b) if two regression coefficient are 0.8 and 0.6 what would be the value of the coefficient of correlation?

7. The following data are given regarding expenditure on advertising and sales of a particular firm:

X (Advertisement Expenditure) Y (Sales)Mean 10 90

SD 3 12(i) Calculate the regression equation of Y on X(ii) Find the likely sales when advertisement budget is Rs. 15 lakhs.(iii) Estimate the advertisement expenditure required to attain a sales target of Rs. 120lakhs.

8. Point out the inconsistency in the statement: the regression of y on x is 2y + 3x = 4 and the correlation coefficient between x and y is 0.8.

9. Find the mean of two variables x and y and the correlation coefficient between x and y from two regression lines x +6y = 6 and 2x +3y = 9 of a sample.

10. In a partially destroyed laboratory record of an analysis of correlation data, the following results only are obtained:

Regression equations are 8x+10y = 64 and 40x – 18 y = 320.

What are (i) the mean values of x and y

(iv) Standard deviation of Y(v) The coefficient of correlation between x and y ?

11. find the regression equation of y on x where y and x are the marks obtained by 10 students are given as below:

Y X20 2060 4555 6545 4075 5535 3525 1590 8010 2550 50

12. a panel of two judges P and Q graded seven dramatic performances by independently awarding marks as follows:

Performance Marks by P Marks by Q1 46 402 42 383 44 364 40 355 43 396 41 37

7 45 41

The eighth performance, which judge Q could not attend was awarded 37 marks by judge P. if the judge Q had also been present, how many marks would be expected to have been awarded by him to the eighth performance?

13. Given the following bivariate data:

X Y-1 -65 13 02 01 11 27 13 5

(a) Fit a regression line of Y on X and predict Y if X = 10(b) Fit a regression line of X on y and predict X if Y = 2.5

14. the personnel manager of an electronic manufacturing company devices a manual dexterity test for job applicants to predict their production rating in the assembly department. In order to do this he selects a random sample of 10 applicants. They are given the test and later assigned a production rating. Results are as follows:

Worker Test Score Production RatingA 53 45B 36 43C 88 89D 84 79E 86 84F 64 66G 45 49H 48 48I 39 43J 69 76

15. the coefficient of correlation between the ages of husbands and wives in a community was found to be +0.8, the average of husbands age was 25 years and that of wives age 22 years. Their standard deviations were 4 and 5 years respectively. Find with the help of regression equations:

(a) the expected age of husband when wife’s age is 16 years and

(b) the expected age of wife when husband’s age is 33 years.

16. There are two series of index numbers, P for price index and S for stock of a commodity. The mean and SD of P are 100 and 8 and of S are 103 and 4 respectively. The correlation between the two series is 0.4. With these data, work out a linear equation to read off values of P for various values of S. Can the same equation be used to read off values of s for various values of P?