REGRESSION ANALYSIS SELF-ASSESSMENT QUESTIONS

1. Explain clearly the concept of Regression. Explain with suitable examples its role in dealing with business problems.

2. What do you understand by linear regression?

3. What is meant by 'regression'? Why should there be in general, two lines of regression for each bivariate distribution? How the two regression lines are useful in studying correlation between two variables?

4. Why is the regression line known as line of best fit?

5. Write short note on

(i) Regression Coefficients

(ii) Regression Equations

(iii) Standard Error of Estimate

(iv) Coefficient of Determination

(v) Coefficient of Non-determination

6. Distinguish clearly between correlation and regression as concept used in statistical analysis.

7. Fit a least-square line to the following data:

(i) Using X as independent variable

(ii) Using X as dependent variable X : 1 3 4 8 9 11 14 Y : 1 2 4 5 7 8 9 Hence obtain

a) The regression coefficients of Y on X and of X on Y

b) X and Y 2

c) Coefficient of correlation between and X and Y

d) What is the estimated value of Y when X = 10 and of X when Y = 5?

8. What are regression coefficients? Show that r2 = byx. bxy where the symbols have their usual meanings. What can you say about the angle between the regression lines when

(i) r = 0,

(ii) r = 1

(iii) r increases from 0 to 1?

9. Obtain the equations of the lines of regression of Y on X from the following data. X : 12 18 24 30 36 42 48 Y : 5.27 5.68 6.25 7.21 8.02 8.71 8.42 Estimate the most probable value of Y, when X = 40.

10. The following table gives the ages and blood pressure of 9 women. Age (X) : 56 42 36 47 49 42 60 72 63 Blood Pressure(Y) 147 125 118 128 145 140 155 160 149 Find the correlation coefficient between X and Y.

(i) Determine the least square regression equation of Y on X.

(ii) Estimate the blood pressure of a woman whose age is 45 years.

11. Given the following results for the height (X) and weight (Y) in appropriate units of 1,000 students: X = 68, Y = 150, Sx = 2.5, S y = 20 and r = 0.6. 3 Obtain the equations of the two lines of regression. Estimate the height of a student A who weighs 200 units and also estimate the weight of the student B whose height is 60 units.

12. From the following data, find out the probable yield when the rainfall is 29". Rainfall Yield Mean 25" 40 units per hectare Standard Deviation 3" 6 units per hectare Correlation coefficient between rainfall and production = 0.8.

13. A study of wheat prices at two cities yielded the following data: City A City B Average Price Rs 2,463 Rs 2,797 Standard Deviation Rs 0.326 Rs 0.207 Coefficient of correlation r is 0.774. Estimate from the above data the most likely price of wheat

(i) at City A corresponding to the price of Rs 2,334 at CityB

(ii) at city B corresponding to the price of Rs 3.052 at City A

14. Find out the regression equation showing the regression of capacity utilisation on production from the following data: Production (in lakh units) Average 35.6 Standard Deviation 10.5 Capacity Utilisation (in percentage) 84.8 8.5 r = 0.62 Estimate the production, when capacity utilisation is 70%.

15. The following table shows the mean and standard deviation of the prices of two shares in a stock exchange. Share Mean (in Rs) Standard Deviation (in Rs) A Ltd. 39.5 10.8 B Ltd. 47.5 16.0 4 If the coefficient of correlation between the prices of two shares is 0.42, find the most likely price of share A corresponding to a price of Rs 55, observed in the case of share B.

16. Find out the regression coefficients of Y on X and of X on Y on the basis of following data: X = 50, X = 5, Y = 60, Y = 6, XY = 350 Variance of X = 4, Variance of Y = 9

17. Find the regression equation of X and Y and the coefficient of correlation from the following data: X = 60, Y = 40, XY = 1150, X 2 = 4160, Y 2 = 1720 and N = 10.

18. By using the following data, find out the two lines of regression and from them compute the Karl Pearson's coefficient of correlation. X = 250, Y = 300,XY = 7900, X 2 = 6500, Y 2 = 10000, N =10

19. The equations of two regression lines between two variables are expressed as 2X - 3Y = 0 and 4Y - 5X-8 = 0.

(i) Identify which of the two can be called regression line of Y on X and of X onY.

(ii) Find X and Y and correlation coefficient r from the equations

20. If the two lines of regression are 4X - 5Y + 30 = 0 and 20X - 9Y - 107 = 0 Which of these is the lines of regression of X and Y. Find rxy and Sy when Sx = 3

21. The regression equation of profits (X) on sales (Y) of a certain firm is 3Y - 5X +108 = 0. The average sales of the firm were Rs 44,000 and the variance of profits is 9/16th of the variance of sales. Find the average profits and the coefficient of correlation between the sales and profits.