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Module 3 (Correlation and Regression) Tutorial Sheet 1.) Random variables X and Y follow a joint distribution ๐(๐ฅ, ๐ฆ) = {
Determine the correlation coefficient between X and Y. 2.) The joint probability distribution of (X,Y) is given below. X\Y 1 3 5 2 0.10 0.20 0. 4 0.15 0.30 0. Determine the correlation coefficient between ๐ and ๐. 3.) Two judges at a college homecoming parade rank eight floats in the following order: Float 1 2 3 4 5 6 7 8 Judge A
Judge B
Calculate the rank correlation coefficient. 4.) The following table gives the recorded grades for 10 students on a midterm test and the final examination in a calculus course: Student Mid-term Test Final Examination A.B. 84 73 B.C. 98 63 C.D. 91 87 D.E. 72 66 E.F. 86 78 F.G. 93 78 G.H. 80 91 H.I. 0 0 I.J. 92 88 J.K. 87 77 Calculate the rank correlation coefficient. 5.) Find the two lines of regression and coefficient of correlation for the data given below. ๐ = 18 , โ^ ๐ฅ = 12 , โ^ ๐ฆ = 18 , โ^ ๐ฅ^2 = 60 , โ^ ๐ฆ^2 = 96 and โ^ ๐ฅ๐ฆ = 48.
6.) The correlation coefficient between two variables x and y is r = 0.6. If ๐๐ฅ = 1. 5 , ๐๐ฆ = 2. 0 , ๐ฅฬ
= 10 , ๐ฆฬ
= 20. Find the regression lines of (a) y on x (b) x on y 7.) Estimate the blood pressure of a cricketer whose age is 45 from the following data. Name A B C D E F Age (X) 40 42 48 35 56 51 BP (Y) 90 93 102 85 105 99 8.) Let X and Y are independent RVs with means 4 and 8 and standard deviations โ 5 and โ^10 respectively. Obtain the correlation coefficient between S and T, where S=2X-4Y and T=3X+2Y. 9.) Consider the following data of X and Y. X 5 10 15 20 25 Y 24 25 23 20 30 Obtain (i) The equations of lines of regression (ii) Correlation coefficient between X and Y. 10.) The equations of lines of regression are given by 4x+8y-20=0 and 8x+12y-32=0 and variance of X is 12. Compute the following. (i) Correlation coefficient of X and Y (ii) The most appropriate value of x when y = 8 11.) From the data relating to the yield of dry bark (X1), height (X2) and girth (X3) for 18 cinchona plants, the following correlation coefficients were obtained: ๐ 12 = 0. 77 , ๐ 13 = 0. 72 and ๐ 23 = 0. 52. Find the partial correlation coefficients ๐ 12. 3 , ๐ 23. 1 and ๐ 13. 2. 12.) From the data relating to the yield of dry bark (X1), height (X2) and girth (X3) for 18 cinchona plants, the following correlation coefficients were obtained: ๐ 12 = 0. 77 , ๐ 13 = 0. 72 and ๐ 23 = 0. 52. Find the multiple correlation coefficients ๐
1. 23 , ๐
2. 13 and ๐
3. 12. 13.) In a tri-variate distribution, the standard deviations and correlation coefficients are given: ๐ 1 = 2 , ๐ 2 = 3 , ๐ 3 = 3 , ๐ 12 = 0. 7 , ๐ 13 = 0. 5 and ๐ 23 = 0. 5. Find the multiple regression. 14.) Find the regression equation of ๐ 1 on ๐ 2 and ๐ 3 from the data: Trait Mean Standard deviation
๐ 2 4.91^ 1.10^ - 0.
