Page 334 - DMTH404_STATISTICS

Statistics

Notes  Y = 5.75 + 0.75X is the fitted line of regression.
C
Estimate of Y when X = 37
Y = 5.75 + 0.75 × 37 = 33.5 marks
C
 It is expected that the Judge Q would have awarded 33.5 marks to the eighth performance.

Example 5:
Find out the regression coefficients of Y on X, X on Y and correlation coefficient between X and
Y on the basis of the following data :
XY = 350, X = 50, Y = 60, n = 10, Variance of X = 4 and Variance of Y = 9.
Solution.

Regression coefficient of Y on X is given by

å XY æ å X ö æ å Y ö 350 æ 50ö æ 60ö
- ç ÷ ç ÷ - ç ÷ ç ÷
n è n ø è n ø 10 è 10 ø è 10 ø
b = 2 = = 1.25
s 4
X
Regression coefficient of X on Y is given by

å XY æ å X ö æ å Y ö
- ç ÷ ç ÷
-
n è n ø è n ø 35 30
d = 2 = = 0.55
s 9
Y
Coefficient of correlation between X and Y is given by

r = 1.25 0.55 = 0.83
´

Example 6:
The following results were worked out from scores in statistics and mathematics in a certain
examination :

Scores in Statistics X) Scores in Mathematics Y)
(
(
Mean 39.5 47.5
Standard Deviation 10.8 17.8

Karl Pearson's correlation coefficient between X and Y = 0.42. Find both the regression lines. Use
these lines to estimate the value of Y when X = 50 and the value of X when Y = 30.
Solution.

(a) Regression of Y on X

s 17.8
Regression coefficient b = × Y = 0.42 ´ = 0.69
r
s X 10.8
´
-
and a = Y bX = 47.5 0.69 39.5 = 20.24
-
 The line of regression of Y on X is Y = 20.24 + 0.69X,
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