Advertisements
Advertisements
Question
Let X be the number of matches played by the player and Y he the number of matches in which he scored more thun 50 runs. The following data is obtained for 5 players :
| No. of Matches Played (X) | Data of matches of 5 players | ||||
| 21 | 25 | 26 | 24 | 19 | |
| Scored more than 50 in a match (Y) | 19 | 20 | 24 | 21 | 16 |
Find the regression line of X on Y.
Solution
| x | y | `x - barx` | `y - bary` | `(x - barx)(y - bary)` | `(y - bary)^2` |
| 21 | 19 | -2 | -1 | 2 | 1 |
| 25 | 20 | 2 | 0 | 0 | 0 |
| 26 | 24 | 3 | 4 | 12 | 16 |
| 24 | 21 | 1 | 1 | 1 | 1 |
| 19 | 16 | -4 | -4 | 16 | 16 |
| 115 | 100 | 31 | 34 |
`barx = (Σx)/n = 115/5 = 23`
and `bary = (Σy)/n = 100/5 = 20`
Regression coefficient of x on y,
`b_(xy) = (Σ(x - barx)(y - bary))/(Σ(y - bary)^2) = 31/34`
= `31/34`
Equation of regression line of x on y is
`(x - barx) = b_(xy)(y - bary)`
`(x - 23) = 31/34(y - 20)`
x - 23 = 0.91(y - 20)
x - 23 = 0.91y - 18.2
x = 0.91y + 4.8
APPEARS IN
RELATED QUESTIONS
The two lines of regressions are 4x + 2y- 3 = 0 and 3x + 6y + 5 =0. Find the correlation co-efficient between x and y.
In a contest, the competitors are awarded marks out of 20 by two judges. The scores of the 10 competitors are given below. Calculate Spearman's rank correlation.
| Competitors | A | B | C | D | E | F | G | H | I | J |
| Judge A | 2 | 11 | 11 | 18 | 6 | 5 | 8 | 16 | 13 | 15 |
| Judge B | 6 | 11 | 16 | 9 | 14 | 20 | 4 | 3 | 13 | 17 |
The regression equation of y on x is given by 3x + 2y - 26 = O. Find byx.
For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y – 5x + 180 = 0. The mean marks in accountancy is 44 and the variance of marks in statistics is `(9/16)^(th)` of the variance of marks in accountancy. Find the mean marks in statistics and the correlation coefficient between marks in the two subjects.
Bring out the inconsistency, if any in the following :
bYX + bXY = 1.30 and r = 0.75
Bring out the inconsistency, if any in the following :
bYX = bXY = 1.50 and r = -0.9
For a bivariate data,
`bar x = 53 , bar y = 28 , "b"_"xy" = -1.5 and "b"_"xy"=- 0.2` Find
Correlation coefficient between X and Y
For a bivariate data,
`bar x = 53 , bar y = 28 , "b"_"yx"=-1.5 and "b"_"xy"=- 0.2` Find Estimate of X for y = 25.
From the data 7 pairs of observations on X and Y following results are obtained :
∑(xi - 70) = - 38 ; ∑ (yi - 60) = - 5 ;
∑ (xi - 70)2 = 2990 ; ∑ (yi - 60)2 = 475 ;
∑ (xi - 70) (yi - 60) = 1063
Obtain :
(a) The line of regression of Y on X.
(b) The line of regression of X on Y.
Values of two regression coefficients between the variables X and Y are `b_"yx" = - 0.4` and `b_"xy"` = - 2.025 respectively. Obtain the value of correlation coefficient.
For the two regression equations 4y = 9x + 15 and 25x = 6y + 7 find correlation coefficient r, `barx, bary`
A psychologist selected a random sample of 22 students. He grouped them in 11 pairs so that the students in each pair have nearly equal scores in an intelligence test. In each pair, one student was taught by method A and the other by method B and examined after the course. The marks obtained by them after the course are as follows:
| Pairs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Methods A | 24 | 29 | 19 | 14 | 30 | 19 | 27 | 30 | 20 | 28 | 11 |
| Methods B | 37 | 35 | 16 | 26 | 23 | 27 | 19 | 20 | 16 | 11 | 21 |
Calculate Spearman’s Rank correlation.
If the regression line of x on y is, 9x + 3y − 46 = 0 and y on x is, 3x + 12y − 7 = 0, then the correlation coefficient ‘r’ is equal to:
The following table shows the Mean, the Standard Deviation and the coefficient of correlation of two variables x and y.
| Series | x | y |
| Mean | 8 | 6 |
| Standard deviation | 12 | 4 |
| Coefficient of correlation | 0.6 | |
Calculate:
- the regression coefficient bxy and byx
- the probable value of y when x = 20
The random variables have regression lines 3x + 2y − 26 = 0 and 6x + y − 31 = 0. Calculate co-efficient of correlations.
