Advertisements
Advertisements
Question
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.
Solution
Given n = 50
Regression line of x on y is
3y – 5x + 180 = 0
⇒ 5x = `[3y + 180]/5`
∴ x = `3/5 y + 180/5`
∴ `b_(xy) = "coefficient of y" = 3/5`
Variance of marks in statistics = `9/16`
Variance of marks in accountancy.
i.e. V(x) = `9/16`V(y)
⇒ `V_(x)/V_(y) = 9/16`
Taking square roots,
`(σ_x)/(σ_y) = 3/4`
We have, `b_(xy) = r. (σ_x)/(σ_y)`
⇒ `3/5 = r xx 3/4`
⇒ `r = 4/5 = 0.8`
Given `bary` = 44
∴ Substituting y = 44 is 3y – 5x + 180 = 0
⇒ 3(44) – 5x + 18 = 0
⇒ 132 – 5x + 180 = 0
⇒ 5x = 132 + 180 = 312
⇒ x = `312/5 ` = 62.4
∴ `barx` = 62.4
∴ Mean marks in statistics `barx` = 62.4
RELATED QUESTIONS
Examine whether the following statement pattern is tautology, contradiction or contingency :
p ∨ – (p ∧ q)
The regression equation of y on x is given by 3x + 2y - 26 = O. Find byx.
Bring out the inconsistency; if any: byx + bxy = 1.30. and r = 0.75
Two samples from bivariate populations have 15 observations each. The sample mean of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from means are 136 and 148. The sum of product of deviations from respective means is 122. Obtain the equation of line of regression of X on Y.
Bring out the inconsistency, if any in the following :
bYX = bXY = 1.50 and r = -0.9
Bring out the inconsistency, if any in the following :
bYX = 2.6 and bXY = `1/2.6`
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"_"xy" = - 0.2` , `"b"_"yx" = -1.5` Find
Estimate of Y , When X = 50.
From the two regression equations y = 4x - 5 and 3x = 2y + 5, find `barx and bary`
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.
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.
By using the data `bar"x"` = 25 , `bar"y" = 30 ; "b"_"yx" = 1.6` and `"b"_"xy" = 0.4` find,
(a) The regression equation y on x.
(b) What is the most likely value of y when x = 60?
(c) What is the coefficient of correlation between x and y?
Find the line of best fit for the following data, treating x as the dependent variable (Regression equation x on y):
| X | 14 | 12 | 13 | 14 | 16 | 10 | 13 | 12 |
| Y | 14 | 23 | 17 | 24 | 18 | 25 | 23 | 24 |
Hence, estimate the value of x when y = 16.
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.
The coefficient of correlation between the values denoted by X and Y is 0.5. The mean of X is 3 and that of Y is 5. Their standard deviations are 5 and 4 respectively.
Find:
(i) the two lines of regression.
(ii) the expected value of Y, when X is given 14.
(iii) the expected value of X, when Y is given 9.
The marks obtained by 10 candidates in English and Mathematics are given below:
| Marks in English | 20 | 13 | 18 | 21 | 11 | 12 | 17 | 14 | 19 | 15 |
| Marks in Mathematics | 17 | 12 | 23 | 25 | 14 | 8 | 19 | 21 | 22 | 19 |
Estimate the probable score for Mathematics if the marks obtained in English are 24.
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:
For 5 observations of pairs (x, y) of variables X and Y, the following results are obtained:
∑x = 15, ∑y = 25, ∑x2 = 55, ∑y2 = 135, ∑xy = 83.
Calculate the value of bxy and byx.
If the two regression coefficients are 0.8 and 0.2, then the value of coefficient of correlation r will be ______.
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
If the correlation coefficient of two sets of variables (X, Y) is `(-3)/4`, which one of the following statements is true for the same set of variables?
Mean of x = 53, mean of y = 28 regression co-efficient y on x = −1.2, regression co-efficient x on y = −0.3. Find coefficient of correlation (r).
The random variables have regression lines 3x + 2y − 26 = 0 and 6x + y − 31 = 0. Calculate co-efficient of correlations.
