Question

In a partially destroyed laboratory, record of an analysis of correlation of data,
only the following results are legible:
Variance of X = 9
Regression equations are
(i) 8x −10y + 66 = 0
(ii) 0 40x −18y − 214 =
Find out the following missing results.
(i) The means of X and Y
(ii) The coefficient of correlation between x and y
(iii) The standard deviation of Y

Answer 1

Since two regression lines always intersect at a point representing mean values of the values xmean and ymean

$$8x-10y+66=0$$ $$40x-18y-214=0$$

$$8x-10y=-66$$

$$32y=544 => ymean=17$$

$$xmean=(10*17-66)/8=13$$

$$xmean=13, ymean=17$$

(ii) To find the given regression equations in such a way that the coefficient of dependent variable is less than one at least in one equation.

$$8x-10y=-66 => y=66/10+8x/10$$

b_yx = 0.8

$$40x-18y=214 => x=214/40+18y/40$$

b_xy = 0.45

$$r = sqrt ( bxy * byx )$$

$$r = sqrt(0.45 * 0.8)=0.6$$

Coefficient of correlation r between x and y is 0.6.

(iii) To determine the standard deviation of y , consider the formula:

$$\sigma y = (\sigma x * byx)/r$$

$$σy= 0.8 * sqrt(9) / 0.6 = 4$$