ISC Class 12th Mathematics Chapter 9 - Linear Regression Important Questions with Answers

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Out of the two regression lines x + 2y – 5 = 0 and 2x + 3y = 8, find the line of regression of y on x.

Question 2.

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 b_xy and b_yx
the probable value of y when x = 20

Question 3.

An analyst analysed 102 trips of a travel company. He studied the relation between travel expenses (y) and the duration (x) of these trips. He found that the relation between x and y was linear. Given the following data, find the regression equation of y on x.

`sumx` = 510, `sumy` = 7140, `sumx^2` = 4150, `sumy^2` = 740200, `sumxy` = 54900

Question 4.

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?

Only one of the two regression lines has a negative coefficient.

Both regression coefficients are positive.

Both regression coefficients are negative.

One of the lines of regression is parallel to the x-axis.

Question 5.

The equations of two lines of regression are 4x + 3y + 7 = 0 and 3x + 4y + 8 = 0. Find the mean value of x and y.

Question 6.

Read the following statements and choose the correct option:

If r = 0, then regression lines are not defined.
If r = 0, then regression lines are parallel.
If r = 0, then regression lines are perpendicular.
If r = ±1, then regression lines coincide.

Which of the following is correct?

Only IV is correct.

Only I and II are correct.

Only I and IV are correct.

Only III and IV are correct.

Question 7.

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).

Question 8.

A survey of 50 families to study the relationships between expenditure on accommodation in (? x) and expenditure on food and entertainment (? y) gave the following results: `sumx = 8500, sumy = 9600, ?_x = 60, ?_y = 20, r = 0.6`

Estimate the expenditure on food and entertainment when expenditure on accommodation is ? 200.

Question 9.

The random variables have regression lines 3x + 2y ? 26 = 0 and 6x + y ? 31 = 0. Calculate mean value of x and y.

Question 10.

The random variables have regression lines 3x + 2y ? 26 = 0 and 6x + y ? 31 = 0. Calculate co-efficient of correlations.

Question 1.

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.

Question 2.

The two lines of regressions are 4x + 2y- 3 = 0 and 3x + 6y + 5 =0. Find the correlation co-efficient between x and y.

Question 3.

Given that the observations are: (9, -4), (10, -3), (11, -1), (12, 0), (13, 1), (14, 3), (15, 5), (16, 8). Find the two lines of regression and estimate the value of y when x = 13·5.

Question 4.

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

Question 5.

If `vecx = 18, vecy=100,?_y=20` , bary` and correlation coefficient xyr 0.8, ? find the regression equation of y on x.

Question 6.

The following results were obtained with respect to two variables x and y.
? x = 15 , ?y = 25, ?xy = 83, ?xy = 55, ?y²=135 and n =5
(i) Find the regression coefficient xy b .
(ii) Find the regression equation of x on y.

Question 7.

Find the equation of the regression line of y on x, if the observations (x, y) are as follows :
(1,4),(2,8),(3,2),(4,12),(5,10),(6,14),(7,16),(8,6),(9,18)
Also, find the estimated value of y when x = 14.

Question 8.

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?

Question 9.

The two lines of regressions are x + 2y – 5 = 0 and 2x + 3y – 8 = 0 and the variance of x is 12. Find the variance of y and the coefficient of correlation.