For the lines of regression 4 x - 2 y = 4 and 2 x - 3 y + 6 = 0 , find the mean of ' x ' and the mean of ' y ' .

Given lines of regression are 4 x - 2 y = 4 . . . . . . i And 2 x - 3 y + 6 = 0 . . . . . . . . . ii We know that the two lines of regression intersect at the point x ¯ , y ¯ . x ¯ and y ¯ are mean of ' x ' and mean of ' y ' respectively. Now finding point of intersection of given lines. Multiplying equation ii by 2 and then subtracting from equation i , 4 x - 6 y + 12 - 4 x - 2 y = 0 - 4 ⇒ - 6 y + 2 y = - 16 ⇒ - 4 y = - 16 ⇒ y = 4 From equation i , 4 x - 2 4 = 4 ⇒ 4 x = 12 ⇒ x = 3 Hence, x ¯ = 3 , y ¯ = 4

E M B I B E

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 14

EASY

12th ICSE

IMPORTANT

Earn 100

Explain the differences between correlation and regression.

Important Questions on Linear Regression

EASY

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 15

Find the regression coefficients for a given data set where the standard deviation of

x

is 12, standard deviation of

y

is

8

and correlation coefficient is

0.45

.

MEDIUM

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 16

If the two lines of regression are

2 x + 3 y - 5 = 0 and 3 x + 4 y - 9 = 0

, determine the regression line of

y

on

x

.

HARD

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 17

The following data relates to total marks obtained and number of students getting a specific marks out of $30$ . Find the variance and the standard deviation of the following data.

Marks obtained	$18$	$19$	$20$	$21$	$22$	$23$	$24$	$25$	$26$	$27$
Number of students	$3$	$7$	$11$	$14$	$18$	$17$	$13$	$8$	$5$	$4$

MEDIUM

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 18

Find the standard deviation for the following data by using assumed mean method.

$20, 23, 24, 27, 28$

MEDIUM

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 19

For the following values find the standard deviation by assumed mean method.

$10, 12, 14, 15, 8, 9$

EASY

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 20

Explain the existence of two Regression Lines and list the assumptions of Linear regression.

EASY

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 21

Define regression analysis and give an explanation for existence of two Regression Lines.

EASY

12th ICSE

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Linear Regression>Exercise>Q 22

Gayathri has found a job in the city and now has to find an apartment in which to live. She surveys the monthly rent of several places and their distance from the city centre.

$\begin{array}{lcccccc} Distance [km] & 3 & 6 & 10 & 12 & 15 & 20 \\ \begin{array}{l} Monthly rent \\ [thousands of \\ rupees] \end{array} & 70 & 60 & 50 & 40 & 35 & 15 \end{array}$

Find the equation of your line of best fit.

Learn and Prepare for any exam you want !

|

|

|

|

|

|

|

|