The following table shows the ages x and systolic blood pressure y of 12 women. Determine the least squares regression line of y on x . Age ( x ) 56 42 72 36 63 47 55 49 38 42 68 60 Blood Pressure ( y ) 147 125 160 118 149 128 150 145 115 140 152 155

Given data can be tabulated as x y x - x y - y ( x - x ) 2 ( y - y ) 2 ( x - x ) ( y - y ) 56 147 3 . 67 6 . 67 13 . 5 44.5 24.5 42 125 - 10 . 33 - 15 . 33 106 . 7 235 158 . 36 72 160 19 . 67 19 . 67 386 . 9 386 . 9 386 . 9 36 118 - 16 . 33 - 22 . 33 266 . 7 498 . 6 364 . 64 63 149 10 . 67 8 . 67 113 . 85 75 . 2 92 . 5 47 128 - 5 . 33 - 12 . 33 28 . 4 152 65 . 7 55 150 2 . 67 9 . 67 7 . 1 93 . 5 25 . 82 49 145 - 3 . 33 4 . 67 11 21 . 8 - 15 . 55 38 115 - 14 . 33 - 25 . 33 205 . 35 641 . 6 363 42 140 - 10 . 33 - 0 . 33 106 . 7 0 . 1 3 . 4 68 152 15 . 67 11 . 67 245 . 5 136 . 2 183 60 155 7 . 67 14 . 67 58 . 8 215 . 2 112 . 5 ∑ x = 628 ∑ y = 1684 ∑ = 0 ∑ = 0 ∑ = 1551 ∑ = 2500 . 6 ∑ = 1765 Mean of x , x = ∑ x n = 628 12 = 52 . 33 Mean of y , y = ∑ y n = 1684 12 = 140 . 33 b y x = ∑ ( x - x ) ( y - y ) ∑ ( x - x ) 2 b y x = 1765 1551 = 1 . 14 Regression line of y on x is y - y = b y x ( x - x ) y - 140 . 33 = 1 . 14 ( x - 52 . 33 ) y = 1 . 14 x + 80 . 67

The following table show final grades of 10 students in Algebra and Physics. Algebra ( x ) 75 80 93 65 87 71 98 68 84 77 Physics ( y ) 82 78 86 72 91 80 95 72 89 74 Find both the least squares lines.

Let assumed mean A = 80 , B = 82 Given data can be tabulated as x y u = x - A v = y - B u 2 v 2 u v 75 82 - 5 0 25 0 0 80 78 0 - 4 0 16 0 93 86 13 4 169 16 52 65 72 - 15 - 10 225 100 150 87 91 7 9 49 81 63 71 80 - 9 - 2 81 4 18 98 95 18 13 324 169 234 68 72 - 12 - 10 144 100 120 84 89 4 7 16 49 28 77 74 - 3 - 8 9 64 24 ∑ x = 798 ∑ y = 819 ∑ u = - 2 ∑ v = - 1 ∑ u 2 = 1042 ∑ v 2 = 599 ∑ u v = 689 Mean of x , x = A + ∑ u n = 80 + - 2 10 = 79 . 8 Mean of y , y = B + ∑ v n = 82 + - 1 10 = 81 . 9 b y x = ∑ u v - 1 n ∑ u ∑ v ∑ u 2 - 1 n ∑ u 2 , b x y = ∑ u v - 1 n ∑ u ∑ v ∑ v 2 - 1 n ∑ v 2 b y x = 689 - 0 . 1 ( - 2 ) ( - 1 ) 1042 - 0 . 1 ( - 2 ) ( - 2 ) = 688 . 8 1041 . 6 = 0 . 66 b x y = 689 - 0 . 1 ( - 2 ) ( - 1 ) 599 - 0 . 1 ( - 1 ) ( - 1 ) = 688 . 8 598 . 9 = 1 . 15 Regression line of y on x is y - y = b y x ( x - x ) y - 81 . 9 = 0 . 66 ( x - 79 . 8 ) y = 0 . 66 x + 29 . 23 Regression line of x on y is x - x = b x y ( y - y ) ( x - 79 . 8 ) = 1 . 15 ( y - 81 . 9 ) x = 1 . 15 y - 14 . 4

EASY

12th ICSE

IMPORTANT

Earn 100

Find the equations of the lines of regression on the basis of following data :

$x$ $1$ $2$ $3$ $4$ $5$

$y$ $166$ $184$ $142$ $180$ $338$

Important Questions on Linear Regression

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 19

A manufacturer of optical lenses has the following data on the cost per unit (in Rs.) of a certain quality of lens and the number of units made in each order:

Order Number

Number of units (

x

)

Cost per unit (

y

)

$1$

$2$

$3$

$4$

$5$

$6$

$1$

$3$

$5$

$7$

$10$

$15$

$58$

$52$

$46$

$40$

$37$

$22$

Find the correlation coefficient. Also determine the two regression equations.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 20

The following observations are given :

$(1, 4), (2, 8), (3, 2), (4, 12), (5, 10), (6, 14), (7, 16), (8, 6), (9, 18)$

Estimate the values of $y$ when the value of $x$ is $10$ and also estimate the value of $x$ when the value of $y$ is $5 .$

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 21

The following table shows the ages $x$ and systolic blood pressure $y$ of $12$ women.

Find the correlation coefficient between $x$ and $y$ . (Answer upto two places of decimal)

Age ( $x$ )	$56$	$42$	$72$	$36$	$63$	$47$	$55$	$49$	$38$	$42$	$68$	$60$
Blood Pressure ( $y$ )	$147$	$125$	$160$	$118$	$149$	$128$	$150$	$145$	$115$	$140$	$152$	$155$

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 21

The following table shows the ages $x$ and systolic blood pressure $y$ of $12$ women.

Determine the least squares regression line of $y$ on $x$ .

Age ( $x$ )	$56$	$42$	$72$	$36$	$63$	$47$	$55$	$49$	$38$	$42$	$68$	$60$
Blood Pressure ( $y$ )	$147$	$125$	$160$	$118$	$149$	$128$	$150$	$145$	$115$	$140$	$152$	$155$

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 21

The following table shows the ages $x$ and systolic blood pressure $y$ of $12$ women.

Estimate the blood pressure of a woman whose age is $45$ years.

Age ( $x$ )	$56$	$42$	$72$	$36$	$63$	$47$	$55$	$49$	$38$	$42$	$68$	$60$
Blood Pressure ( $y$ )	$147$	$125$	$160$	$118$	$149$	$128$	$150$	$145$	$115$	$140$	$152$	$155$

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 22

The following table show final grades of $10$ students in Algebra and Physics.

Algebra ( $x$ )	$75$	$80$	$93$	$65$	$87$	$71$	$98$	$68$	$84$	$77$
Physics ( $y$ )	$82$	$78$	$86$	$72$	$91$	$80$	$95$	$72$	$89$	$74$

Find both the least squares lines.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 22

The following table show final grades of $10$ students in Algebra and Physics.

Algebra (x)	$75$	$80$	$93$	$65$	$87$	$71$	$98$	$68$	$84$	$77$
Physics (y)	$82$	$78$	$86$	$72$	$91$	$80$	$95$	$72$	$89$	$74$

If a student receives

75

marks in Algebra, what is his expected score in Physics ?

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 2 - Linear Regression>EXERCISE>Q 22

The following table show final grades of $10$ students in Algebra and Physics.

Algebra ( $x$ )	$75$	$80$	$93$	$65$	$87$	$71$	$98$	$68$	$84$	$77$
Physics ( $y$ )	$82$	$78$	$86$	$72$	$91$	$80$	$95$	$72$	$89$	$74$

If a student receives

95

marks in Physics, what is his expected score in Algebra?

Find the equations of the lines of regression on the basis of following data : x 1 2 3 4 5 y 166 184 142 180 338

Important Questions on Linear Regression

Learn and Prepare for any exam you want !

Find the equations of the lines of regression on the basis of following data :

$x$ $1$ $2$ $3$ $4$ $5$

$y$ $166$ $184$ $142$ $180$ $338$