Maharashtra State BoardHSC Commerce 12th Board Exam
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Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 3 - Linear Regression [Latest edition]

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Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com
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Chapter 3: Linear Regression

Exercise 3.1Exercise 3.2Exercise 3.3Miscellaneous Exercise 3
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Exercise 3.1 [Pages 41 - 42]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 3 Linear RegressionExercise 3.1 [Pages 41 - 42]

Exercise 3.1 | Q 1 | Page 41

The HRD manager of a company wants to find a measure which he can use to fix the monthly income of persons applying for the job in the production department. As an experimental project, he collected data of 7 persons from that department referring to years of service and their monthly incomes.

Years of service (X) 11 7 9 5 8 6 10
Monthly Income (₹ 1000's)(Y) 10 8 9 5 9 7 11
  1. Find the regression equation of income on years of service.
  2. What initial start would you recommend for a person applying for the job after having served in a similar capacity in another company for 13 years?
Exercise 3.1 | Q 2 | Page 41

Calculate the regression equations of X on Y and Y on X from the following data:

X 10 12 13 17 18
Y 5 6 7 9 13
Exercise 3.1 | Q 3 | Page 41

For a certain bivariate data on 5 pairs of observations given

∑ x = 20, ∑ y = 20, ∑ x2 = 90, ∑ y2 = 90, ∑ xy = 76

Calculate: 

  1. cov (X, Y)
  2. bYX and bXY
  3. r
Exercise 3.1 | Q 4 | Page 41

From the following data estimate y when x =125.

X 120 115 120 125 126 123
Y 13 15 14 13 12 14
Exercise 3.1 | Q 5.1 | Page 41

The following table gives the aptitude test scores and productivity indices of 10 workers selected at random.

Aptitude score (X) 60 62 65 70 72 48 53 73 65 82
Productivity Index (Y) 68 60 62 80 85 40 52 62 60 81

Obtain the two regression equations and estimate the productivity index of a worker whose test score is 95.

Exercise 3.1 | Q 5.2 | Page 41

The following table gives the aptitude test scores and productivity indices of 10 workers selected at random.

Aptitude score (X) 60 62 65 70 72 48 53 73 65 82
Productivity Index (Y) 68 60 62 80 85 40 52 62 60 81

Obtain the two regression equations and estimate the test score when the productivity index is 75.

Exercise 3.1 | Q 6 | Page 42

Compute the appropriate regression equation for the following data:

X
[Independent Variable]
2 4 5 6 8 11
Y [dependent Variable] 18 12 10 8 7 5
Exercise 3.1 | Q 7 | Page 42

The following are the marks obtained by the students in Economics (X) and Mathematics (Y)

X 59 60 61 62 63
Y 78 82 82 79 81

Find the regression equation of Y on X.

Exercise 3.1 | Q 8 | Page 42

For the following bivariate data obtain the equations of two regression lines:

X 1 2 3 4 5
Y 5 7 9 11 13
Exercise 3.1 | Q 9 | Page 42

From the following data obtain the equation of two regression lines:

X 6 2 10 4 8
Y 9 11 5 8 7
Exercise 3.1 | Q 10 | Page 42

For the following data, find the regression line of Y on X

X 1 2 3
Y 2 1 6

Hence find the most likely value of y when x = 4.

Exercise 3.1 | Q 11 | Page 42

From the following data, find the regression equation of Y on X and estimate Y when X = 10.

X 1 2 3 4 5 6
Y 2 4 7 6 5 6
Exercise 3.1 | Q 12 | Page 42

The following sample gives the number of hours of study (X) per day for an examination and marks (Y) obtained by 12 students.

X 3 3 3 4 4 5 5 5 6 6 7 8
Y 45 60 55 60 75 70 80 75 90 80 75 85

Obtain the line of regression of marks on hours of study.

Exercise 3.2 [Pages 47 - 48]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 3 Linear RegressionExercise 3.2 [Pages 47 - 48]

Exercise 3.2 | Q 1.1 | Page 47

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find Correlation coefficient between X and Y.

Exercise 3.2 | Q 1.2 | Page 47

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.

Exercise 3.2 | Q 1.3 | Page 47

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.

Exercise 3.2 | Q 2 | Page 47

From the data of 20 pairs of observations on X and Y, following results are obtained.

`barx = 199, bary = 94,`

`sum(x_i - barx)^2 = 1200, sum(y_i - bary)^2 = 300,`

`sum(x_i - bar x)(y_i - bar y) = - 250`

Find:

  1. The line of regression of Y on X.
  2. The line of regression of X on Y.
  3. Correlation coefficient between X and Y.
Exercise 3.2 | Q 3 | Page 47

From the data of 7 pairs of observations on X and Y, following results are obtained.

∑(xi - 70) = - 35,  ∑(yi - 60) = - 7,

∑(xi - 70)2 = 2989,    ∑(yi - 60)2 = 476, 

∑(xi - 70)(yi - 60) = 1064

[Given: `sqrt0.7884` = 0.8879]

Obtain

  1. The line of regression of Y on X.
  2. The line regression of X on Y.
  3. The correlation coefficient between X and Y.
Exercise 3.2 | Q 4 | Page 47

You are given the following information about advertising expenditure and sales.

  Advertisement expenditure
(₹ in lakh) (X)
Sales (₹ in lakh) (Y)
Arithmetic Mean 10 90
Standard Mean 3 12

Correlation coefficient between X and Y is 0.8

  1. Obtain the two regression equations.
  2. What is the likely sales when the advertising budget is ₹ 15 lakh?
  3. What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?
Exercise 3.2 | Q 5.1 | Page 47

Bring out the inconsistency in the following:

bYX + bXY = 1.30 and r = 0.75 

Exercise 3.2 | Q 5.2 | Page 47

Bring out the inconsistency in the following:

bYX = bXY = 1.50 and r = - 0.9 

Exercise 3.2 | Q 5.3 | Page 47

Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25

Exercise 3.2 | Q 5.4 | Page 47

Bring out the inconsistency in the following:

bYX = 2.6 and bXY = `1/2.6`

Exercise 3.2 | Q 6 | Page 47

Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.

Exercise 3.2 | Q 7 | Page 48

For a certain bivariate data

  X Y
Mean 25 20
S.D. 4 3

And r = 0.5. Estimate y when x = 10 and estimate x when y = 16

Exercise 3.2 | Q 8 | Page 48

Given the following information about the production and demand of a commodity obtain the two regression lines:

  X Y
Mean 85 90
S.D. 5 6

The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.

Exercise 3.2 | Q 9 | Page 48

Given the following data, obtain a linear regression estimate of X for Y = 10, `bar x = 7.6, bar y = 14.8, sigma_x = 3.2, sigma_y = 16` and r = 0.7

Exercise 3.2 | Q 10 | Page 48

An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment (₹ y) gave the following results: 

∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6

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

Exercise 3.2 | Q 11.1 | Page 48

The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

  Sales Adv. Exp.
Mean 40 6
S.D. 10 1.5

Coefficient of correlation between sales and advertisement expenditure is 0.9.

Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.

Exercise 3.2 | Q 11.2 | Page 48

The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

  Sales Adv. Exp.
Mean 40 6
S.D. 10 1.5

Coefficient of correlation between sales and advertisement expenditure is 0.9.

What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?

Exercise 3.2 | Q 12 | Page 48

For certain bivariate data the following information is available.

  X Y
Mean 13 17
S.D. 3 2

Correlation coefficient between x and y is 0.6. estimate x when y = 15 and estimate y when x = 10.

Exercise 3.3 [Pages 49 - 50]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 3 Linear RegressionExercise 3.3 [Pages 49 - 50]

Exercise 3.3 | Q 1 | Page 49

From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17

Exercise 3.3 | Q 2 | Page 49

In a partially destroyed laboratory record of an analysis of regression data, the following data are legible:

Variance of X = 9
Regression equations:
8x − 10y + 66 = 0
and 40x − 18y = 214.
Find on the basis of above information

  1. The mean values of X and Y.
  2. Correlation coefficient between X and Y.
  3. Standard deviation of Y.
Exercise 3.3 | Q 3 | Page 50

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 two subjects.

Exercise 3.3 | Q 4 | Page 50

For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.

Exercise 3.3 | Q 5 | Page 50

The equations of two regression lines are
2x + 3y − 6 = 0
and 2x + 2y − 12 = 0 Find 

  1. Correlation coefficient
  2. `sigma_"X"/sigma_"Y"`
Exercise 3.3 | Q 6 | Page 50

For a bivariate data: `bar x = 53, bar y = 28,` bYX = - 1.5 and bXY = - 0.2. Estimate Y when X = 50.

Exercise 3.3 | Q 7 | Page 50

The equations of two regression lines are x − 4y = 5 and 16y − x = 64. Find means of X and Y. Also, find correlation coefficient between X and Y.

Exercise 3.3 | Q 8 | Page 50

In a partially destroyed record, the following data are available: variance of X = 25, Regression equation of Y on X is 5y − x = 22 and regression equation of X on Y is 64x − 45y = 22 Find

  1. Mean values of X and Y
  2. Standard deviation of Y
  3. Coefficient of correlation between X and Y.
Exercise 3.3 | Q 9 | Page 50

If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find

  1. `bar x`,
  2. `bar y`,
  3. bYX
  4. bXY
  5. r [Given `sqrt0.375` = 0.61]
Exercise 3.3 | Q 10 | Page 50

The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.

Exercise 3.3 | Q 11 | Page 50

Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.

Exercise 3.3 | Q 12 | Page 50

For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.

Exercise 3.3 | Q 13 | Page 50

Regression equations of two series are 2x − y − 15 = 0 and 3x − 4y + 25 = 0. Find `bar x, bar y` and regression coefficients. Also find coefficients of correlation.  [Given `sqrt0.375` = 0.61]

Exercise 3.3 | Q 14 | Page 50

The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
and 20x − 3y − 900 = 0
Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.

Miscellaneous Exercise 3 [Pages 51 - 54]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 3 Linear RegressionMiscellaneous Exercise 3 [Pages 51 - 54]

Miscellaneous Exercise 3 | Q 1.01 | Page 51

Choose the correct alternative:

Regression analysis is the theory of

  • Estimation

  • Prediction

  • Estimation and Prediction

  • Calculation

Miscellaneous Exercise 3 | Q 1.02 | Page 51

Choose the correct alternative:

We can estimate the value of one variable with the help of other known variable only if they are

  • Correlated

  • Positively correlated

  • Negatively correlated

  • Uncorrelated

Miscellaneous Exercise 3 | Q 1.03 | Page 51

Choose the correct alternative:

There are ______ types of regression equations

  • 4

  • 2

  • 3

  • 1

Miscellaneous Exercise 3 | Q 1.04 | Page 51

Choose the correct alternative.

In the regression equation of Y on X

  • X is independent and Y is dependent.

  • Y is independent and X is dependent.

  • Both X and Y are independent.

  • Both X and Y are dependent.

Miscellaneous Exercise 3 | Q 1.05 | Page 52

Choose the correct alternative:

In the regression equation of X on Y

  • X is independent and Y is dependent

  • Y is independent and X is dependent

  • Both X and Y are independent

  • Both X and Y are dependent

Miscellaneous Exercise 3 | Q 1.06 | Page 52

Choose the correct alternative.

bXY is _____

  • Regression coefficient of Y on X

  • Regression coefficient of X on Y

  • Correlation coefficient between X and Y

  • Covariance between X and Y

Miscellaneous Exercise 3 | Q 1.07 | Page 52

Choose the correct alternative.

bYX is __________.

  • Regression coefficient of Y on X

  • Regression coefficient of X on Y

  • Correlation coefficient between X and Y

  • Covariance between X and Y

Miscellaneous Exercise 3 | Q 1.08 | Page 52

Choose the correct alternative.

‘r’ is __________.

  • Regression coefficient of Y on X

  • Regression coefficient of X on Y

  • Correlation coefficient between X and Y

  • Covariance between X and Y

Miscellaneous Exercise 3 | Q 1.09 | Page 52

Choose the correct alternative.

bXY .bYX is _________.

  • v(x)

  • `sigma_"x"`

  • r2

  • `(sigma_"y")^2`

Miscellaneous Exercise 3 | Q 1.1 | Page 52

Choose the correct alternative.

bYX > 1 then bXY is _______

  • > 1

  • < 1

  • > 0

  • < 0

Miscellaneous Exercise 3 | Q 1.11 | Page 52

Choose the correct alternative.

|bxy + byx | ≥ _______

  • |r|

  • 2 |r|

  • r

  • 2r

Miscellaneous Exercise 3 | Q 1.12 | Page 52

Choose the correct alternative.

bxy and byx are _______

  • Independent of change of origin and scale

  • Independent of change of origin but not of scale

  • Independent of change of scale but not of origin

  • Affected by change of origin and scale

Miscellaneous Exercise 3 | Q 1.13 | Page 52

Choose the correct alternative.

If u = `("x - a")/"c" and "v" = ("y - b")/"d"  "then"   "b"_"yx"` = _________

  • `"d"/"c" "b"_"vu"`

  • `"c"/"d" "b"_"vu"`

  • `"a"/"b" "b"_"vu"`

  • `"b"/"a" "b"_"vu"`

Miscellaneous Exercise 3 | Q 1.14 | Page 52

Choose the correct alternative.

If u = `("x - a")/"c" and "v" = ("y - b")/"d"  "then"   "b"_"xy"` = _________

  • `"d"/"c" "b"_"uv"`

  • `"c"/"d" "b"_"uv"`

  • `"a"/"b" "b"_"uv"`

  • `"b"/"a" "b"_"uv"`

Miscellaneous Exercise 3 | Q 1.15 | Page 52

Choose the correct alternative.

Corr (x, x) = _____

  • 0

  • 1

  • - 1

  • can't be found

Miscellaneous Exercise 3 | Q 1.16 | Page 52

Choose the correct alternative.

Corr (x, y) = _____

  • corr (x,x)

  • corr (y,y)

  • corr (y,x)

  • cov (y,x)

Miscellaneous Exercise 3 | Q 1.17 | Page 52

Choose the correct alternative.

Corr `("x - a"/"c", "y - b"/"d")` = - corr (x, y) if,

  • c and d are opposite in sign

  • c and d are same in sign

  • a and b are opposite in sign

  • a and b are same in sign

Miscellaneous Exercise 3 | Q 1.18 | Page 52

Choose the correct alternative.

Regression equation of X on Y is ____

  • `"y" - bar "y" = "b"_"yx" ("x" - bar "x")`

  • `"x" - bar "x" = "b"_"xy" ("y" - bar "y")`

  • `"y" - bar "y" = "b"_"xy" ("x" - bar "x")`

  • `"x" - bar "x" = "b"_"yx" ("y" - bar "y")`

Miscellaneous Exercise 3 | Q 1.19 | Page 53

Choose the correct alternative.

Regression equation of Y on X is ____

  • `("y" - bar "y") = "b"_"yx" ("x" - bar "x")`

  • `("x" - bar "x") = "b"_"xy" ("y" - bar "y")`

  • `("y" - bar "y") = "b"_"xy" ("x" - bar "x")`

  • `("x" - bar "x") = "b"_"yx" ("y" - bar "y")`

Miscellaneous Exercise 3 | Q 1.2 | Page 53

Choose the correct alternative.

byx = ______

  • `"r" sigma_"x"/sigma_"y"`

  • `"r" sigma_"y"/sigma_"x"`

  • `1/"r"  sigma_"y"/sigma_"x"`

  • `1/"r"  sigma_"x"/sigma_"y"`

Miscellaneous Exercise 3 | Q 1.21 | Page 53

Choose the correct alternative.

bxy = ______

  • `"r" sigma_"x"/sigma_"y"`

  • `"r" sigma_"y"/sigma_"x"`

  • `1/"r"  sigma_"y"/sigma_"x"`

  • `1/"r" sigma_"x"/sigma_"y"`

Miscellaneous Exercise 3 | Q 1.22 | Page 53

Choose the correct alternative.

Cov (x, y) = __________

  • `sum (x - bar x)(y - bar y)`

  • `(sum (x - bar x)(y - bar y))/"n"`

  • `(sum xy)/"n" - bar x  bar y`

  • both `(sum (x - bar x)(y - bar y))/"n"` and `(sum xy)/"n" - bar x  bar y`

Miscellaneous Exercise 3 | Q 1.23 | Page 53

Choose the correct alternative.

If bxy < 0 and byx < 0 then 'r' is __________

  • > 0

  • < 0

  • > 1

  • not found

Miscellaneous Exercise 3 | Q 1.24 | Page 53

Choose the correct alternative.

If equations of regression lines are 3x + 2y − 26 = 0 and 6x + y − 31 = 0 then means of x and y are __________

  • (7, 4)

  • (4, 7)

  • (2, 9)

  • (-4, 7)

Miscellaneous Exercise 3 | Q 2.01 | Page 53

Fill in the blank:

If bxy < 0 and byx < 0 then ‘r’ is __________

Miscellaneous Exercise 3 | Q 2.02 | Page 53

Fill in the blank:

Regression equation of Y on X is_________

Miscellaneous Exercise 3 | Q 2.03 | Page 53

Fill in the blank:

Regression equation of X on Y is_________

Miscellaneous Exercise 3 | Q 2.04 | Page 53

Fill in the blank:

There are __________ types of regression equations.

Miscellaneous Exercise 3 | Q 2.05 | Page 53

Fill in the blank:

Corr (x, −x) = __________

Miscellaneous Exercise 3 | Q 2.06 | Page 53

Fill in the blank:

If u = `"x - a"/"c" and  "v" = "y - b"/"d"` then bxy = _______

Miscellaneous Exercise 3 | Q 2.07 | Page 53

Fill in the blank:

If u = `"x - a"/"c" and  "v" = "y - b"/"d"` then byx = _______

Miscellaneous Exercise 3 | Q 2.08 | Page 53

Fill in the blank:

|bxy + byx| ≥ ______

Miscellaneous Exercise 3 | Q 2.09 | Page 53

Fill in the blank:

If byx > 1 then bxy is _______

Miscellaneous Exercise 3 | Q 2.1 | Page 53

Fill in the blank:

bxy . byx = _______

Miscellaneous Exercise 3 | Q 3.01 | Page 53

State whether the following statement is True or False.

Corr (x, x) = 1

  • True

  • False

Miscellaneous Exercise 3 | Q 3.02 | Page 53

State whether the following statement is True or False.

Regression equation of X on Y is `("y" - bar "y") = "b"_"yx" ("x" - bar "x")`

  • True

  • False

Miscellaneous Exercise 3 | Q 3.03 | Page 53

State whether the following statement is True or False.

Regression equation of Y on X is `("y" - bar "y") = "b"_"yx" ("x" - bar "x")`

  • True

  • False

Miscellaneous Exercise 3 | Q 3.04 | Page 53

State whether the following statement is True or False.

Corr (x, y) = Corr (y, x)

  • True

  • False

Miscellaneous Exercise 3 | Q 3.05 | Page 53

State whether the following statement is True or False.

bxy and byx are independent of change of origin and scale. 

  • True

  • False

Miscellaneous Exercise 3 | Q 3.06 | Page 53

State whether the following statement is True or False.

‘r’ is regression coefficient of Y on X

  • True

  • False

Miscellaneous Exercise 3 | Q 3.07 | Page 53

State whether the following statement is True or False.

byx is correlation coefficient between X and Y

  • True

  • False

Miscellaneous Exercise 3 | Q 3.08 | Page 53

State whether the following statement is True or False.

If u = x - a and v = y - b then bxy = buv 

  • True

  • False

Miscellaneous Exercise 3 | Q 3.09 | Page 53

State whether the following statement is True or False.

If u = x - a and v = y - b then rxy = ruv 

  • True

  • False

Miscellaneous Exercise 3 | Q 3.1 | Page 53

State whether the following statement is True or False.

In the regression equation of Y on X, byx represents slope of the line.

  • True

  • False

Miscellaneous Exercise 3 | Q 4.01 | Page 54

The data obtained on X, the length of time in weeks that a promotional project has been in progress at a small business, and Y, the percentage increase in weekly sales over the period just prior to the beginning of the campaign.

X 1 2 3 4 1 3 1 2 3 4 2 4
Y 10 10 18 20 11 15 12 15 17 19 13 16

Find the equation of the regression line to predict the percentage increase in sales if the campaign has been in progress for 1.5 weeks.

Miscellaneous Exercise 3 | Q 4.02 | Page 54

The regression equation of y on x is given by 3x + 2y − 26 = 0. Find byx

Miscellaneous Exercise 3 | Q 4.03 | Page 54

If for bivariate data `bar x = 10, bar y = 12,` v(x) = 9, σy = 4 and r = 0.6 estimate y, when x = 5.

Miscellaneous Exercise 3 | Q 4.04 | Page 54

The equation of the line of regression of y on x is y = `2/9` x and x on y is x = `"y"/2 + 7/6`.
Find (i) r,  (ii) `sigma_"y"^2 if sigma_"x"^2 = 4`

Miscellaneous Exercise 3 | Q 4.05 | Page 54

Identify the regression equations of x on y and y on x from the following equations, 2x + 3y = 6 and 5x + 7y − 12 = 0

Miscellaneous Exercise 3 | Q 4.06 | Page 54

If for a bivariate data byx = – 1.2 and bxy = – 0.3 then find r.

Miscellaneous Exercise 3 | Q 4.06 | Page 54

From the two regression equations y = 4x – 5 and 3x = 2y + 5, find `bar x and bar y`.

Miscellaneous Exercise 3 | Q 4.07 | Page 54

The equations of the two lines of regression are 3x + 2y − 26 = 0 and 6x + y − 31 = 0 Find

  1. Means of X and Y
  2. Correlation coefficient between X and Y
  3. Estimate of Y for X = 2
  4. var (X) if var (Y) = 36
Miscellaneous Exercise 3 | Q 4.08 | Page 54

Find the line of regression of X on Y for the following data:

n = 8, `sum(x_i - bar x)^2 = 36, sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`

Miscellaneous Exercise 3 | Q 4.09 | Page 54

Find the equation of line of regression of Y on X for the following data:

n = 8, `sum(x_i - barx)(y_i - bary) = 120, bar x = 20, bar y = 36, sigma_x = 2, sigma_y = 3`

Miscellaneous Exercise 3 | Q 4.1 | Page 54

The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.

  X Y
Mean 50 140
Variance 150 165

and `sum (x_i - bar x)(y_i - bar y) = 1120`

Find the prediction of blood pressure of a man of age 40 years.

Miscellaneous Exercise 3 | Q 4.11 | Page 54

The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:

  1. `bar x and bar y`
  2. `"b"_"YX" and "b"_"XY"`
  3. If var (Y) = 36, obtain var (X)
  4. r
Miscellaneous Exercise 3 | Q 4.12 | Page 54

If bYX = − 0.6 and bXY = − 0.216, then find correlation coefficient between X and Y. Comment on it.

Chapter 3: Linear Regression

Exercise 3.1Exercise 3.2Exercise 3.3Miscellaneous Exercise 3
Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 3 - Linear Regression

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 3 (Linear Regression) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 3 Linear Regression are Regression, Types of Linear Regression, Fitting Simple Linear Regression, The Method of Least Squares, Lines of Regression of X on Y and Y on X Or Equation of Line of Regression, Properties of Regression Coefficients.

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Get the free view of chapter 3 Linear Regression 12th Board Exam extra questions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation

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