#### Chapters

Chapter 2: Algebra

Chapter 3: Analytical Geometry

Chapter 4: Trigonometry

Chapter 5: Differential Calculus

Chapter 6: Applications of Differentiation

Chapter 7: Financial Mathematics

Chapter 8: Descriptive Statistics and Probability

Chapter 9: Correlation and Regression Analysis

Chapter 10: Operations Research

## Chapter 9: Correlation and Regression Analysis

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 9 Correlation and Regression Analysis Exercise 9.1 [Pages 217 - 218]

**Calculate the correlation coefficient for the following data.**

X |
5 | 10 | 5 | 11 | 12 | 4 | 3 | 2 | 7 | 1 |

Y |
1 | 6 | 2 | 8 | 5 | 1 | 4 | 6 | 5 | 2 |

**Find the coefficient of correlation for the following:**

Cost (₹) |
14 | 19 | 24 | 21 | 26 | 22 | 15 | 20 | 19 |

Sales (₹) |
31 | 36 | 48 | 37 | 50 | 45 | 33 | 41 | 39 |

Calculate the coefficient of correlation for the ages of husbands and their respective wives:

Age of husbands |
23 | 27 | 28 | 29 | 30 | 31 | 33 | 35 | 36 | 39 |

Age of wives |
18 | 22 | 23 | 24 | 25 | 26 | 28 | 29 | 30 | 32 |

Calculate the coefficient of correlation between X and Y series from the following data.

Description |
X |
Y |

Number of pairs of observation | 15 | 15 |

Arithmetic mean | 25 | 18 |

Standard deviation | 3.01 | 3.03 |

Sum of squares of deviation from the arithmetic mean | 136 | 138 |

Summation of product deviations of X and Y series from their respective arithmetic means is 122.

**Calculate the correlation coefficient for the following data.**

X |
25 | 18 | 21 | 24 | 27 | 30 | 36 | 39 | 42 | 48 |

Y |
26 | 35 | 48 | 28 | 20 | 36 | 25 | 40 | 43 | 39 |

**Find the coefficient of correlation for the following:**

X |
78 | 89 | 96 | 69 | 59 | 79 | 68 | 62 |

Y |
121 | 72 | 88 | 60 | 81 | 87 | 123 | 92 |

An examination of 11 applicants for a accountant post was taken by a finance company. The marks obtained by the applicants in the reasoning and aptitude tests are given below.

Applicant |
A | B | C | D | E | F | G | H | I | J | K |

Reasoning test |
20 | 50 | 28 | 25 | 70 | 90 | 76 | 45 | 30 | 19 | 26 |

Aptitude test |
30 | 60 | 50 | 40 | 85 | 90 | 56 | 82 | 42 | 31 | 49 |

Calculate Spearman’s rank correlation coefficient from the data given above.

The following are the ranks obtained by 10 students in commerce and accountancy are given below:

Commerce |
6 | 4 | 3 | 1 | 2 | 7 | 9 | 8 | 10 | 5 |

Accountancy |
4 | 1 | 6 | 7 | 5 | 8 | 10 | 9 | 3 | 2 |

To what extent is the knowledge of students in the two subjects related?

A random sample of recent repair jobs was selected and estimated cost and actual cost were recorded.

Estimated cost |
300 | 450 | 800 | 250 | 500 | 975 | 475 | 400 |

Actual cost |
273 | 486 | 734 | 297 | 631 | 872 | 396 | 457 |

Calculate the value of spearman’s correlation coefficient.

The rank of 10 students of the same batch in two subjects A and B are given below. Calculate the rank correlation coefficient.

Rank of A |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Rank of B |
6 | 7 | 5 | 10 | 3 | 9 | 4 | 1 | 8 | 2 |

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 9 Correlation and Regression Analysis Exercise 9.2 [Pages 226 - 227]

From the data given below:

Marks in Economics: |
25 | 28 | 35 | 32 | 31 | 36 | 29 | 38 | 34 | 32 |

Marks in Statistics: |
43 | 46 | 49 | 41 | 36 | 32 | 31 | 30 | 33 | 39 |

Find

- The two regression equations,
- The coefficient of correlation between marks in Economics and Statistics,
- The mostly likely marks in Statistics when the marks in Economics is 30.

The heights (in cm.) of a group of fathers and sons are given below:

Heights of fathers: |
158 | 166 | 163 | 165 | 167 | 170 | 167 | 172 | 177 | 181 |

Heights of Sons: |
163 | 158 | 167 | 170 | 160 | 180 | 170 | 175 | 172 | 175 |

Find the lines of regression and estimate the height of the son when the height of the father is 164 cm.

The following data give the height in inches (X) and the weight in lb. (Y) of a random sample of 10 students from a large group of students of age 17 years:

X |
61 | 68 | 68 | 64 | 65 | 70 | 63 | 62 | 64 | 67 |

Y |
112 | 123 | 130 | 115 | 110 | 125 | 100 | 113 | 116 | 125 |

Estimate weight of the student of a height 69 inches.

Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X^{2 }= 1680, ∑Y^{2} = 320 and ∑XY = 480.

Given the following data, what will be the possible yield when the rainfall is 29.

Details |
Rainfall |
Production |

Mean | 25`` | 40 units per acre |

Standard Deviation | 3`` | 6 units per acre |

Coefficient of correlation between rainfall and production is 0.8.

The following data relate to advertisement expenditure (in lakh of rupees) and their corresponding sales (in crores of rupees)

Advertisement expenditure |
40 | 50 | 38 | 60 | 65 | 50 | 35 |

Sales |
38 | 60 | 55 | 70 | 60 | 48 | 30 |

Estimate the sales corresponding to advertising expenditure of ₹ 30 lakh.

You are given the following data:

Details |
X |
Y |

Arithmetic Mean | 36 | 85 |

Standard Deviation | 11 | 8 |

If the Correlation coefficient between X and Y is 0.66, then find

- the two regression coefficients,
- the most likely value of Y when X = 10.

Find the equation of the regression line of Y on X, if the observations (X_{i}, Y_{i}) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18).

A survey was conducted to study the relationship between expenditure on accommodation (X) and expenditure on Food and Entertainment (Y) and the following results were obtained:

Details |
Mean |
SD |

Expenditure on Accommodation (₹) | 178 | 63.15 |

Expenditure on Food and Entertainment (₹) | 47.8 | 22.98 |

Coefficient of Correlation | 0.43 |

Write down the regression equation and estimate the expenditure on Food and Entertainment, if the expenditure on accommodation is ₹ 200.

For 5 observations of pairs of (X, Y) of variables X and Y the following results are obtained. ∑X = 15, ∑Y = 25, ∑X^{2} = 55, ∑Y^{2} = 135, ∑XY = 83. Find the equation of the lines of regression and estimate the values of X and Y if Y = 8; X = 12.

The two regression lines were found to be 4X – 5Y + 33 = 0 and 20X – 9Y – 107 = 0. Find the mean values and coefficient of correlation between X and Y.

The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficients.

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 9 Correlation and Regression Analysis Exercise 9.3 [Pages 227 - 229]

#### Choose the correct answer

Example for positive correlation is

Income and expenditure

Price and demand

Repayment period and EMI

Weight and Income

If the values of two variables move in same direction then the correlation is said to be

Negative

Positive

Perfect positive

No correlation

If the values of two variables move in the opposite direction then the correlation is said to be

Negative

Positive

Perfect positive

No correlation

Correlation co-efficient lies between

0 to ∞

–1 to +1

–1 to 0

–1 to ∞

If r(X,Y) = 0 the variables X and Y are said to be

Positive correlation

Negative correlation

No correlation

Perfect positive correlation

The correlation coefficient from the following data N = 25, ∑X = 125, ∑Y = 100, ∑X^{2} = 650, ∑Y^{2} = 436, ∑XY = 520

0.667

− 0.006

– 0.667

0.70

From the following data, N = 11, ∑X = 117, ∑Y = 260, ∑X^{2} = 1313, ∑Y^{2} = 6580, ∑XY = 2827 the correlation coefficient is

0.3566

– 0.3566

0

0.4566

The correlation coefficient is

r(X, Y) = `(sigma_"x" sigma_"y")/("cov"("x","y"))`

r(X, Y) = `("cov"("x","y"))/(sigma_"x" sigma_"y")`

r(X, Y) = `("cov"("x","y"))/(sigma_"y")`

r(X, Y) = `("cov"("x","y"))/(sigma_"x")`

The variable whose value is influenced (or) is to be predicted is called

dependent variable

independent variable

regressor

explanatory variable

The variable which influences the values or is used for prediction is called

Dependent variable

Independent variable

Explained variable

Regressed

The correlation coefficient

r = `± sqrt("b"_"xy" xx "b"_"yx")`

r = `1/("b"_"xy" xx "b"_"yx")`

r = b

_{xy}× b_{yx}r = `± sqrt(1/("b"_"xy" xx "b"_"yx")`

The regression coefficient of X on Y

b

_{xy }= `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)`b

_{yx }= `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)`b

_{xy }= `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)`b

_{y }= `("N"sum"xy" - (sum"x")(sum"y"))/(sqrt("N"sum"x"^2 - (sum"x")^2) xx sqrt("N"sum"y"^2 - (sum"y")^2))`

The regression coefficient of Y on X

b

_{xy }= `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)`b

_{yx }= `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)`b

_{yx }= `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)`b

_{xy }= `("N"sum"xy" - (sum"x")(sum"y"))/(sqrt("N"sum"x"^2 - (sum"x")^2) xx sqrt("N"sum"y"^2 - (sum"y")^2))`

When one regression coefficient is negative, the other would be

Negative

Positive

Zero

None of them

If X and Y are two variates, there can be at most

One regression line

Two regression lines

Three regression lines

More regression lines

The lines of regression of X on Y estimates

X for a given value of Y

Y for a given value of X

X from Y and Y from X

none of these

Scatter diagram of the variate values (X, Y) give the idea about

functional relationship

regression model

distribution of errors

no relation

If the regression coefficient of Y on X is 2, then the regression coefficient of X on Y is

`≤1/2`

2

`>1/2`

1

If two variables moves in decreasing direction then the correlation is

positive

negative

perfect negative

no correlation

The person suggested a mathematical method for measuring the magnitude of linear relationship between two variables say X and Y is

Karl Pearson

Spearman

Croxton and Cowden

Ya Lun Chou

The lines of regression intersect at the point

(X, Y)

`(bar"X", bar"Y")`

(0, 0)

(σ

_{x}, σ_{y})

The term regression was introduced by

R. A. Fisher

Sir Francis Galton

Karl Pearson

Croxton and Cowden

If r = – 1, then correlation between the variables

perfect positive

perfect negative

negative

no correlation

The coefficient of correlation describes

the magnitude and direction

only magnitude

only direction

no magnitude and no direction

If Cov(x, y) = – 16.5, `sigma_"x"^2` = 2.89, `sigma_"y"^2` = 100. Find correlation coefficient.

– 0.12

0.001

– 1

– 0.97

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 9 Correlation and Regression Analysis Miscellaneous Problems [Pages 229 - 230]

**Find the coefficient of correlation for the following data:**

X |
35 | 40 | 60 | 79 | 83 | 95 |

Y |
17 | 28 | 30 | 32 | 38 | 49 |

**Calculate the coefficient of correlation from the following data:**

∑X = 50, ∑Y = – 30, ∑X^{2} = 290, ∑Y^{2} = 300, ∑XY = – 115, N = 10

**Calculate the correlation coefficient from the data given below:**

X |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Y |
9 | 8 | 10 | 12 | 11 | 13 | 14 | 16 | 15 |

**Calculate the correlation coefficient from the following data:**

∑X = 125, ∑Y = 100, ∑X^{2} = 650, ∑Y^{2} = 436, ∑XY = 520, N = 25

A random sample of recent repair jobs was selected and estimated cost, actual cost were recorded.

Estimated cost |
30 | 45 | 80 | 25 | 50 | 97 | 47 | 40 |

Actual cost |
27 | 48 | 73 | 29 | 63 | 87 | 39 | 45 |

Calculate the value of spearman’s correlation.

The following data pertains to the marks in subjects A and B in a certain examination. Mean marks in A = 39.5, Mean marks in B = 47.5 standard deviation of marks in A = 10.8 and Standard deviation of marks in B = 16.8. coefficient of correlation between marks in A and marks in B is 0.42. Give the estimate of marks in B for the candidate who secured 52 marks in A.

X and Y are a pair of correlated variables. Ten observations of their values (X, Y) have the following results. ∑X = 55, ∑XY = 350, ∑X^{2} = 385, ∑Y = 55, Predict the value of y when the value of X is 6.

**Find the line regression of Y on X**

X |
1 | 2 | 3 | 4 | 5 | 8 | 10 |

Y |
9 | 8 | 10 | 12 | 14 | 16 | 15 |

Using the following information you are requested to

- obtain the linear regression of Y on X
- Estimate the level of defective parts delivered when inspection expenditure amounts to ₹ 82

∑X = 424, ∑Y = 363, ∑X^{2}= 21926, ∑Y^{2}= 15123, ∑XY = 12815, N = 10.

Here X is the expenditure on inspection, Y is the defective parts delivered.

The following information is given.

Details |
X (in ₹) |
Y (in ₹) |

Arithmetic Mean | 6 | 8 |

Standard Deviation | 5 | `40/3` |

Coefficient of correlation between X and Y is `8/15`. Find

- The regression Coefficient of Y on X
- The most likely value of Y when X = ₹ 100.

## Chapter 9: Correlation and Regression Analysis

## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 9 - Correlation and Regression Analysis

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Concepts covered in Class 11th Business Mathematics and Statistics Answers Guide chapter 9 Correlation and Regression Analysis are Correlation, Rank Correlation, Regression Analysis.

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