Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

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

## Chapter 9: Correlation and Regression Analysis

Exercise 9.1Exercise 9.2Exercise 9.3Miscellaneous Problems
Exercise 9.1 [Pages 217 - 218]

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

Exercise 9.1 | Q 1 | Page 217

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
Exercise 9.1 | Q 2 | Page 217

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
Exercise 9.1 | Q 3 | Page 217

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
Exercise 9.1 | Q 4 | Page 217

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.

Exercise 9.1 | Q 5 | Page 218

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
Exercise 9.1 | Q 6 | Page 218

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
Exercise 9.1 | Q 7 | Page 218

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.

Exercise 9.1 | Q 8 | Page 218

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?

Exercise 9.1 | Q 9 | Page 218

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.

Exercise 9.1 | Q 10 | Page 218

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
Exercise 9.2 [Pages 226 - 227]

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

Exercise 9.2 | Q 1 | Page 226

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

1. The two regression equations,
2. The coefficient of correlation between marks in Economics and Statistics,
3. The mostly likely marks in Statistics when the marks in Economics is 30.
Exercise 9.2 | Q 2 | Page 226

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.

Exercise 9.2 | Q 3 | Page 226

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.

Exercise 9.2 | Q 4 | Page 226

Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.

Exercise 9.2 | Q 5 | Page 227

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.

Exercise 9.2 | Q 6 | Page 227

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.

Exercise 9.2 | Q 7 | Page 227

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

1. the two regression coefficients,
2. the most likely value of Y when X = 10.
Exercise 9.2 | Q 8 | Page 227

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

Exercise 9.2 | Q 9 | Page 227

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.

Exercise 9.2 | Q 10 | Page 227

For 5 observations of pairs of (X, Y) of variables X and Y the following results are obtained. ∑X = 15, ∑Y = 25, ∑X2 = 55, ∑Y2 = 135, ∑XY = 83. Find the equation of the lines of regression and estimate the values of X and Y if Y = 8; X = 12.

Exercise 9.2 | Q 11 | Page 227

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.

Exercise 9.2 | Q 12 | Page 227

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.

Exercise 9.3 [Pages 227 - 229]

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

#### Choose the correct answer

Exercise 9.3 | Q 1 | Page 227

Example for positive correlation is

• Income and expenditure

• Price and demand

• Repayment period and EMI

• Weight and Income

Exercise 9.3 | Q 2 | Page 227

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

• Negative

• Positive

• Perfect positive

• No correlation

Exercise 9.3 | Q 3 | Page 227

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

• Negative

• Positive

• Perfect positive

• No correlation

Exercise 9.3 | Q 4 | Page 228

Correlation co-efficient lies between

• 0 to ∞

• –1 to +1

• –1 to 0

• –1 to ∞

Exercise 9.3 | Q 5 | Page 228

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

• Positive correlation

• Negative correlation

• No correlation

• Perfect positive correlation

Exercise 9.3 | Q 6 | Page 228

The correlation coefficient from the following data N = 25, ∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520

• 0.667

• − 0.006

• – 0.667

• 0.70

Exercise 9.3 | Q 7 | Page 228

From the following data, N = 11, ∑X = 117, ∑Y = 260, ∑X2 = 1313, ∑Y2 = 6580, ∑XY = 2827 the correlation coefficient is

• 0.3566

• – 0.3566

• 0

• 0.4566

Exercise 9.3 | Q 8 | Page 228

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")

Exercise 9.3 | Q 9 | Page 228

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

• dependent variable

• independent variable

• regressor

• explanatory variable

Exercise 9.3 | Q 10 | Page 228

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

• Dependent variable

• Independent variable

• Explained variable

• Regressed

Exercise 9.3 | Q 11 | Page 228

The correlation coefficient

• r = ± sqrt("b"_"xy" xx "b"_"yx")

• r = 1/("b"_"xy" xx "b"_"yx")

• r = bxy × byx

• r = ± sqrt(1/("b"_"xy" xx "b"_"yx")

Exercise 9.3 | Q 12 | Page 228

The regression coefficient of X on Y

• bxy = ("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)

• byx = ("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)

• bxy = ("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)

• by = ("N"sum"xy" - (sum"x")(sum"y"))/(sqrt("N"sum"x"^2 - (sum"x")^2) xx sqrt("N"sum"y"^2 - (sum"y")^2))

Exercise 9.3 | Q 13 | Page 228

The regression coefficient of Y on X

• bxy = ("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)

• byx = ("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)

• byx = ("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)

• bxy = ("N"sum"xy" - (sum"x")(sum"y"))/(sqrt("N"sum"x"^2 - (sum"x")^2) xx sqrt("N"sum"y"^2 - (sum"y")^2))

Exercise 9.3 | Q 14 | Page 228

When one regression coefficient is negative, the other would be

• Negative

• Positive

• Zero

• None of them

Exercise 9.3 | Q 15 | Page 229

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

• One regression line

• Two regression lines

• Three regression lines

• More regression lines

Exercise 9.3 | Q 16 | Page 229

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

Exercise 9.3 | Q 17 | Page 229

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

• functional relationship

• regression model

• distribution of errors

• no relation

Exercise 9.3 | Q 18 | Page 229

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

Exercise 9.3 | Q 19 | Page 229

If two variables moves in decreasing direction then the correlation is

• positive

• negative

• perfect negative

• no correlation

Exercise 9.3 | Q 20 | Page 229

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

Exercise 9.3 | Q 21 | Page 229

The lines of regression intersect at the point

• (X, Y)

• (bar"X", bar"Y")

• (0, 0)

• x, σy)

Exercise 9.3 | Q 22 | Page 229

The term regression was introduced by

• R. A. Fisher

• Sir Francis Galton

• Karl Pearson

• Croxton and Cowden

Exercise 9.3 | Q 23 | Page 229

If r = – 1, then correlation between the variables

• perfect positive

• perfect negative

• negative

• no correlation

Exercise 9.3 | Q 24 | Page 229

The coefficient of correlation describes

• the magnitude and direction

• only magnitude

• only direction

• no magnitude and no direction

Exercise 9.3 | Q 25 | Page 229

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

Miscellaneous Problems [Pages 229 - 230]

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

Miscellaneous Problems | Q 1 | Page 229

Find the coefficient of correlation for the following data:

 X 35 40 60 79 83 95 Y 17 28 30 32 38 49
Miscellaneous Problems | Q 2 | Page 229

Calculate the coefficient of correlation from the following data:

∑X = 50, ∑Y = – 30, ∑X2 = 290, ∑Y2 = 300, ∑XY = – 115, N = 10

Miscellaneous Problems | Q 3 | Page 229

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
Miscellaneous Problems | Q 4 | Page 230

Calculate the correlation coefficient from the following data:

∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520, N = 25

Miscellaneous Problems | Q 5 | Page 230

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.

Miscellaneous Problems | Q 6 | Page 230

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.

Miscellaneous Problems | Q 7 | Page 230

X and Y are a pair of correlated variables. Ten observations of their values (X, Y) have the following results. ∑X = 55, ∑XY = 350, ∑X2 = 385, ∑Y = 55, Predict the value of y when the value of X is 6.

Miscellaneous Problems | Q 8 | Page 230

Find the line regression of Y on X

 X 1 2 3 4 5 8 10 Y 9 8 10 12 14 16 15
Miscellaneous Problems | Q 9 | Page 230

Using the following information you are requested to

1. obtain the linear regression of Y on X
2. Estimate the level of defective parts delivered when inspection expenditure amounts to ₹ 82
∑X = 424, ∑Y = 363, ∑X2 = 21926, ∑Y2 = 15123, ∑XY = 12815, N = 10.
Here X is the expenditure on inspection, Y is the defective parts delivered.
Miscellaneous Problems | Q 10 | Page 230

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

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

## Chapter 9: Correlation and Regression Analysis

Exercise 9.1Exercise 9.2Exercise 9.3Miscellaneous Problems

## 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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