Chapter 3: Linear Regression

Regression is a functional relation between two correlated variables.

Details

We have previously studied that correlation coefficient shows us whether the correlation between two variables is positive or negative. However, the correlation coefficient fails to provide the expected value of one variable for the given value of the other variable. For this, it is necessary to use the concept of regression.

The literal meaning of regression is 'to avert' or 'return to the mean value'. The term regression was first used by a statistician Sir Francis Galton during his study of human inheritance.

Curriculum

Lecture 1 Basic Concepts and Formulas

Basic Concepts of Regression and Illustration 3 live
Lecture 1 Basic Concepts classroom
Linear Regression Full Chapter

9.9 MB

Lecture 2 Basic Concepts and Sums

Regression - XY Formula and sums Ex3.1 Q2 and Illustration 2 with error of estimation concept digital
Basic Concepts and Ex. 3.1 Q1 and Q2 classroom

Lecture 3 Method of Least Square and Short Formulas

Lecture 3 Method of Least Square - UV Formula Ex3.2 Q3 Illustration 6 digital
Lecture 3 continued Imp Sums of UV Ex 3.2 Q4,5 digital

Lecture 4 Short Sums

Short Sums Ill 8,9 Ex 3.2 Q7,Q9,Q8 digital
Ex 3.2 Q1, Q4, Q5, short sums - Q6, Q7 classroom

Lecture 5 Coefficient of Determination - Important Illustrations

Coefficient of Determination Illustration 15,16 digital
Coefficient of Determination - Illustration 14, 15, 16, 17, 18, 19 Classroom
Homework/Practice Work

1 m

Lecture 6 Typical Sums

Typical Illustration Sums 16 to 21 digital
Short Sums Section B,C,D, F Digital
Typical Sums Illustration 21, Section B Q13, Sec F Q7 classroom

Definitions

1. Independent Variable

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2. Dependent Variable

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3. Regression

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4. Linear Regression

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5. Linear Regression Model

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6. Error of Disturbance Variable

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7. Regression Line

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8. Regression Coefficient

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9. Coefficient of Determination:

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10. Error of Approximation

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11. Line of Best Fit

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Answer in short

True or False Quiz

20 questions
1. By whom was the concept of regression first given?

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2. What does correlation coefficient tell us about? What does it fail to provide?

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3. Under what assumption shall we study the concept of regression?

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4. Which are two variables out of random variable having cause-effect relationship? What are they called? Denote them by symbols.

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5. What are the parameters of Linear Regression Model?

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6. When does the regression Model become perfectly linear, i.e. Y=a+bx?

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7. Which are two methods of fitting a regression line?

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8. Who gave the method of Least Square?

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9. Write an equation of regression line Y on X and X on Y.

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10. When it is said that two regression coefficients are reciprocals of each other?

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11. Interpret 'b'.

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12. State two uses of study of Regression.

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13. What is Prediction Formula?

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14. State the most important property of byx.

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15. If the value of R² is 1 which relation exists between X and Y?

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16. What happens when R² = 0?

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17. Under what circumstances two regression lines are obtained?

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18. Which precautions are to be taken while using a regression line?

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19. State utility of coefficient of determination

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20. When there is no perfect linear correlation between two variables, which line is called the line of regression?

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21. State the nature of linear regression model, if there prevails some uncertainty in the relation between X and Y?

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22. Why is the line of regression obtained by the method of least squares is called the best fitted line?

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23. What can you say about the assumption of linear correlation when the values of R² are close to 0?

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24. Why is the element of uncertainty included in regression model?

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25. Which is the best method of obtaining line of regression?

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26. Recognize dependent and independent variable in the following cases.

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Answer 26

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Textual Questions and Answers

1. Define Linear Regression.

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2. Define Regression co-efficient.

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3. State the linear regression model.

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4. What is an error in context with a regression line?

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5. Which method should be used to obtain the best fitted regression line?

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6. The regression co-efficient is independent of which transformation?

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7. The regression co-efficient is not independent of which transformation?

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8. What is the value of error if a sample point is on the fitted line?

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9. Will the regression coefficient change if values of both the variables are doubled with the help of transformation of scale?

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12. If Y and X have the relation y = a + bx where b > 0 then what is the value of r?

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13. If Y = 5 – 3x is the relation between Y and X then what is the value of r?

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Chapter 3 Practice Material

710 KB
Statistics Important Theory

2.9 MB

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