Chapter 2: Linear Correlation

Let's understand the relationship between two mutually related variables.

Details

There are situations where it is desirable and necessary to study two or more variables at a time. For example, if we study the yearly sale of the product of a company, we would also like to know its profit, because from that we can find the nature and degree of relation between these two variables 'sale of product' and 'profit'.

The yearly rainfall and yield of rice in some region, price and demand for an item, income and expenditure of a family, height of a father and his son, age of a husband and wife, are some well known examples where we see the relation between paired variables.

Curriculum

Scatter Diagram and Karl Pearson First Formula

Karl Pearsons Other Imp Formulas

Lecture 2 - Karl Pearson Formula Sums - Live
Lecture 2 Continued.. Sums with Fractional Values - imp for exam ill 12ex2.2q10, 11 digital
Lecture 2 classroom

Short Sums and Imp Sums

Important Short Sums using Cov(x,y), Sx, Sy Ill 13, 14, Ex 2.2 Q12 Digital
Lecture 3 Short Sums

Rank Correlation

Rank Correlation Concepts and Sums Illustration 16,17, Ex 2.3 Q4 Digital
Lecture 4 Rank Correlation

TIE OBSERVATION RANK CORRELATION

Lecture 5- Tie Observation Rank Correlation Sums - live

Typical Sums

Lecture 6 Typical Sums
Lecture 6 Typical Sums live Section F q10, Illustration 30, 26, 27

TYPICAL ILLUSTRATIONS

Lecture 7 Typical Sums Live - Illustration 31, 28, 32, 29, Sec F Q9

RANK CORRELATION TYPICAL SUMS SECTION F

Revison of TYPICAL Rank Correlation Sums Live Section F Q7, 8, 11, 12

Practice Section

Practice Quiz

52 questions
1. Define Correlation.

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2. Define correlation coefficient.

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Note:

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3. The age of an adult person and life insurance premium at the time of taking an insurance under a plan.

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4. The sales and profit of last five years for a mostly accepted product of a company.

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5. The rate of inflation and the purchase power of common man of a country when income of the common man is stable.

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6. Altitude and amount of oxygen in air

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7. What can be said about the correlation between the annual import of crude oil and the number of marriages during the same time period?

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8. The correlation coefficient between X and Y is 0.4. What will be the value of correlation coefficient if 5 is added in each observation of X and 10 is subtracted from each observation of Y?

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9. What is the main limitation of scatter method?

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10. If the value of n (n² - 1) is six times the value of ∑d² then what is the value of r?

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11. What will be the sign of r if the value of the covariance is negative?

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12. When can we say that "There is a correlation between two variables" ?

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13. What is meant by correlate random variable?

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15. What is meant by cause and effect relation?

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16. What is meant by linear correlation?

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17. How many types of correlation are there?

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18. Give two examples of positive correlation.

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19. Give two examples of Negative Correlation.

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20. What is Correlation co-efficient?

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21. Which type of measurement is correlation coefficient ?

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22. Who was the first statistician to suggest the measurement of correlation ?

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23. Describe the methods of Correlation.

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24. Define Perfect Positive Linear Correlation.

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25. Define Perfect Negative Linear Correlation.

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26. What does 'Lack of Linear Correlation' mean?

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27. Which method is generally used to determine only the type of correlation between two correlated random variables?

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28. If the two value random variables x and y are changed in the same direction and in the same proportion, then which type of correlation is there between them?

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29. Which assumption is the Karl Pearson's Correlation Coefficient based on?

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30. Write the Interval of correlation co-efficient r.

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31. For which value Correlation coefficient (r) is equal or bigger than that?

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32. State whether the statement '1 ≤ r ≤ -1' is true or false. Give reasons.

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33. Which is the maximum and minimum value of correlation of co-efficient r ?

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34. What is the effect of change of origin and scale (of variable) on the correlation coefficient?

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35. State the formula of covariance.

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36. Is correlation coefficient absolute or relative measurement?

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37. Give the interval of value of 'r²'

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38. What does the sign of correlation coefficient depend on?

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39. If there is negative correlation coefficient between two variables x and y, then is it possible on negative value of covariance cov(x, y) between two variables x and y?

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40. "If all the points of a scatter diagram are not collinear, then there is no correlation between two variable." Discuss this statement.

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41. If r(x,y) = 0.5, then what is the value of (x, 1/2 y) ?

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42. If r(x, y) = -0.8 then which are the values of r(-x,-y) and r(-x, y)?

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43. How will you interpret -1 < r < 0 ?

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44. How will you interpret 0 < r < 1?

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45. Can we say that x and y are independent variable when r = 0 ? Why/why not?

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46. If correlation r = 0.6 between two variables x and y, then what is the value of correlation co-efficient between two variable where a > 0, b > 0 ? Give reason.

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47. If r = 0 what is the interpretation of relation between two variables?

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48. In the exam of 12th standard students received the following values of correlation coefficient: -1.5 , 1.5, 1.05 and -0.92. Which of these is the correct value?

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49. If linear correlation between two variable x and y is presented in equation as y = a + bx, then what is the value of correlation ?

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50. If the relation between two random variable x and y is y = ax + b; a < 0, then what type of relation exists between x and y?

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51. If the relation between x and y = ax + b a > 0, then what is the value of r (x, y) ?

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52. Which method is helpful for the qualitative type of data?

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53. If the observation values of variable x and y are very large with more dispersion then which method should be used for find out correlation coefficient?

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54. When is it best to use Spearman's Rank Correlation method?

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55. State the minimum and maximum value of Rank correlation coefficient.

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56. What is the sum of difference of rank in correlation coefficient method?

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57. When all the ranks of the two variables are similar and when all the rank of the two variables are opposite in the rank correlation, then which type of correlation is obtained ?

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58. What is meant by tie? How can the situation of tie be solved ?

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59. State formula of Rank correlation co-efficient when there is a tie in the rank correlation coefficient method.

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60. What is the value of r in Rank correlation method when n = 10 and each di = 0 (i = 1, 2, 3…. 10).

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61. Which method is best method for accurate measurement when two related variable are highly correlated?

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Chapter 2 Practice Material

440 KB
Statistics Important Theory

2.9 MB
Text Book

15 MB

EXTRA PRACTICE ASSIGNMENT OF CORRELATION

EXTRA PRACTICE ASSIGNMENT MATERIAL OF CORRELATION

1.6 MB

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