worksheet on Correlation

Model paper for kerala university subsidiary statistics for

Bsc mathematics students

Topic:  Correlation

1.      What is a scatter diagram? What information about the data is conveyed by a scatter diagram? How is it constructed?

2.      Explain the principle of least squares

3.      A. Explain the principle of least squares for fitting a second degree curve of the form y=ax²+bx+c for n pairs of observations

B. fit a parabola of the type y=a+bx+cx² to the following data

X    10   15   20   25   30   35   40

Y    11   13   16   20   27   34   41

4.      Obtain the least square estimates of a and b for the line y=a+bx.

Fit a straight line of the form y=ax+b to the following data

X   1   3   5   7   8   10

Y   8   12   15   17   18   20

5.      Explain how the principle of least squares is used in fitting the curve y=ae^bx

For the data given below find the equation to the best fitting exponential curve of the form y=ae^bx

X   Y

1                 1    6

            2        4.5

            3        13.8

            4        40.2

            5        125

            6        300

6.      Explain the invariance of the correlation coefficient under linear transformation

7.      What are the limits within which the correlation coefficient can vary? What are your inferences when r=0, -1,1?

8.      The following table gives data concerning the SB deposits and number of strikes and lock outs over a period of 7 years. Calculate the correlation coefficient

SB deposits            No: of strikes and lock outs

X                              Y

51                       38

54                      44

55                      33

59                      36

65                     33

60                     23

70                     10