**Unit – 4: Correlation analysis**

**AHSEC Class 11 Economics Chapterwise Notes**

**Q.N.1. Define Correlation analysis. What are its various kinds?**

Ans: – Definition: – Correlation is the degree of the relationship between two or more variables. It does not explain the cause behind the relationship. Kinds of correlation may be studied on the basis of:

I. Change in proportion.

II. Number of variation.

III. Change in direction.

**(I) Basis of change in proportion**:-There are two important correlations on the basis of change in proportion. They are:

(a) Linear correlation (b) Non-linear correlation

(a) Linear correlation: – Correlation is said to be linear when one variable move with the other variable in fixed proportion

(b) Non-linear correlation: – Correlation is said to be non-linear when one variable move with the other variable in changing proportion.

**(II) On the basis of number of variables:** On the basis of number of variables, correlation may be:

(a) Simple (b) Partial (c) Multiple

(a) Simple correlation: – When only two variables are studied it is a simple correlation.

(b) Partial correlation: – When more than two variables are studied keeping other variables constant, it is called partial correlation.

(c) Multiple correlations: – When at least three variables are studied and their relationships are simultaneously worked out, it is a case of multiple correlations

**(III) On the basis of Change in direction:** On the basis of Chang in direction, correlation may be

(a)Positive Correlation (b) Negative Correlation

(a) Positive Correlation: – Correlation is said to be positive when two variables move in same direction.

(b) Negative Correlation: – Correlation is said to be negative when two variables moves in opposite direction.

**Q.N.2.What are the uses and limitations of Correlation?**

Ans: – Following are the main advantages of correlation:

a) It gives a precise quantitative value indicating the degree of relationship existing between the two variables.

b) It measures the direction as well as relationship between the two variables.

c) Further in regression analysis it is used for estimating the value of dependent variable from the known value of the independent variable

d) The effect of correlation is to reduce the range of uncertainty in predictions.

**Following are the main limitations of correlation: **

a) Extreme items affect the value of the coefficient of correlation.

b) Its computational method is difficult as compared to other methods.

c) It assumes the linear relationship between the two variables, whether such relationship exist or not.

**Q.N.3. What are the different degrees of Correlation? Or When correlation is positive or negative or zero**

Ans: The different degrees of correlation are:

a) Perfect Correlation: – It two variables vary in same proportion, and then the correlation is said to be perfect correlation.

b) Positive Correlation: If increase (decrease) in the values of one variable result a corresponding increase (decrease) in the values of another variable then the variables are said to be positively correlated. For example heights and weights, income and expenditure etc. are positively correlated.

c) Negative Correlation: If increase (decrease) in the values of one variable result a corresponding decrease (increase) in the values of another variable then the variables are said to be negatively correlated. For example, demand and price of commodities.

d) Zero Correlation: Two variables are said to have Zero correlation between them if they tend to change with no connection to each other. For example one should expect zero correlation between the heights of the students and the marks obtained by them.

**Q.N.4. What are the different methods of studying correlation?**

**Ans**: – The different methods of studying relationship between two variables are:

a) Scatter diagram method.

b) Graphic method

c) Karl Pearson’s coefficient of correlation

d) Rank correlation method

**a) Scatter Diagram Method**: – It is a graphical representation of finding relationship between two or more variables. Independent variable are taken on the x-axis and dependent variable on the y-axis and plot the various values of x and y on the graph. If all values move upwards then there is positive correlation, if they move downwards then there is negative correlation.

Merits:

i) It is easy and simple to use and understand.

ii) Relation between two variables can be studied in a non-mathematical way.

Demerits:-

i) It is non-mathematical method so the results are non-exact and accurate.

ii) It gives only approximate idea of the relationship.

**b) Graphic Method**: – This is an extension of linear graphs. In this case two or more variables are plotted on graph paper. If the curves move in same direction the correlation is positive and if moves in opposite direction then correlation is negative. But if there is no definite direction, there is absence of correlation. Although it is a simple method, but this shows only rough estimate of nature of relationship.

Merits: –

i) It is easy and simple to use and understand.

ii) Relation between two variables can be studied in a non-mathematical way.

Demerits:-

i) It is non-mathematical method so the results are non-exact and accurate.

ii) It gives only approximate idea of the relationship.

**c) Karl Pearson’s Coefficient of correlation**: – Correlation coefficient is a mathematical and most popular method of calculating correlation. Arithmetic mean and standard deviation are the basis for its calculation. The Correlation coefficient (r), also called as the linear correlation coefficient measures the strength and direction of a linear relationship between two variables. The value of r lies between -1 to +1.

Properties of r:-

a) r is the independent to the unit of measurement of variable.

b) r does not depend on the change of origin and scale.

c) If two variables are independent to each other, then the value of r is zero.

Merits:-

a) The co-efficient of correlation measures the degree of relationship between two variables.

b) It also measures the direction.

c) It may be used to determine regression coefficient provided s.d. of two variables are known.

Demerits:-

a) It assumes always the linear relationship between the variables even if this assumption is not correct.

b) It is affected by extreme values.

c) It takes a lot of time to compute.

**d) Spearman’s rank Coefficient of correlation**: – This is a qualitative method of measuring correlation co-efficient. Qualities such as beauty, honesty, ability, etc. cannot be measured in quantitative terms. So, ranks are used to determine the correlation coefficient.

Merits:-

a) It is easy and simple to calculate and understand.

b) This method is most suitable if the data are qualitative.

c) This is the only method that can be used where we are given the ranks not the actual data.

Demerits:-

a) This method is not accurate as Karl Pearson’s correlation coefficient.

b) This method cannot be used in case of grouped frequency distribution.

c) Where the number of items exceeds 30 the calculations become quite tedious and require a lot of time.

The rank method has two principal uses:

a) The initial data are in the form of ranks or qualitative in nature.

b) If N is fairly small (say, not larger than 25 or 30) rank method is sometimes applied to interval data as on approximation to the more time consuming R. This requires that the interval data be transferred to rank orders for both variables. If N is much in excess of 30, the labour required in ranking the scores, becomes greater than is justified by the anticipated saving of time through the rank formula.

Difference between Karl Pearson’s coefficient and Spearmen’s Rank correlation

Karl Pearson |
Rank Correlation |

1. This method is used when actual data is given. | 1. This method is used when we are given rank not the actual data. |

2. It measures only linear relationship between two variables. | 2. It measures nonlinear monotonic relationship between two variables. |

3. It is quantitative in nature. | 3. It is qualitative in nature. |