Economics 3 Marks Question

No, correlation does not imply causation. The correlation between the two variables does not imply that one variable causes the other. In other words, cause and effect relationship is not a prerequisite for the correlation. Correlation only measures the degree and intensity of the relationship between the two variables, but surely not the cause and effect relationship between them.

The advantages of Spearman's Rank Correlation are:

1. This method is simple to calculate and easy to understand.
2. This method can be used in qualitative facts.
3. If ranks are given and the actual values are missing, then also this method can be used.

The disadvantages of Spearman's Rank Correlation are:

1. It cannot be used for computing correlation in case of grouped frequency distribution.
2. It can be used conveniently only when the number of observation is small.

"r" i.e. correlation coefficient is preferred to covariance as a measure of association because

• r is independent of change in scale and origin.
• r has a specific range (-1 to +1 ), so it comes handy to interpret the results quickly.
• Covariance is a part of correlation coefficient.

No, Zero correlation does not mean absence of correlation but it means absence of linear correlation. There may be a non linear relationship between two variables but variables which have non linear relationship will depict zero correlation when put to scatter diagram and low correlation when used Pearson's or Spearman's method. Consider a shape as shown below:
It will be taken as zero correlation but to a certain level, X and Y are positively related and thereafter their relationship becomes negative.

"Scatter Diagram” is a graphic method of finding out correlation between the two variables. For constructing a scatter diagram, X-variable is represented on the x-axis and Y-variable on y-axis. Each pair of values is plotted. Different plotted points may be scattered in various directions whose analysis gives us an idea of the type and magnitude of correlation:Scatter diagram is a useful technique for visually:

• Examining the form of relationship, without calculating any numerical value.
• We can get a fairly good idea of the relationship between the variables from the scatter diagram.

Degree of correlation measures the extent to which items are correlated. Nearer is the value of r to 1 higher is the degree of correlation, nearer is the value of r to zero, closer is the value of r to zero. Direction is indicated by sign of + or - A + sign indicates positive correlation- i.e. when x increases, y increases and vice verca and a - sign shows negative correlation i.e. when x increases, y decreases and vice versa.

The difference between correlation and causation is that correlation is the mutual relation that exists between two or more things while causation is the fact that something causes an effect. The correlation between two variables does not imply that one is as a result of the other. Two or more variables considered to be related, in a statistical context, if their values change so that as the value of one variable increases or decreases so does the value of the other variable (although it may be in the opposite direction). For example, for the two variables "hours worked" and "income earned" there is a relationship between the two if the increase in hours worked is associated with an increase in income earned. If we consider the two variables "price" and "purchasing power", as the price of goods increases a person's ability to buy these goods decreases (assuming a constant income). But we cannot say that one is the cause of other.

Merits:

1. Knowledge of Direction of Correlation: Pearson's co-efficient of correlation gives to the knowledge about the direction of relationship whether it is positive or negative.
2. Size of Correlation: This method also indicates the size of relationship between the variables i.e. correlation ranges between +1 and -1.
3. Ideal Measure: It is an ideal measure of correlation because it is based on most important statistical measures like mean and standard deviation.

Demerits:

1. Difficult to calculate: Karl Pearson's method is a complicated method and involves complex calculations.

The merits of rank correlation method are:

1. It is simple to calculate and easy to understand.
2. This method is very useful when the data is of qualitative nature.
3. When ranks are given instead of actual data, this is the only method for finding out the degree of correlation.

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Scatter diagram is a graphic method of studying correlation. To construct a scatter diagram, X variable is taken on X-axis and Y variable is taken on Y-axis. The cluster of points, so plotted is referred to as a scatter diagram. In a scatter diagram, the degree of closeness of scatter points and their overall direction gives us an idea of the nature of the relationship.
It is stated in the points below:

1. If the dots move from left to right, in an upward direction then correlation is said to be positive whereas the movement of dots from left to right downwards indicates negative correlation.
2. Dots in a straight line indicate perfect correlation.
3. Dots falling close to each other in a straight line indicate high degree of correlation.

Correlation studies and measures the direction and intensity of relationship among variables. If the two variables X and Y move in the same direction, i.e., with an increase in one variable, the other variable also increases or with the fall in one variable, the other variable also falls, the correlation is said to be positive. E.g. When the income rises, consumption also rises. There is a positive correlation between them.
Whereas if the two variables X and Y move in the opposite direction, i.e., with the increase in one variable, the other variable falls or with the fall in one variable, the other variable rises, the correlation is said to be "Negative correlation”.
E.g. When the price of a commodity rises, its demand falls. There is a negative correlation between them.

When two variables reflect correlation statistically but logically we can't expect them to be correlated, it is called spurious correlation. Two examples are as follows:

1. Where there were more doctors, death rates were high.
2. When there was high rainfall, more students has A grades.
3. Number of storks and birth rate in Denmark.
4. Number of priests in America and alcoholism.
5. In the start of the 20th century it was noted that there was a strong correlation between 'Number of radios' and 'Number of people in Insane Asylums'.

If there is no evident or sensible connection between two variables, then the correlation between these variables is said to be spurious, non-sense or chance correlation. For example correlation between rainfall recorded and production of steel. These two variables are not connected by any way. So, the correlation between these variables is said to be spurious.

The properties of Spearman's Rank Correlation are:

1. Spearman's rank correlation also lies between +1 and -1.
2. It is not affected by either change in scale or change in origin.

The advantages of Karl Pearson's coefficient of correlation are:

1. Karl Pearson's coefficient of correlation indicates the relationship as positive or negative and thus direction of the relationship can be ascertained.
2. This measure gives summarised and precise quantitative figure of correlation which can be interpreted easily and can provide meaningful results.
3. This coefficient of correlation indicates the direction and also the degree of relationship between the two variables. It shows whether the relationship is high, moderate or low.

The pair of points are (4, 78), (5, 72), (6, 66), (7, 60), (8, 54), (9, 48), (10, 42), (11, 36), (12, 30), (13, 24), (14, 18) and (15, 12). Now we plot the points on a graph paper, which is shown below:
The diagram indicates that there is perfect negative correlation between the values of the two variables X and Y.

Now, we plot the points on a graph paper which is shown below:
The diagram indicates that there is perfect positive correlation between the values of the two variables X and Y.

Simple Correlation: When there are only two variables involved in a problem, it is called simple correlation. For example, study of correlation between height and weight is simple correlation.
Partial Correlation: when we study two variable keeping some other variables which have an influence constant, it is called partial correlation. For example, if we study price rise with reference to only crop failure, keeping other factors like external factors, government policies constant, it is partial correlation.
Multiple Correlation: When we study relationship between two or more variables simultaneously, it is called multiple correlation. For example, study of price rise with crop failure and weaknesses of government policies.

In this method the values of the two variables are plotted on a graph paper. One is taken along the horizontal (x-axis) and the other along the vertical (y-axis). By plotting the data, we get points (dots) on the graph which are generally scattered and hence the name Scatter Plot'.
The manner in which these points are scattered, suggest the degree and the direction of correlation. The degree of correlation is denoted by 'r' and its direction is given by the signs positive and negative.

The graphic method of measuring dispersion is called “Scatter diagram”. Its three demerits are:

1. It does not indicate the numerical value of correlation as it is a non-mathematical method.
2. It provides only a broad and rough idea of the correlation between the two variables.
3. In case of more than two variables, it is not possible to draw a scatter diagram.

The disadvantages of Karl Pearson's coefficient of correlation are:

1. The value of coefficient is affected by extreme items.
2. The calculation process consumes a lot of time.
3. Correlation coefficient needs very careful interpretation, otherwise it may be misinterpreted.

The study of correlation is of great significance because of reasons given below:

1. To understand relationship between two or more variables: Correlation is very helpful when we want to study relationship between two or more variables.
2. To find dependence: Correlation also helps in finding if one variable is dependent on other or not.
3. Provides base for Regression Analysis: When two variables are correlated then the value of one variable can be estimated given the value of another variable using regression equations.
4. Helps in decision making: It helps in taking important decisions to a business man, government and sociologists.

No, Avantika is not correct. Points on a downward sloping straight line depict perfect negative correlation.

If the points in a scatter diagram tend to cluster in a straight line which makes an angle of 30° with the X-axis, it means that the change in the value of Y is less proportionate than the change in the value of x. Thus, the strength of association between X and Y is moderate.

The pair of points are (2, 6), (3, 5), (5, 7), (6, 8), (8, 12) and (9, 11). Now, we plot the points on a graph paper, which is shown below:
The diagram indicates that there is high degree of positive correlation because the plotted points are near to each other and the trend of the points is upward.