types of correlation- Parul sukhlecha

Correlation coefficient (or "r")

·         It ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related.

·         If r is close to 0, it means there is no relationship between the variables. Consider X and Y as two variables and it is denoted by the symbol R.

·         If the correlation coefficient, R, is positive, then a increase in X would result in a increase in Y, however if R was negative, an increase in X would result in a decrease in Y. Larger correlation coefficients, such as 0.8 would suggest a stronger relationship between the variables, whilst figures like 0.3 would suggest weaker ones. 

 There are two important types of correlation.

1) Positive and Negative correlation

2) Linear and Non – Linear correlation.

Positive correlation:

Some examples of series of positive correlation are:

(i) Heights and weights;

(ii) Household income and expenditure;

(iii) Price and supply of commodities;

(iv) Amount of rainfall and yield of crops.

Negative corelation:

       Some examples of series of negative correlation are:

(i) Volume and pressure of perfect gas;

(ii) Current and resistance [keeping the voltage constant

(iii) Price and demand of goods.

Linear correlation

The correlation between two variables is said to be linear if the change of one unit in one variable result in the corresponding change in the other variable over the entire range of values.

For example consider the following data.

x	2	4	6	8	10
y	7	13	19	25	31

  Thus, for a unit change in the value of x, there is a constant change in the corresponding values of y and the above data can be expressed by the relation

 y = 3x +1

Nonlinear correlation:

The relationship between two variables is said to be non – linear if corresponding to a unit change in one variable, the other variable does not change at a constant rate but changes at a fluctuating rate. In such cases, if the data is plotted on a graph sheet we will not get a straight line curve. For example, one may have a relation of the form y = a + bx + cx2 or more general polynomial

Group No. 5: Formulas to be used in Excel by Preshita Chaurasiya

Formulas to be used in Excel:

• Mean/ Average: Select the observation. Put =Mean(Range) and Enter.
• Median: Select the observation. Arrange it in ascending order. Put =Median(Range) and Enter.
• Mode: Select the observation. Put =Mode(Range) and Enter.
• Variations: Observation less Mean of the range. Put =(Observation-Mean) and Enter.
• Variations*2 / (Variations)^2:

1. Put =Power((observation),2) and Enter                        OR 
2. Put =(observation)^2 and Enter                                    OR 
3. Put =(observation)*(observation) and Enter

• Variance: Variance is average of Variations*2. Put =Mean(Range of Variations*2) and Enter.
• Standard Deviation: Standard Deviation is the square root of Variance. Put =SQRT(Variance) and Enter.

Bar graph v/s Histogram - by Parul sukhlecha-PGDM 2013027

DIFFERENCE BETWEEN BAR GRAPHS AND HISTOGRAM

BAR CHARTS:

A BAR graph, is a way of showing a comparison of values. It is a chart wherein each bar is in proportion to the value that it represents. Bar graphs are used to help organize data and information.
Here is how to read a bar chart:

§  The columns are positioned over a label that represents a categorical variable

§  The height of the column indicates the size of the group defined by the column label

HISTOGRAMS:

A histogram allows a visual interpretation of data by indicating the number of data points that lie within a range of values, called a class.

The frequency of data that falls within each class is depicted by the use of bar.

Like a bar chart, a histogram is made up of columns plotted on a graph. Usually, there is no space between adjacent columns. Here is how to read a histogram.

• The columns are positioned over a label that represents quantitative variable
• The column label can be a single value or a range of values.
• The height of the bar corresponds to the relative frequency of the amount of data in a class

The difference between bar chart and histogram:

§  Bar graphs measure the frequency of categorical data, and the classes for a bar graph are these categories. On the other hand, histograms are used for data that is at least at the ordinal level of measurement. The classes for a histogram are ranges of values

§  One implication of this distinction: it is always appropriate to talk about the skewness of a histogram; that is, the tendency of the observations to fall more on the low end or the high end of the X axis.

§  With bar charts, however, the X axis does not have a low end or a high end; because the labels on the X axis are categorical - not quantitative. As a result, it is less appropriate to comment on the skewness of a bar chart.