Meaning: -- If two quantities vary in such a way that movement in one are accompanied by movement in other, these quantities are correlated. For example, there exits some relationship between age of husband and age of wife, price of commodity and amount demanded etc. The degree of relationship between variables under consideration is measured through correlation analysis. The measure of correlation called correlation coefficient. Thus,

Correlation analysis refers to the statistical techniques used in measuring the closeness of the relationship between variables.

Definition: -- According to Simpson & Kafka, “Correlation analysis deals with the association between two or more variable.”
According to Ya Lun Chou, “Correlation analysis attempts to determine the degree of relationship between variables.”
Thus correlation is a statistical device, which helps us in analysis the co-variation of two or more variables.
The problem of analysis the relation between different series should be broken down into 3 steps: - 1. Determining whether a relation exists & if it does, measuring it. 2. Testing whether it is significant.

3. Establishing the cause & effect relation, if any.

It should be noted that detection & analysis of correlation (i.e., co variation) between two statistical variables requires relationship of some sort, which associates the observation in pairs, one of each pair being a value of each of two variables. In general, the pairing relationship may be of almost any nature, such as observation at the time or place or over a period of time or different places.

SIGNIFICANCE OF THE STUDY OF CORRELATION

The study of correlation is of immense use in statistical analysis & practical life because of following reasons: -- 1. Shows Relationship: -- Most of variables show some kind of relationship. For example, there is relationship between price & supply, income & expenditure etc. Through correlation...

...Correlationanalysis:
The correlationanalysis refers to the techniques used in measuring the closeness of the relationship between the variables. The degree of relationship between the variables under consideration is measured through the correlationanalysis. And the measure of correlation called as correlation coefficient or correlation index summarizes in one figure the direction and degree of correlation.
Thus correlation is a statistical device which helps us in analyzing the covariation of two or more variables.
The problem of analyzing the relation between different series should be broken down nto 3 steps:
* Determining whether a relation exists and, if it does, measuring it
* Testing whether it is significant
* Establishing the cause and effect relation, if any.
A real life example:
An extremely high and significant correlation between the increase in smoking and increase in lung cancer would not prove that smoking causes lung cancer. The proof of a cause and effect relation can be developed only by means of an exhaustive study of the operating elements themselves.
Correlation and causation:
Correlationanalysis helps us in determining the degree of relationship between two or more variables, it does not tell anything about cause...

...The Spearman Correlation Coefficient remains one of the most important nonparametric measures of statistical dependence between two variables. The Spearman Correlation Coefficient facilitates the assessment of two variables using a monotonic function. This representation is only possible if the variables are perfect monotones of each other and if there are no repeated data values. This enables one to obtain a perfect Spearman correlation of either +1 or -1. The Spearman correlation coefficient nonparametric because, a perfect Spearman correlation results when X and Y are related by any monotonic function, can be contrasted with the Pearson correlation, giving a perfect value only when X and Y are related by a linear function. The other reason being, exact sampling distributions can be obtained without requiring knowledge of the joint probability distribution of X and Y (Sheskin, 2003). The Spearman correlation coefficient is based on the assumption that both the predictor and response variables have numeric values, this assumption, however, the Spearman correlation coefficient can be used to analyze variables that are markedly skewed. The Spearman correlation coefficient operates on the null hypothesis that the ranks of one variable does not vary the same with the ranks of the other variable, meaning that, an increase in the ranks of one...

...14: Correlation
Introduction | Scatter Plot | The Correlational Coefficient | Hypothesis Test | Assumptions | An Additional Example
Introduction
Correlation quantifies the extent to which two quantitative variables, X and Y, “go together.” W hen high values of X are associated with high values of Y, a positive correlation exists. W hen high values of X are associated with low values of Y, a negative correlation exists. Illustrative data set. W e use the data set bicycle.sav to illustrate correlational methods. In this cross-sectional data set, each observation represents a neighborhood. The X variable is socioeconomic status measured as the percentage of children in a neighborhood receiving free or reduced-fee lunches at school. The Y variable is bicycle helmet use measured as the percentage of bicycle riders in the neighborhood wearing helmets. Twelve neighborhoods are considered: X Neighborhood Fair Oaks Strandwood W alnut Acres Discov. Bay Belshaw Kennedy Cassell Miner Sedgewick Sakamoto Toyon Lietz Three are twelve observations (n = 12). Overall, (% receiving reduced-fee lunch) 50 11 2 19 26 73 81 51 11 2 19 25 = 30.83 and Y (% wearing bicycle helmets) 22.1 35.9 57.9 22.2 42.4 5.8 3.6 21.4 55.2 33.3 32.4 38.4 = 30.883. W e want to explore the relation
between socioeconomic status and the use of bicycle helmets. It should be noted that an outlier (84, 46.6) has been removed from this data set so that we may...

...Understanding the Pearson Correlation Coefficient (r)
The Pearson product-moment correlation coefficient (r) assesses the degree that quantitative variables are linearly related in a sample. Each individual or case must have scores on two quantitative variables (i.e., continuous variables measured on the interval or ratio scales). The significance test for r evaluates whether there is a linear relationship between the two variables in the population. The appropriate correlation coefficient depends on the scales of measurement of the two variables being correlated.
There are two assumptions underlying the significance test associated with a Pearson correlation coefficient between two variables.
Assumption 1: The variables are bivariately normally distributed.
If the variables are bivariately normally distributed, each variable is normally distributed ignoring the other variable and each variable is normally distributed at all levels of the other variable. If the bivariate normality assumption is met, the only type of statistical relationship that can exist between two variables is a linear relationship. However, if the assumption is violated, a non-linear relationship may exist. It is important to determine if a non-linear relationship exists between two variables before describing the results using the Pearson correlation coefficient. Non-linearity can be assessed visually by examining a scatterplot of...

...What is Correlational Research?
The correlation research method is appropriate when researchers want to study and “assess relationships among naturally occurring variables.” Assessment means making predictions about the nature of the relationships being studied. It also means describing the relations and assigning them a “correlation coefficient” that describes the direction and magnitude of the movement of variables to one another.
There are many types of correlational research. The commonality among all types of correlational research is that they explore relationships between variables. Where descriptive research only described what was going on, correlational research talks about the link between different things. It is important to understand that correlational research does NOT tell us that Variable A caused Variable B, but rather that they are somehow related.
For example, if I told you that there was a correlation between domestic violence (violence between family members) and bowling, you would look at me strangely. But there is a relationship between the variables (variable 1- domestic violence, and variable 2- bowling). As more people bowl in the US, more domestic violence occurs.
[pic] [pic]
Does that mean that bowling causes domestic violence- like you had bad game and take it out on a loved one? Or domestic violence causes bowling- like you fight with a sibling and feel the need to take it out on...

... ➢ Consumption has a positive relation with disposable income.
➢ From the scatter diagram made by the given data, it is noted that as the disposable income increases the annual sales also increases.
[pic]
➢ Again, We know that the coefficient correlation is,
r = [pic][pic]
Here,
r = [pic]
= [pic]
= 0.70
Therefore, there is a strong positive correlation between the disposable income and the annual sales.
➢ The regression coefficient is 0.193. That means sales will increase by $0.193 if disposable income increase by $1.00.
“Based on these points we can conclude that, the average disposable income should be used to predict sales based on the sample of 14 sunflowers stores.”
Question no. 02
Should the management of Sunflowers accept the claims of Triangle’s leasing agents? Why or why not?
Answer to the question no. 02
The management should accept the claims of Triangle leasing agents.
The reasons are:
➢ There is a strong positive correlation between disposable income and sales, so it is easily predictable that there is a direct relationship between these two variables.
➢ Value of the coefficient of correlation is 0.70 and it is near to 1.00. That is if one variable, the disposal income increases, another variable, the annual sales will also increase.
➢ The regression coefficient is 0.193. Which means that,...

...monthly food expenditure takes up a significant portion of the monthly budget. While a large number of factors affect family food expenses; this paper is concerned with only 4 factors of these : income, Gender, level of education and family size .In order to study the relationship between MFE & the 4 variables, a sample of 50 families were chosen randomly out of 500 Omani families.
Different types of statistical analysis were applied on the sample e.g. measures of location and dispersion as well as using graphical and tabular methods to represent data.
METHODS :
A simple random sample of 50 households were selected and a number of statistical analysis were done.
1-numirecal methods:
(table 1,numerical analysis)
Let X =monthly income, y=monthly food expenditure: *
Sample covariance between x & y {sxy}= 7945.804
Sample correlation coefficient {rxy} =0.921165
Let X= family size, Y=monthly food expenditure*
Sample covainc btween x & y {sxy}= 78.936
Sample correlation coefficient {rxy} =0.985828
...