correlation and its types

Definition

Degree and type of relationship between any two or more quantities (variables) in which they vary together over a period; for example, variation in the level of expenditure or savings with variation in the level of income. A positive correlation exists where the high values of one variable are associated with the high values of the other variable(s). A 'negative correlation' means association of high values of one with the low values of the other(s). Correlation can vary from +1 to -1. Values close to +1 indicate a high-degree of positive correlation, and values close to -1 indicate a high degree of negative correlation. Values close to zero indicate poor correlation of either kind, and 0 indicates no correlation at all. While correlation is useful in discovering possible connections between variables, it does not prove or disprove any cause-and-effect (causal) relationships between them. See also regression

Positive Correlation

Positive correlation occurs when an increase in one variable increases the value in another.

The line corresponding to the scatter plot is an increasing line.

Negative Correlation

Negative correlation occurs when an increase in one variable decreases the value of another.

The line corresponding to the scatter plot is a decreasing line.

No Correlation

No correlation occurs when there is no linear dependency between the variables.

Perfect Correlation

Perfect correlation occurs when there is a funcional dependency between the variables.

In this case all the points are in a straight line.

Strong Correlation

A correlation is stronger the closer the points are located to one another on the line.

Weak Correlation

A correlation is weaker the farther apart the points are located to one another on the line.

Comments

Double exponential distribution

Double Exponential Distribution Probability Density Function The general formula for the probability density function of the double exponential distribution is where is the location parameter and is the scale parameter . The case where = 0 and = 1 is called the standard double exponential distribution . The equation for the standard double exponential distribution is Since the general form of probability functions can be expressed in terms of the standard distribution , all subsequent formulas in this section are given for the standard form of the function. The following is the plot of the double exponential probability density function. Cumulative Distribution Function The formula for the cumulative distribution function of the double exponential distribution is The following is the plot of the double exponential cumulative distribution function. Percent Point Function The formula for the percent point function of the double exponential distribution

Runs Test for Detecting Non-randomness

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Basics of Sampling Techniques

Population A population is a group of individuals(or)aggregate of objects under study.It is also known as universe. The population is divided by (i)finite population (ii)infinite population, (iii) hypothetical population, subject to a statistical study . A population includes each element from the set of observations that can be made. (i) Finite population : A population is called finite if it is possible to count its individuals. It may also be called a countable population. The number of vehicles crossing a bridge every day, (ii) Infinite population : Sometimes it is not possible to count the units contained in the population. Such a population is called infinite or uncountable. ex, The number of germs in the body of a patient of malaria is perhaps something which is uncountable (iii) Hypothetical population : Statistical population which has no real existence but is imagined to be generated by repetitions of events of a certain typ

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