Correlation Co-efficient Definition:
A measure of the strength of linear association between two variables. Correlation will always between -1.0 and +1.0. If the correlation is positive, we have a positive relationship. If it is negative, the relationship is negative.

Correlation
Correlation can be easily understood as co relation. To define. correlation is the average relationship between two or more variables. When the change in one variable makes or causes a change in other variable then there is a correlation between these two variables.

These correlated variables can move in the same direction or they can move in opposite direction. Not always there is a cause and effect relationship between the variables when there is a change; that might be due to uncertain change.

Simple Correlation is a correlation between two variables only; meaning the relationship between two variables. Event correlation and simple event correlation are the types of correlations mainly used in the industry point of view.

Types of Correlation

In Research Methodology of the Management, Correlation is broadly classified into six types as follows :

(1) Positive Correlation
(2) Negative Correlation
(3) Perfectly Positive Correlation
(4) Perfectly Negative Correlation
(5) Zero Correlation
(6) Linear Correlation

Positive Correlation

When two variables move in the same direction then the correlation between these two variables is said to be Positive Correlation. When the value of one variable increases, the value of other value also increases at the same rate.

For examplethe training and performance of employees in a company. Negative Correlation

In this type of correlation, the two variables move in the opposite direction. When the value of a variable increases, the value of the other variable decreases.

For example, the relationship betwwen price and demand.

... ➢ 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,...

...CORRELATION ANALYSIS (V. Imp)
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 calledcorrelation 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...

...
CORRELATION
Md. Musa Khan
Lecturer
DBA, IIUC
musa_stat@yahoo.com
Definition:
If two or more variables vary in such a way that change in one are accompanied by changes in the other, these variables are said to be correlated. For example, here exists some relationship between family income and expenditure on luxury items, price of a commodity and amount demanded, increase in rainfall up to a point and production of a rice, etc. The statistical tool with the help of which these relationships between two or more than two variables is studied is called correlation. Therefore the relationship between two or more variables is called correlation.
Co-efficient of correlation:
The measure of correlation is called the coefficient of correlation summarizes in one figure the direction and degree of correlation. It is denoted by r.
Types of correlation:
There are four types of correlations. They are
i. Simple correlation
ii. Multiple...

...-------------------------------------------------
Simple regression and correlation
Submitted by Sohaib Roomi
Submitted to:Miss Tahreem
Roll No M12BBA014
Simple Regression
And Correlation
Introduction
The term regression was introduced by the English biometrician, Sir Francis Galton (1822-1911) to describe a phenomenon in which he observed in analyzing the heights of children and their parents. He solved a tendency toward the average height of all men. Today, the word “Regression” is used in quiet different sense. Its investigation depends upon two variables. Dependent and Independent Variable.
Definition
“Regression provides an equation to be used for estimating the average value of the dependent variable from the known values of independent variable.”
Determination and Probabilistic Relation or Model
The relation among variable may or may not be governed by an exact physical law. For convenience, let us consider a set of n pairs of observations (Xi , Yi). If the relation between the variables is exactly linear, then the mathematical equation describing the linear relation is generally written as
Yi = a + bXi
Where a is the value of Y when X equals zero and is called Y-intercept and b indicates the change in Y for a one-unit change in X and is called the slope of the line. Substituting a value for X in the equation, we can completely determine a unique value of Y. The linear relation in such a case is said to be a...

...Correlation
Chapter 10
Covariance and Correlation
What does it mean to say that two variables are associated with one another?
How can we mathematically formalize the concept of association?
Differences between Data Handling in Correlation & Experiment
1. Summarize entire relationship
• We don’t compute a mean Y (e.g., aggressive behavior) score at each X (e.g., violent tv watching). We summarize the entire relationship formed by all pairs of X-Y scores. This is the major advantage of correlation.
2. N = number of pairs
• Because we look at all X-Y pairs at once, we have ONE sample, with N representing the number of pairs
3. Variable X and Variable Y are arbitrary
• Either variable can be X or Y. It’s arbitrary. There is no IV or DV.
4. Scatterplot
• Data are graphed as a scatterplot of pairs of scores.
--HW Q--
The statistic that we calculate to determine the relationship between our variables is the Correlation Coefficient
This number tells us two things about the relationship:
Type of relationship
Strength of relationship
Types of Relationships
Linear: as scores on one variable increase, scores on the other variable either increase or decrease
Nonlinear: relationship between X and Y changes direction at some point
U: Age & difficulty moving
Inverted U: Alcohol consumed & feeling well
Correlational research focuses almost entirely on linear...

...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...

...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...

...Correlation and Regression Assignment
Problem 1.
a. Explain which variable you chose as the explanatory variable and discuss why.
* The explanatory variable is the height. This is because I am assuming that as height increases, the weight will increase as well. So the weight is the dependent variable
b. Produce a scatter plot and insert the result here.
* Scatter plot
c. Find the equation of the regression line, Write it in the form of y=a+bx, where a is the y-intercept and b is the slope.
* Y=-84.2941 + 0.79941x
d. Add the regression line to the graph and insert the result here
* Regression line
e. Calculate the correlation coefficient
* R= 0.9551913
Problem 2.
a. Explain which variable you chose as the explanatory variable and discuss why.
- The explanatory variable is games won, because that was stated in the problem. I guess this is because if more games are won, then more balls are hit.
b. Produce an scatter plot and insert the result here.
-scatter plot
c. Find the equation of the regression line. Write it in the form of y=a+bx, where a is the y-intercept and b is the slope.
- y = 0.2485320 + 0.0003213x
d. Add the regression line to the graph and insert the result here.
- regression line
e. Calculate the correlation coefficient
* r= 0.5587557
Problem 5
a. Explain which variable you chose as the explanatory...