Regression and Correlation

• Properties of the Regression Line

Regression is concerned with the study of relationship among variables. The aim of regression (or regression analysis) is to make models for prediction and for making other inferences. Two variables or more than two variables may be treated by regression. Regression line usually written as . The general properties of the regression line are given […]

• Linear Regression

Regression: The word regression was used by Frances Galton in 1985. It is defined as “The dependence of one variable upon other variable”. For example, a weight depends upon the heights. The yield of wheat depends upon the amount of fertilizer. In regression we can estimate the unknown values of one (dependent) variable from known […]

• Example Method of Least Squares

The given example explains you that how to find the equation of straight line or least square line by using the method of least square, which is very useful in statistics as well as in mathematics. Example: Fit a least square line to the following data. Also find trend values and show that . 1 […]

• Curve Fitting and Method of Least Squares

Curve Fitting: Curve fitting is a process of introduction mathematical relationship between dependent and independent variables in the form of an equation for a given set of data. Method of Least Square: The method of least square helps us to find the values of unknowns and in such a way that following two conditions are […]

• Examples of Correlation

Calculate and analyze the correlation coefficient between the number of study hours and the number of sleeping hours of different students. Number of Study hours 2 4 6 8 10 Number of Sleeping hours 10 9 8 7 6 Solution: The necessary calculation is given below: 2 10 -4 +2 -8 16 4 4 9 […]

• Properties of Coefficient of Correlation

The correlation coefficient is symmetrical with respect to and i.e. The correlation coefficient is the geometric mean of the two regression coefficients.    or   . The correlation coefficient is independent of origin and unit of measurement i.e. . The correlation coefficient lies between and . i.e. .

• Coefficient of Correlation

The degree or level of correlation is measured with the help of correlation coefficient or coefficient of correlation. For population data, the correlation coefficient is denoted by . The joint variation of and is measured by the covariance of and . The covariance of and denoted by is defined as: The may be positive, negative […]

• Perfect Correlation

Perfect Correlation: If there is any change in the value of one variable, the value of the others variable is changed in a fixed proportion, the correlation between them is said to be perfect correlation. It is indicated numerically as and . Perfect Positive Correlation: If the values of both the variables are move in […]

• Positive and Negative Correlation

Positive Correlation: The correlation in the same direction is called positive correlation. If one variable increase other is also increase and one variable decrease other is also decrease. For example, the length of an iron bar will increase as the temperature increases. Negative Correlation: The correlation in opposite direction is called negative correlation, if one […]

• Linear and Non Linear Correlation

Linear Correlation: Correlation is said to be linear if the ratio of change is constant. The amount of output in a factory is doubled by doubling the number of workers is the example of linear correlation. In other words it can be defined as if all the points on the scatter diagram tends to lie […]

• Correlation

Correlation is a technique which measures the strength of association between two variables. Both the variables and may be random or may be that one variable is independent (non-random) and the other to be correlated are dependent. When the changes in one variable appear to be linked with the changes in the other variable, the […]

• Scatter Diagram

Scatter diagram is a graphic picture of the sample data. Suppose a random sample of n pairs of observations has the values. These points are plotted on a rectangular co-ordinate system taking independent variable on -axis and the dependent variable on -axis. Whatever be the name of the independent variable, it is to be taken […]