EXCEL

TODay's assignment

LINEAR REGRESSION

In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more variables denoted X.

In linear regression, models of the unknown parameters are estimated from the data using linear functions. Such models are called linear models. 

Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. 

Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X.

Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of yX, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis. 

 

Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications.

This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.

Linear regression has many practical uses. Most applications of linear regression fall into one of the following two broad categories:

• If the goal is prediction, or forecasting, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y.
• Given a variable y and a number of variables X₁, ..., X_p that may be related to y, then linear regression analysis can be applied to quantify the strength of the relationship between y and the X_j, to assess which X_j may have no relationship with y at all, and to identify which subsets of the X_j contain redundant information about y, thus once one of them is known, the others are no longer informative.

quadratic regression

Quadratic Regression is a process by which the equation of a parabola of "best fit" is found for a set of data

is a form of linear regression in which the relationship between the independent variable x and the dependent variable y is modeled as an nth order polynomial. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y|x), and has been used to describe nonlinear phenomena such as the growth rate of tissues, the distribution of carbon isotopes in lake sediments , and the progression of disease epidemics.

Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y|x) is linear in the unknown parameters that are estimated from the data.

For this reason, polynomial regression is considered to be a special case of multiple linear regression

alldone for part one of KOS 1110.

THANKS MADAM LINDA

alhamdullilah . . .