R-squaredis a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression. 0% indicates that the model explains none of the variability of the response data around its mean.Instatistics, thecoefficient of determination, denotedR2orr2and pronouncedR squared, is a number that indicates how well data fit a statistical model sometimes simply a line or curve. It is astatisticused in the context ofstatistical modelswhose main purpose is either thepredictionof future outcomes or the testing ofhypotheses, on the basis of other related informationR2does not indicate whether: the independent variables are a cause of the changes in thedependent variable; omitted-variable biasexists; the correctregressionwas used; the most appropriate set of independent variables has been chosen; there iscollinearitypresent in the data on the explanatory variables;

Adjusted r sqaure: R2shows how well terms (data points) fit a curve or line; Adjusted R2also indicates how well terms fit a curve or line, but adjusts for the number of terms in a model. If you add more and moreuselessvariables to a model, adjusted r-squared will decrease, but if you add moreusefulvariables, adjusted r-squared will increase.Adjusted R2will always be less than or equal to R2. Use of the adjusted R2is only necessary when you are dealing withsamples. In other words, R2isnt necessary when you have data from an entire populationThe use of an adjustedR2(often written asand pronounced "R bar squared") is an attempt to take account of the phenomenon of theR2automatically and spuriously increasing when extra explanatory variables are added to the modelDIFFERENCE One major difference between R-squared and the adjusted R-squared is that R-squared supposes that every independent variable in the model explains the variation in the dependent variable. It gives the percentage of explained variation as if all independent variables in the model affect the dependent variable, whereas the adjusted R-squared gives the percentage of variation explained by only those independent variables that in reality affect the dependent variable. R-squared cannot verify whether the coefficient ballpark figure and its predictions are prejudiced. It also does not show if a regression model is satisfactory; it can show an R-squared figure for a good model, or a high R-squared figure for a model that doesnt fit.

The adjusted R-squared is a modified version of R-squared for the number of predictors in a model. The adjusted R-squared can be negative, but isn't always, while an R-squared value is between zero and 100 and shows the linear relationship in the sample of data even when there is no basic relationship. The adjusted R-squared is the best estimate of the degree of relationship in the basic population. To showcorrelationof models with R-squared, pick the model with the highest limit, but the best and easiest way to compare models is to select one with the smaller adjusted R-squared. Adjusted R-squared is not a typical model for comparing nonlinear models, but multiple linear regressions.

REGRESSION AND CORRELATIONCorrelation analysis studies the joint variation of two or more variables for determining the amount of correlation between two or more variables. Causal analysis is concerned with the study of how one or more variables affect changes in another variable. It is thus a study of functional relationships existing between two or more variables. This analysis can be termed as regression analysis. The correlations term is used when 1) both variables arerandom variables, and 2) the end goal is simply to find a number that expresses the relation between the variables The regression term is used when 1) one of the variables is afixed variable, and 2) the end goal is use the measure of relation to predict values of the random variable based on values of the fixed variable

Univariate, bivariate and multivariate are the various types of data that are based on the number of variables. Variables mean the number of objects that are under consideration as a sample in an experiment. Usually there are three types of data sets. These are;UNIVARIATE DATA:Univariate data is used for the simplest form of analysis. It is the type of data in which analysis are made only based on one variable. For example, there are sixty students in class VII. If the variable marks obtained in math were the subject, then in that case analysis will be based on the number of subjects fall into defined categories of marks.BIVARIATE DATA:Bivariate data is used for little complex analysis than as compared with univariate data. Bivariate data is the data in which analysis are based on two variables per observation simultaneously.MULTIVARIATE DATA:Multivariate data is the data in which analysis are based on more than two variables per observation. Usually multivariate data is used for explanatory purposes.EXAMPLES;Univariate:Example: Pie charts of sales via territory, bar chart of support call volume by products, line charts of profit over several quarters - all of these descriptions involve one variable at a time. They are all considered part of an univariate analysis.Bivariate:Example: A presentation of two variables at a time as in a scatter plot. Any analysis that is performed on the scatter plot. Attempt to understand the relationship between sales volume and ad spending. These are all examples ofbivariateanalysis.A bivariate analysis may or may not have a target variable. If there is no target variable, then a complete bivariate analysis will involve studying n* (n-1)*0.5 total scatter plots, where n is the number of variables.Multivariate:When there are more than one target (or response) variables, any analysis involving studying the effect of predictors on the responses and their interactions is termedmultivariateanalysis.

Thegoodness of fitof astatistical modeldescribes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used instatistical hypothesis testing, e.g. totest fo r normalityofresiduals, to test whether two samples are drawn from identical distributions , or whether outcome frequencies follow a specified distribution