Regression Analysis

Regression analysis is a statistical test or method used in estimation. It is used to evaluate the relationship between a dependent variable (outcome) to one or more independent variables (called predictors). The analysis does examine the impact each of the predictor variables have on the outcome variable in a way that model an equation that can be used to predict the outcome variables based on the values of the predictor variable. In simpler words, regression analysis and test are used when one wants to predict the value of a certain variable given the value of another variable or variables. For instance, a regression would be used to determine whether the performance in a school test can be predicted using the amount of time spent studying by the student. In this case, the regression analysis will examine the relationship between test score and study time and whether/ how study time impact test scores.

1. Regression analysis assumptions
   When conducting a regression analysis, the first part of the process is determining whether the available data can actually be used for a regression analysis. This means checking for various assumptions required for a regression analysis. These assumptions are;

• The variables involved should be measured as scale or continuous variables.
• There should be a linear relationship between the variables used in the regression test (can be checked using a scatter plot or correlation analysis)
• There should be no outliers in the variables (they distort the accuracy of the results)
• There should be independence of observations
• The data need to shown presence of homoscedasticity (this can eb examined using a scatter plot)
• The residual errors from the regression analysis should be nearly and approximately normally distributed.
1. Simple linear regression
   In a simple linear regression, the model estimates the relationship between a dependent variable (outcome) and one independent variable (outcome). It is generally expressed using the following linear equation.
Y= a + bX + ϵ
Where; Y is the dependent variables, X is the independent variable, a is the regression model intercept/ constant, b is the slope of the model and ϵ is an error term.
2. Multiple linear regression
   In a multiple linear regression, the model estimates the relationship between a dependent variable (outcome) and two or more independent variables (outcome variables). It is generally expressed using the following linear equation.
Y = a + bX1 + cX2 + dX3 + … zXn + ϵ
Where; Y is the dependent variables, X1, X2, X3, to Xn are the independent variable, a is the regression model intercept/ constant, b, c, d to z (z= last variable) are the slope of the model for each independent variable and ϵ is an error term.

3. Interpreting regression analysis
   In most statistical tools and software’s, a regression analysis has three components, a model summary, a goodness of fit analysis and the coefficient summary.
4. Model summary
   The model summary presents the regression model’s coefficient of determination (R2). It is a measure of the amount of variation in the dependent variable that can be explained by the independent variables.
5. Goodness of fit analysis
   The goodness of fit analysis also (ANOVA) or F test usually reports how well the overall regression fits the data. It is a measure of whether the overall regression model predicts the dependent variable significantly.
6. Coefficient summary
   The coefficient summary table in a regression analysis provides the slope/ beta (β) values for each independent variable. The slope of each independent variables represents the amount of change to the dependent variable caused by a 1 (one) unit change of the independent variable

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