# Regression analysis is a kind  of statistical method used to determine the relationship between dependent variables and independent variables. The technique can be used to investigate the strength of this relationship and forecast its future. Let’s understand regression with an example. Suppose you want to determine the growth of a company’s sales based on the current economic conditions. You have been provided with the most current sales data of the company, which points out the growth in sales to be about three times that of the economy. Using this information alone, you can easily forecast the future of the company sales.

There are different types of regression methods available for making predictions. The most common ones include:

Simple linear regression: This technique studies the relationship between one dependent variable and a single independent variable. It is based on the following fundamental assumptions:

• Both the dependent and independent variables demonstrate a linear relationship between the gradient and the point where they intercept.
• The independent variable is not a random value.
• The value of the error (also known as the residue) is zero
• The value of the error (residue) remains constant across all observations
• The value of the error (residue) is not correlated across observations
• The error (residue) values follow a normal distribution

Linear regression can be demonstrated using the following formula:

Y = a + bX + ϵ, where Y is the dependent variable, a the intercept, b the slope, X the independent (explanatory) variable, andϵ the error (residue)

Multiple linear regression: This method is almost similar to simple linear regression except that the multiple linear technique uses more than one variable.

It can be presented as the following:

Y = a + bX1 + cX+ dX3 + ϵ, where Y is the dependent variable, athe intercept, b, c, and d the slopes, X1, X2, X3 the independent variables, and ϵ the error (residue)

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### Regression Analysis Topics Covered By Our Experts

There are numerous topics administered under regression analysis, all of which require in-depth research for students to complete their assignmentseffectively. Some of the topics that have given students sleepless nights when it comes to preparing their regression analysis projects include:

• Logistic regression: This regression model is used to evaluate and explain data as well as the relationship between a single dependent variable and one or more ordinal, ratio level, nominal, or interval independent variables.
• Probit regression: This is a type of regression in which the dependent variable takes only two values. The purpose of this technique is to approximate the probability value that a certain observation with specific characteristics will assume  under one specific category.
• Nonlinear regression: In this type of regression analysis, the observational data is modeled by a specific function that uses a non-linear combination of the parameters of the model and depends on a single or many independent variables. The data is usually fitted by successive approximations.
• Ordinary least squares regression: This is a type of regression analysis method used to estimate unknown parameters in linear regression models.
• Nonparametric regression: This methodology is used to describe the trend between a certain response variable and a single or many predictions. The difference between nonparametric regression and other classical regression models is that this specific approach does not rely on assumptions pertaining to the nature of the relationships between variables.
• Robust regression:This technique was designed to overcome some of the problems faced by the traditional parametric and nonparametric methods. It is used to investigate the relationship between a dependent variable and a single or many independent variables.
• Stepwise regression: This methodology is used in fitting regression models whereby the choice of the predictive variables is determined using an automated procedure. In every step of the procedure, a variable is added or subtracted from a given set of independent variables based on a pre-specified criterion.
• Multivariate analysis (MVA):This statistical method involves observing and analyzing one outcome variable at a time. It is commonly used to address situations where more than one measurement is taken on an experiment.
• Heteroskedasticity: In statistics, Heteroskedasticity occurs when the standard error of a variable observed over a given period of time is non-constant. There are two forms of Heteroskedasticity; conditional, and unconditional. The conditional Heteroskedasticity is used to identify non-constant volatilityin instances where the future periods of low and high volatility cannot be determined. UnconditionalHeteroskedasticity on the other hand is used in instances where the future periods of low and high volatility can be determined.
• Multicollinearity: Also known as collinearity, multicollinearity is a phenomenon that occurs in multi regression models whereby one predictor variable is used to predict another variable. This often creates redundant information, affecting the results of a regression model.

Other topics covered under regression analysis include:

• Assessing overall fit
• Binary predictors
• Common misconceptions about data fitting
• Fitted regression
• Confidence intervals
• Significant predictor
• One predictor model
• Two predictor model
• Non-linearity and interaction tests

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