# How to solve regression analysis

Regression is a statistical method that is used to determine the relationship between one or more independent variables and dependent variables. In other words, it helps to assess the robustness of the relationship between two or more variables and thus by evaluating the following variable it would be using the ascertained value for modelling the relationship between those variables in the nearby future. Regression analysis consists of several variations, such as linear, multiple linear and nonlinear. The non-linear regression is widely used for more complex data types in which the dependent and the independent variables exhibit a nonlinear relationship. The simple linear model assumption is based on the six fundamental assumptions, are as, the independent and the dependent variable exhibits a linear relationship between the slope and the intercept, the independent variable is not random, the value of the residual is always zero, the value of the residual is fixed beyond all observations, there is no correlated value in contrast with the value of the residual over all observations, normal distribution is followed by the residual values.

In simple linear regression analysis, it is used to estimate the relationship between an independent variable and a dependent variable, the equation that can be expressed:

**Y= a + bX + e**

Where, Y= Dependent variable, X= Independent variable, a= Intercept, b= Slope, e= Residual (error) value.

The formula for calculating intercept that is represented as “a” and the formula for calculating slope, that is represented as “b” are as follows:

**a= (****Σy) (Σx^2) – (Σex) (Σxy)/ n(Σx^2) – (Σx) ^2**

**b= n (Σxy) – (Σx) (Σy)/ n(Σx^2) – (Σx) ^2**

In the multiple linear regression analysis model, it is known for its similarity with the simple linear model, with deviation that multiple independent variables are being used in the model as simple linear model only uses one. The mathematical equation formula that can be expressed:

**Y= a + bX****1**** + cX****2 ****+ dX****3**** + e**

Where, Y= Dependent variable, X1, X2, X3= Independent variable, a= Intercept,

b, c, d= Slopes, e= Residual (error) value

Multiple linear regression method applies the same order as the simple linear equation, as there are various independent variables in the multiple linear analysis, the model follows a mandatory condition, non-collinearity. The conditions shows that independent variables manifest a minimum correlation with each other. If somehow the independent variables have an elevated tally with each other, it would be very difficult to ascertain the true relationship among the dependent and independent variables. It is a method that is majorly used to find equations that relevant to the data, the linear equation and multiple linear equation is a type of regression analysis. The Y dependent variable helps to predict the future value if the X, which is an independent variable, changed a certain value. Whereas the value of “a” which represents the intercept, the value will always remain constant, even if the independent variables change. The term “b” represents the slope, it helps to indicate the variable and how much of it is dependent variable is upon the independent one.

**Regression Analysis in Finance:** Regression analysis is also applicable in finance; it comes with several applications in finance. It is elementary to the Capital Asset Pricing Model (CAPM). The analysis helps to forecast the returnable amount from the securities, that is based on various factor on the basis of the performance of the business. Regression analysis is used to evaluate the Beta for a stock. The slope function is used for the following calculation. The multiple regression analysis also helps to ascertain the changes or the assumptions of the business that might affect the revenue or the expenses of the business in the future. Regression tool is used Microsoft Excel, the following application helps to conduct the basic regression analysis.

Regression analysis is known for its flexibility and it is one of the most suitable method that can be useful in any set of conditions due to its malleability. As it is helpful in ascertaining a wide variety of relationships. It is useful is various aspects such as to calculate model multiple independent variables, to include continuous and categorical variables, using polynomial terms to model curvature and assessing interactions terms to evaluate the effect of one independent variable and its dependability on the value of other variables. Regression output is interpreted by certain things, firstly a model is needed, then in the model a person needs to go through the regression co efficient and the p values. If the p value is typically lower that is (<0.5) then the independent variable is statistically significant. The coefficient of the regression constitutes the change in average in the dependent variable that gives a one-unit change in the independent variable, which is represented as (IV), while administering the other IVs.

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