The explanation of simple and multiple linear regression starts from the notion of simple linear regression, is a method used to see the relationship between one independent variable (free) and its dependent variable (bound), the relationship is illustrated to have a straight line relationship. But in reality the relationship between the independent variable and the dependent variable is rarely that simple. Usually many factors or in this case we call many independent variables that determine or can affect the dependent variable. For such cases it will be solved by Multiple Linear Regression.

There are several ways that can be used to determine the regression line, namely:

• The free way (Weakness: there is no reliable standard method because everyone can be different)
• Connecting the two lowest and highest points (Weaknesses: This regression equation only uses two lowest and highest points and the other points are ignored and very dangerous if there are extreme values)
• Divide the data into two equal groups, then find the average of each (Advantage: We have included all points because we are looking for the average, and this is the best way than the previous 2 methods. Weaknesses: the average is influenced by the extreme values ​​of each each, both the extreme low value and the extreme high value, so that it does not describe the actual regression)
• Least square method

Basic concepts:

• At a certain value of X there will be many possible values ​​of Y (Y will be distributed following a certain probability function: Normal distribution) with an average value of E(Y) and a certain value of variance 2
• The average value of E(Y) is assumed to change systematically following the change in the value of X, which is depicted in the form of a linear line
• The value of variance 2 on each value of X will be the same
• The first thing to do in performing simple linear regression is to identify the model using a scatter plot (scatter diagram) which is useful for identifying the model relationship between X and Y variables. linear, then the linear regression model is feasible to use. After that, the estimation of the model parameters can be carried out.

Assumptions that must be met to perform regression analysis:

• Yi (Independent Variable) is a random variable/stochastic
• Xi (independent variable) is fixed/non stochastic (not a random variable)
• E(εi) = 0
• E(εi j) = E(εi2) = 2 for i = j (Homoscedastic)
• E(εi j) = 0 for i j (Non autocorrelation)
• i is a random variable that is independently and identically distributed following a normal distribution with a mean of 0 and a variance of 2
• The estimation method used in simple linear regression is the Least Square Method with the principle of minimizing i2

Least Squares estimator properties:

• If all the assumptions applied to the regression model are met, then according to a theorem (Gauss Markov theorem) the estimator will be BLUE (Best Linear Unbiased Estimator).
• Best = Best, has a minimum variance
• Linear = Linear in Random Variable Y
• Unbiased = Unbiased

This means that the estimator will be unbiased, linear and have a minimum variance among all other unbiased & linear estimators.
In simple linear regression, the coefficient of determination (r2) is defined as a measure of the ability of all independent variables to explain the dependent variance. Because the coefficient of determination (r2) is the square of the correlation coefficient (r) then the formula for the coefficient of determination (r2) is the same as the formula for the correlation coefficient (r) raised to the power of.

For example, if the correlation coefficient is 0.92, the coefficient of determination is 0.85, which is obtained from (0.92)2. This means that the ability of the independent variable to explain the dependent variable variants is 85% or there are still around 15% of the dependent variable variance explained by other factors.

Steps to make linear regression:

• First find out whether the two variables have a linear relationship or not
• First determine the independent variable (x) and the dependent variable (y)
• Create a scatter diagram from the data x and y
• From the scatter diagram, a description of the distribution pattern of x and y will be obtained. Does it form a linear relationship? If yes, then the regression model is simple linear regression, if not linear, the regression can be sought.
• Calculating a and b
• Calculate y^=a+bx, where y^= estimated value of y if x is substituted into the regression equation
• Draw a line y^=a+bx  on the x and y axes

Terms in linear regression:

• Correlation Coefficient (r) is a value that states whether or not the relationship is strong between 2 variables
• The standard error of the regression coefficient (E) is a measure of the accuracy of the regression coefficient in predicting the population value. The standard error is measured based on the square root of the deviation or variance of the sample regression coefficient with the population regression coefficient
• The regression coefficient of determination(r 2) is a. A value that indicates how much variation in Y (dependent variable) is reduced when one or more X (independent variable) is entered into the regression model. b. The amount of the contribution / share of the variable x to the variation or rise and fall of y.
• Constant (a) is the intersection of the regression line with the Y axis (estimate value if x = 0)
• The directional coefficient of linear regression (b) is a value that shows how much the value of Y (dependent variable) changes when X (independent variable) increases by one unit.