Relationship between variables in Linear Regression
Linear regression is a mathematical equation used in statistics and machine learning. In a linear regression, an independent variable (usually called x) is being used to predict the dependent variable (usually called y). Linear equations are created by using an intercept, a slope, and one or more values of the independent variable as input.
This type of regression has three components:
-the intercept is the point where y=0;
-the slope describes the change in y with respect to the change in x; and
-one or more values of x are input that describe the direction of these changes.
In the equation, “change” can refer to either increases or decreases in x value. If the value of y is constant, then the equation reduces to a linear regression.
This is an example of a linear regression with two predictor variables and one dependent variable that shows how the explanatory power of each predictor variable changes when the dependent variable increases. The multiple correlation coefficient (R) indicates that the variables are related to each other – that is, there is some impact (correlation) between them.
The linear regression software that comes with SPSS provides several ways to create linear regressions which can be fully customized by professional statisticians — which might include things like fitting models using polynomials or cubic equations. Linear regression is a form of regression analysis. Linear regression can also be used for classification and if the dependent variable is categorical (such as a dichotomous dependent variable), logistic regression can be used.
If two numeric variables are significantly linearly connected, a correlation or basic linear regression analysis can be used to detect this. A correlation study reveals the degree and direction of a linear relationship between two variables, whereas a basic linear regression analysis estimates parameters in a linear equation that may be used to forecast the values of one variable based on the values of the other.
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