A non-zero beta coefficients means that there is a significant relationship between the predictors (x) and the outcome variable (y). Once, the beta coefficients are calculated, a t-test is performed to check whether or not these coefficients are significantly different from zero. This method of determining the beta coefficients is technically called least squares regression or ordinary least squares (OLS) regression. Mathematically, the beta coefficients (b0 and b1) are determined so that the RSS is as minimal as possible. Since the mean error term is zero, the outcome variable y can be approximately estimated as follow: This is one the metrics used to evaluate the overall quality of the fitted regression model. The average variation of points around the fitted regression line is called the Residual Standard Error ( RSE). The sum of the squares of the residual errors are called the Residual Sum of Squares or RSS. Some of the points are above the blue curve and some are below it overall, the residual errors (e) have approximately mean zero.
e is the error term (also known as the residual errors), the part of y that can be explained by the regression model.b1 is the slope of the regression line.b0 is the intercept of the regression line that is the predicted value when x = 0.b0 and b1 are known as the regression beta coefficients or parameters:.
The mathematical formula of the linear regression can be written as y = b0 + b1*x + e, where:
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