![]() The estimated regression equation can be written as follow: sales = 8.38 + 0.046*youtube. The intercept ( b0) is 8.38 and the coefficient of youtube variable is 0.046. The output above shows the estimate of the regression beta coefficients (column Estimate) and their significance levels (column Pr(>|t|). The R function lm() can be used to determine the beta coefficients of the linear model, as follow: model |t|) The regression equation can be written as sales = b0 + b1*youtube. In the following example, we’ll build a simple linear model to predict sales units based on the advertising budget spent on youtube. The simple linear regression is used to predict a continuous outcome variable (y) based on one single predictor variable (x). 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.
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