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Ah, the stochastic error term and the residual are like happy little clouds in our painting. The stochastic error term represents the random variability in our data that we can't explain, while the residual is the difference between the observed value and the predicted value by our model. Both are important in understanding and improving our models, just like adding details to our beautiful landscape.
The F-statistic is a test on ratio of the sum of squares regression and the sum of squares error (divided by their degrees of freedom). If this ratio is large, then the regression dominates and the model fits well. If it is small, the regression model is poorly fitting.
y(i) = a + b1.x1(i) + b2.x2(i) + b3.x3(i) + ... + bk.xk(i) + e(i)where i = 1, 2, ... n are n observations ofthe independent variables x1, x2, ... xk,y is the dependent variablea and the b are regression parameters.The e are independent, identically distributed random variables (representing the error).
+ Linear regression is a simple statistical process and so is easy to carry out. + Some non-linear relationships can be converted to linear relationships using simple transformations. - The error structure may not be suitable for regression (independent, identically distributed). - The regression model used may not be appropriate or an important variable may have been omitted. - The residual error may be too large.
in general regression model the dependent variable is continuous and independent variable is discrete type. in genral regression model the variables are linearly related. in logistic regression model the response varaible must be categorical type. the relation ship between the response and explonatory variables is non-linear.