![]() ![]() For a typical alpha level of 0.05, a p-value lesser than 0.05 like we have in our output, means that we have evidence to reject the null hypothesis and accept the alternate hypothesis that the ms of the model is significantly greater than that of the residual. The Prob > F is the probability of obtaining the estimated F-statistics or greater (the p-value). ![]() From the table, we see that the mean sum of squares of the model is about 209.31 times greater than that of the residual. The null hypothesis is that the mean explainable variance is same as the mean unexplainable variance. To know how well the predictors (taken together as a group) reliably predicts the dependent variable, Stata conducts an hypothesis test using the F-statistics. The 3 and 6 simply represents the model’s and residual degrees of freedom respectively. It measures how the ratio of the explainable mean variance to the unexplainable mean variance is statistically greater than 1. The F-statistics is the ratio of the mean sum of squares ( ms) of the model to that of the residual. Since the data has 20 observations, Number of obs is equal to 20.į(3, 16) is the F-statistics of an ANOVA test run on the model. Number of obs is simply the number of observations used in the regression. It answers the question “how well does the model use the predictors to model the target variable?”. Model fit : This table summarizes the overall fit of the model. It is the sum of squares per unit degree of freedom (sum of squares divided by the degree of freedom).įrom the output, the mean sum of squares of the model, residual, and total are respectively 1883.16, 8.997, and 304.917.Ģ. It is given by:įrom the output, we see that the degrees of freedom of the model, and residuals are 3 and 16 respectively, while that of whole data (total) is 19. The residual degree of freedom is the difference between the total degree of freedom and the model degree of freedom. Where is the number of predictors (independent variables), the +1 represents the intercept. Since the model estimates number of variables (including the intercept), the degree of freedom in the ANOVA table is given by: ![]() The total degree of freedom is where is the number of observations in the data. Degree of freedom is the number of independent values that can vary. The model’s sum of squares (explainable variance) would thus be:įrom the output, we can see that out of a variation of 5793.43 in the dependent variable, 5649.48 is explainable by the model, while the remaining 143.95 is unexplainable.ĭf is the degree of freedom associated with a variance. Is the predicted value of the target variable for a given observation. This is the variation of the residual and is given by: On the other hand, SS residual is represents the unexplainable variation of the target variable (the variation of around its mean that our model cannot explain or capture). Is the value of the target variable for a given observation. Where represents the total variation that the target variable has. The total SS is the total variation of the target variable around its mean. The variance of the target variable comprises of that of the model (explainable variance) and that of the residuals (unexplainable variance). SS is short for “sum of squares” and it is used to represent variation.
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