Mohit Arora
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Interpretation of f & t- statistics
F-Statistics
Significance value of F Statistics basically indicates the fit of the Overall Linear regression model built..It tells us whether the model provides a better fit to the data than a model that has no independent variable (in which we take the mean as the only data predicting point) .This test is basically the Hypothesis test for relationship.
The F-test uses its p-value for overall significance has 2 hypothesis : . H0: there is no significant relationship i.e Slope of population is “0” . Ha: there is significant relationship .i.e slope of Population is not “0” We compare the p-value of the F-test with LOS(alpha) i.e Level of significance . If p value is less than alpha we can come to the conclusion that the regression model fits the data better as H0 will be rejected and Ha will be accepted. It also mean the model is adding significant predictability for variable y by x.
But if p-value of F-test is more than Level of significance we can conclude that our regression model is not significant . Now we have two models for which the assumptions are to be checked the name of the models are f23 & ft3
T-statistics
The interpretation of significance of the slope of the predictors based on significance value or p-value associated with the t statistics is comparing it with the level of Significance.
A t-test is always associated with a hypothesis testing.In the Regression analysis a t-test is done for testing the slope of the predictor whether it has any significant relation with the dependent variable or not .and this t-test has p value associated with it which is compared with the LOS(alpha) So this interpretation tells us whether slope of predictor has some linear relationship with response variable or not.
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The hypothesis associated with the testing of the slope is as follows for Simple Regression . Ho: Beta1=0 , there is no significant relationship of slopeof predictor . Ha: Beta1 != zero, there is significant relationship with slope of that predictor
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The hypothesis associated with the testing of the slope is as follows for multiple Regression . Ho: Beta1=0 , there is no significant relationship . Ha: at least one slope of one predictor is not equal to “zero”, there is significant relationship with slope of that predictor
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Significance value or p-value for our t-test is used for the above hypothesis testing for slope test . If we get to know that the p-value > LOS(alpha=0.05) then null hypothesis will be accepted and it will mean that slope of that variable has no significant effect on the dependent variable & if we p-value< LOS(alpha=0.05) ,we reject the null hypothesis meaning that there is significant relationship between them
For our Model “ft3” the value of Pr(>|t|) or p-value for our predictor total is 2e-16 & for quiz3 is 6.19e-14 .Both almost equal to “zero” and less than LOS meaning both the predictors have significant slope for our model ( p-value< LOS (alpha=0.05))
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For our Model “f23” the value of Pr(>|t|) or p-value for our predictor quiz2 is 00456 & for quiz3 is 0.00198 .Both less than LOS meaning both the predictors have significant slope for our model.( p-value< LOS (alpha=0.05))