Coefficient Interpretation
The coefficient values are interpreted as to how much of a unit change in Y will occur for a unit increase in a particular X predictor variable, given that the other variables are held constant. For example, with DummyGender represented by 0 for Female and 1 for Male, if we held Quiz Average and Midterm constant, then for Males we would expect a 1.26 percent decrease (since slope is negative!) on the Final
t−Test for Individual Coefficients
A t−test on an individual coefficient is a test of its significance in the presence of all other explanatory variables. For instance, the slope test for Quiz Average is equal to zero versus not equal to zero given that Midterm and DummyGender are already present in the model, we have0.000 as the p-value for this test. If we use α of 0.05 to perform this test, with the p-value less than alpha we would reject the null hypothesis and decide that the slope for Quiz Average differs from zero. Our conclusion is that Quiz Average is a significant linear predictor of Final when Midterm and DummyGender are present in the model; we should include Quiz Average in a model containing the other two predictors
Notice that the p-values for the other two predictor variables is greater than our 0.05 level of significance. This indicates that neither variable is a significant linear predictor of Final when the other two variables are in the model. This does NOT imply that both variables should be dropped; only that when Quiz Average and Midterm are in the model, DummyGender is not offer significant predictive value, or if Quiz Average and DummyGender are in the model, Midterm does not provide significant predictive value.
F-Test of Overall Significance
From the ANOVA table output the p-value of 0.000 shows that we would reject the null hypothesis that all the slopes equal 0 and conclude that at least one of the slopes differs significantly from zero. HOWEVER, this does not tells us how many differ and/or which one(s) differ.
Coefficient of Determination R2
The R2 (i.e. R−sq in the output) of 37.3% is interpreted as "37.3 percent of the variation in Final scores are explained by Quiz Average, Midterm, and Gender." This is not a very high percentage as roughly 63% is left unexplained.
Since Sum of Squares Total (SST) = Sum of Squares Regression (SSR) + Sum of Squares Error (SSE), we calculate R2 as follows:
R2 = SSR / SST or by 1 − SSE / SST. Since R-squared is typically reported as a percentage, we then multiple this value by 100%.