The inferences and interpretations made in multiple linear regression are similar to those made in simple linear regression (in fact, the assumptions required for multiple linear regression are the same as those for simple linear regression except here they must hold for all predictors and not just the one used in simple linear regression) with four major differences

1. The t-tests for the slope coefficients are conditional tests. That is, the tests are analyzing the significant predictive value that a variable adds to the model when the other variables are already included in the model
2. The values of the slopes 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
3. The coefficient of determination, R², still measures the amount of variation in the response variable Y that is explained by all of the predictor variables in the model. However, where before the square root of R² could be interpreted as the correlation between X and Y, this result no longer holds true in multiple linear regression. Since we now have more than one X, this square root is no longer representative of a linear relationship between two variables which is what correlation measures.
4. The ANOVA F−test is a test that all of the slopes in the model are equal to zero (this is the null hypothesis, H₀, versus the alternative hypothesis, H₀ that the slopes are not all equal to zero; i.e. at least one slope does not equal zero. This test is called the F−test for Overall Significance. The hypotheses statements appear as follows:

F statistic [MSR is Mean Square Regression and MSE is Mean Square Error]:

\(F=\frac{MSR}{MSE}\)