Final answer:
Yes, removing the intercept term can lead to an inflated R² value, but this can sometimes be misleading. Excluding the intercept should be theoretically justified, and taking into account outliers is critical for improving your model.
Step-by-step explanation:
The scenario where removing the intercept from a multiple regression model increases the R² value from 0.3 to 0.8 is possible but misleading. Without the intercept, the model is constrained to pass through the origin, which can significantly inflate the R² value. This does not necessarily indicate a better fit; rather, it might be a statistical artifact. It's essential to consider the role of an intercept in a regression model and whether it's theoretically justifiable to exclude it. For example, if we look at the case of the sparrow hawks, removing an intercept could lead to nonsensical predictions, such as a baseline percentage of new sparrows at a value different from 100% when there are no returning birds.
When analyzing influential points like the outlier (65, 175), if the point is erroneous, removing it improves the correlation and the overall model. When the coefficient of determination, R², is 0.4397, it indicates that about 44% of the variation in the dependent variable is explained by the model. In the context of the example provided (ŷ = -173.51 + 4.83x), this means that approximately 44 percent of the variation in the final exam grades can be explained by the grades on the third exam.