Question

For each of these questions, your audience are persons that are not experts in statistics. Write with complete sentences and paragraphs. Cite any references that you use.

a. Imagine you fit a regression model to a dataset and find that R‐squared = 0.69. Is this a good regression model or not? If you cannot tell, what additional information do you need?  

b. Research and then explain the "regression fallacy". Provide at least one example.

Answer 1

Solution 1: R² or commonly known as R-squared is a performance metric that is actually used for evaluating the performance of a linear regression model. It basically determines what extent of variance is actually explained by the independent variable in a dependent variable. It is also known as the coefficient of determination for the same reason and it ranges from 0 to 100%, a value of 80% to 100% means that the independent variables present within the data are actually able to determine 80%-100% of variance that is present within the dependent variable present within the data and it is actually considered as a good score for a regression model. Now, coming to the question, you are getting a value of 69% as R-squared and it is not a good value for a regression model to achieve as it means that the independent variable is only able to predict the 69% of variance present within the dependent variable of the data. This is not at all a good performance score for a regression model.

Solution 2: An informal fallacy basically refers to the property by virtue of which this assumption can be made that a particular condition or a problem has actually returned to normal due to the preventive actions that were taken while it was abnormal. It is a fallacy as it fails to model the natural fluctuations occuring in natural phenomena. For example, a student starting to improve his/her performance once he/she was punished for their poor performance in the past examinations is one such fallacy in which the reason for performance is actually considered as the punishment of the teacher and not the hard work carried out by the student themselves.

Here's the solution to your question, please provide it a 100% rating. Thanks for asking and happy learning!!