https://statisticsbyjim.com/regression/interpret-r-squared-regression/

How To Interpret R-squared in Regression Analysis

Statistical measure of how close the data are to the fitted regression line.
r - correlation coefficient
r squared - coefficient of determination


University of Michigan - Ann Arbor

Method of fitting regression models in which the choice of predictive variables is carried out by an automatic procedure - adding or subtracting variables at each step depending on the results of predetermined tests 
Examples of tests that could be used:
1. F-tests
2. t-tests
3. R Squared

Stepwise Model Selection

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Used for the purpose of comparing statistical models
Test statistic must have an f-distribution under the null hypothesis.
Example of application: finding the model that best fits the population from which the data were sampled.

F-test

R Squared

The $$t$$-test is the most frequently used null hypothesis test for evaluating the statistical relationship between two means. There are three primary variations of this procedure—the one-sample $$t$$-test, the dependent-samples $$t$$-test, and the independent-samples $$t$$-test—each designed to accommodate slightly different research designs.

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