linear regression and F-test - Cross Validated most recent 30 from stats.stackexchange.com 2019-07-18T22:17:55Z https://stats.stackexchange.com/feeds/question/364184 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/364184 2 linear regression and F-test CJD https://stats.stackexchange.com/users/218847 2018-08-27T15:56:34Z 2018-08-28T03:22:51Z <p>I have three data points. (110,1.95), (120, 3.03), and (130, 4.75) Y-values are observed deltas of means and X-values represent temperature settings. After plotting and running a linear regression I get an R\$^2\$ value 0.983 (Adjusted R\$^2\$ = 0.966). An F-statistic of 57.42 with a p-value of 0.08.</p> <p>Would the observation that as temperature increases so do the predicted Y-value, be valid? Am I confusing myself by looking at the F-test? With the p-value > 0.05? </p> <p>I have checked <a href="https://stats.stackexchange.com/questions/56881/whats-the-relationship-between-r2-and-f-test">Whats the relationship between \$R^2\$ and F-Test?</a></p> <p>and <a href="https://stats.stackexchange.com/questions/288000/if-the-f-test-is-insignificant-but-coefficients-are-significant-can-i-use-it">If the f-test is insignificant but coefficients are significant, can I use it?</a></p> <p>so if your comment is to refer me to these answers please add something to help me see the connection.</p> <p>In case it matters—For linear regression and OLS regression results I used Python scipy.stats.linregress(x,y) and statsmodels.formula.api</p> https://stats.stackexchange.com/questions/364184/-/364277#364277 1 Answer by Glen_b for linear regression and F-test Glen_b https://stats.stackexchange.com/users/805 2018-08-28T03:08:02Z 2018-08-28T03:22:51Z <p>You certainly see that there's an increasing slope in the three <em>sample</em> values. But what you probably want to consider is whether such a thing could have arisen by chance for unrelated variables in the presence of noisy data. </p> <p>(Without some random noise you'd know the exact relationship from just two values) </p> <p>Three data points whose deviation from no relationship is just due to noise could either be in increasing or decreasing order quite easily (for continuous data there are 6 equally-likely orders, one of which is purely increasing and one purely decreasing).</p> <p>On the basis of a naive test like that there's little reason to conclude that there's really anything but noise causing the appearance of a relationship. </p> <p>The p-value you got is simply based on a more sophisticated* version of that sort of thinking.</p> <p>You mention that your y-values are observed changes in means. If you have the original data you may be able to do more than you could with three points**, but you'd need to consider more about how the data were obtained (e.g. whether some model with a random-effects term is needed)</p> <p>* it's often more powerful in that it's more likely to pick up a relationship - if one is present in the underlying "population" of possible samples you might take - under the specific assumptions it makes. For example, it assumes a linear relationship, from which much of the increase in power arises, while my naive calculation only looked at the more general case of monotonicity. </p> <p>** for some reason there's a very common tendency to lose much of the original information by taking averages, while not even retaining the standard deviations of the averaged values</p>