Statistical Learning: 3.2 Hypothesis Testing and Confidence Intervals

[@zarinskie]

NOTES: null hypothesis: b1 = 0 t-test: = estimated slope/its standard error t-distribution good for small samples p-value - the probability of getting a value of t p < 0.05 = significant t should be at least 2 it is good to compute confidence intervals and hypothesis test RSE = residual sum of squares (should be low) R^2 = fraction of variance completed 08.08.2024

[@عبدالرؤوف-ع9ض]

Why using a T-distribution instead of a Gaussian one?

[@goatfishplays]

I assume it is because in practice we will not know the true population standard deviation as we are using sampled data from real world, as such we must use the t-distribution which will account for how much data we do have(but then again I forgot everything from my statistics class so don't take my word for it lol)

[@anassheashaey]

This answer is true. you don't have the population standard deviation, so the best you could do is to use the sample standard deviation instead. but you do that your distribution doesn't follow a normal distribution anymore but follows a t distribution. that doesn't really make a big difference if you have a sufficiently large sample size, say over 30, because at these sample sizes , your distribution looks pretty much like the normal distribution ​@goatfishplays