Week 10 - Confidence Interval And Statistical Inference Flashcards
What is a confidence interval
It’s the point estimate +/- the margin of error
why do we do statistical Hypothesis Tests for linear regression coefficient
to test if β=0 in the population is likely
or in other words to test if a Null hypothesis is likely, and if an alternative hypothesis is likely (two sided test)
two sided test means testing is β ≠ 0 is likely in the population, meaning β can be positive and negative
what conclusion can we draw if we find that β=0 in the population is likely (meaning the confidence interval for β includes 0)
- we don’t reject the null
- β is statistically insignificant (β is NOT statistically distinguishable from 0)
both the null and alternative hypotheses are likely which gives us inconclusive evidence for either β=0 or β≠ 0 in the population
what conclusion can we draw if the confidence interval for β does NOT include 0
- we can reject the null
- β is statistically significant (statistically distinguishable from 0)
we can conclude that β=0 in the population is unlikely, but β≠0 in the population is likely
so if i say that β1 is statistically significant at the 5% level, we can say that at this level , the true relationship is likely to be…?
non zero β≠0
To conclude whether our statistical inference suggests that the relationship found in our sample linear regression may be due to chance alone, we conduct a (statistical) hypothesis test. For this (statistical) hypothesis test, we need to formulate only a null hypothesis. True or false? Correct it if it is false.
For a (statistical) hypothesis test, we need to formulate a null hypothesis and an alternative hypothesis.
In general, a null hypothesis is the statement that the population parameter of interest equals a certain value. An alternative hypothesis is the statement that the population parameter of interest takes values different from the value specified in the null hypothesis.
