Khan Academy: Advanced Regression Flashcards
What is inference about slope in linear regression?
Using sample regression line statistics (slope and intercept) we estimate (infer) population regression line statistics.
Statistics are things we got from the sample and we’re trying to estimate true population parameters.
What are the inference conditions when using regression lines?
Abbreviated: LINER
L: Linear, meaning the actual relationship in the population between two variables is linear In a lot of cases we have to assume it’s true
I: Independence, Independent observations or adhering to the 10% rule
N: Normal, for any given X in the true population, the distribution Y’s that you expect is normal. Usually assumed true
E: Equal Variance, each of the normal distributions in the normal condition, should have the same spread
R: Random, sample data comes from a random process
How do we calculate the degree of freedom and the confidence interval for a regression slope?
Degree of freedom for regression slope is # of data points - 2
In the example there are 20 data points so we use the T table to find the confidence interval (of 95%)
How can we calculate t statistic for slope of regression line?
Much like before, to calculate t statistic we use this formula: (sample slope- Expected slope)/ sample SD (aka SE)
Because we assume Ho is true, Ho for slope of regression line is that it’s 0.
How can we use P-value to make conclusions in a test about the slope?
Basically, it’s as if the slope of the sample is the mean of sample
And the SE of the sample is the SE of the sample when the statistic we test for is the mean. The processes are the same:
Assuming Ho is true, finding t critical value and then the p-value
