Topcis

1. Inference for Linear Regression
   • The sample regression line can be used to estimate or test a claim about the population (true) regression line
   • The conditions are:
     • Linear: The actual relationship between x and y is linear
     • Independent: Individual observations are independent. If sampling without replacement, check the 10% condition
     • Normal: For any fixed value of x, the response y varies according to a normal distribution
     • Equal SD: The sd of y is the same for all values of x
     • Random: The data comes from a random sample or experiment
   • The slope b and intercept a of a sample regression line estimate the slope $\beta$ and intercept $\alpha$ of the population regression line
   • Confidence intervals and significance tests for the slope $\beta$ are based on a t distribution with $df=n-2$
   • The t-interval for the slope $\beta$ has a standard error of the slope $\frac{s}{s_x \sqrt{n-1}}$
   • The test statistic for a t-test for the slope is $\frac{b-\beta_0}{\textrm{SE}_b}$
     • $H_0$ is generally $\beta=0$
2. Transforming to Achieve Linearity
   • When you suspect that the relationship between two variables follows a power model of the form $y=ax^p$, you can either raise x to the power p or take the pth root of y.
   • logs can also be used to straighten a curved pattern by taking the log of one or both sides.

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