Inference for Regression CHAPTER 15 Inference for Regression

Regression Inference USUALLY ABOUT TRUE SLOPE OF A LINEAR RELATIONSHIP. The mean response has a straight-line relationship with x. UNKNOWN PARAMETERS For intercept and slope

CONDITIONS! Observations are independent. True relationship is LINEAR. Standard deviation of the response about the true line is the same everywhere. Response varies Normally about the true regression line

Observations are Independent Observations on different individuals will often be independent. Repeated observations on the same individual would violate this condition.

True Relationship is Linear We cannot observe the true regression line but we can look at the sample’s relationship. Check the scatterplot to see if a linear relationship is present. ALSO CHECK THE RESIDUAL PLOT!

Standard Deviation of the response about the true line is the same everywhere Check the RESIDUAL PLOT. Make sure the spread about the axis is roughly the same everywhere.

Response varies Normally about the true regression line. Check the RESIDUALS! Make sure they follow a normal distribution. Make a histogram to see shape. You can also check the NPP! (Inference for regression is not very sensitive to a minor lack of Normality. Watch out for influential points)

CHECKING the RESIDUALS Remember the calculator can find the residuals for you!! (and make the residual plot) Enter your data points Run LinReg(a+bx) STAT PLOT For residual plot – scatterplot xlist = L1 , ylist=RESID For histogram – RESID as your xlist

Confidence Interval for the True Slope Standard Error of the least-squares slope USUALLY GIVEN!

df = n-2

Hypothesis Test! H0 : There is no true linear relationship  = 0 (This would also test a null hypothesis of there being no correlation between the two variables. Testing about correlation requires our observations to be from a random sample)

T-TEST!!

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