STA Class 5: Regression Assumptions

We use regression for __________ to predict Y given a particular set of values.

prediction

Regression is used for __________ to understand the relationship between Y and a particular predictor after holding constant other predictors.

adjustment

In regression, we use it for __________ to infer something about the population relationships between Y and the predictors based on the sample.

inference

Y is a linear function of the X’s, which means we expect __ _____ ___ to represent the overall pattern of the data.

a linear function

A violation of linearity indicates a trend or _____ _____ in the residuals.

discernible pattern

The prediction errors (residuals) in regression should be __________ distributed to satisfy independence.

normally

A violation of independence would indicate __________ amongst observations.

correlation

For predictions to be accurate within ± 2*RSE, the residuals must be ____ ______.

normally distributed

In a normal Q-Q plot, if the dots line up in a straight line, __________ is satisfied.

Normality

The variance of Y should be the same for any value of X, known as __________.

homoscedasticity

A violation of equal variance would indicate a ____/______ shape in the plots.

fan/funnel

All four line assumptions in regression are required for __________.

inference

If only __________ is satisfied in regression, we cannot put reliable Confidence Intervals on predictions.

linearity

Influential observations in a regression context are outliers that have __________ leverage.

high

For an observation to be influential, it needs both a large __________ and high leverage.

residual

Leverage refers to when an observation has a very unusual __________ value.

x

Outliers are points with large residuals, meaning they are unusual __________ for the given x.

y

High leverage points can inflate ____-______ and provide a false sense of confidence in the model.

R-squared