data science final

What does b1 represent in simple linear regression?,

The expected change in Y for a one-unit increase in X.

Why is extrapolation a problem in regression?

,Predictions made outside the observed range of X are unreliable.

Why does correlation not imply causation?,

Regression captures association not causality unless proper design/controls exist.

What does b0 represent in simple regression?,

The predicted value of Y when X equals zero.

Why is b0 sometimes meaningless?

X may never equal zero in the data so the intercept may have no real interpretation.

How do you make a prediction in simple linear regression?,

Use Y-hat = b0 + b1*X.

How do you test if X and Y have a significant linear relationship?,

Check the p-value for b1; if small, the relationship is significant.

How do you interpret a coefficient in multiple regression?,It is the expected change in Y from a one-unit increase in that predictor holding all others constant.

What are the units of a coefficient?,Units of Y divided by units of X.

How does adding or removing variables change coefficients?,It can change magnitude or sign due to omitted variable bias or controlling for confounders.

How do you make predictions from a multiple regression summary table?,Plug values into Y-hat = b0 + b1X1 + b2X2 + …

What is a parallel slopes model?,A model where categories have different intercepts but the same slope.

What does LOCATIONDowntown L.A. represent?,A dummy variable equal to 1 if the observation is in Downtown L.A., otherwise 0.

How do you identify the baseline category?,It is the category not shown in the regression output.

How do you interpret a categorical coefficient?,It is the expected difference from the baseline category.

What does an interaction term allow?,It allows different slopes depending on the level of another variable.

Why include an interaction between a numerical and categorical variable?,Because the effect of X on Y may differ across groups.

What does X:Category mean?,It is an interaction term between X and that category.

What is a numerical-numerical interaction?,When the effect of one predictor depends on the value of another numerical variable.

How do you make predictions from an interaction model?,Include all pieces: intercept, main effects, and interaction term.

What is the population regression model?,Y = beta0 + beta1X + error.

What is the estimated regression line?,Y-hat = b0 + b1X.

What is the difference between bj and betaj?,bj is the sample estimate while betaj is the true unknown parameter.

What does a p-value test for in regression?,Whether the coefficient is significantly different from zero.

What is BIC used for?,Model selection balancing fit and complexity.

What is variable selection?,Choosing which predictors to include to avoid overfitting.

What should ideal residuals look like?,Centered at zero with constant variance and no pattern.

How do you fix nonconstant variance?,Use a log transform of Y.

How do you fix nonlinear patterns in residuals?,Use polynomial terms like X-squared.

How do you check if a quadratic term is needed?,Look for curvature or test the p-value for X-squared.

What is leverage?,A point with an unusual X value.

What is an outlier?,A point with an unusual Y value.

What are studentized residuals used for?,Identifying outliers; large absolute values indicate potential issues.

What is overfitting?,When a model fits noise and performs poorly on new data.

What is the difference between training and test data?,Training fits the model; test evaluates generalization.

How do training and test error typically compare?,Test error is usually higher.

What is cross-validation?,Repeatedly splitting data into training and test to estimate test error.

What is MSE?,The mean squared error, average squared prediction error.

Why not use linear regression for classification?,Predictions can fall outside 0–1 and assumptions fail.

What are odds?,Probability of success divided by probability of failure.

How do you interpret a logistic regression coefficient?,A one-unit increase in X multiplies the odds by e^coefficient.

How do you predict probability in logistic regression?,Use p = exp(η) / (1 + exp(η)).

How do you predict odds in logistic regression?,Odds = exp(η).

How do odds change when X increases by 1?,Multiply the odds by e^coefficient.

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