Branches of statistical
inference
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Taking a step back: branches of statistical inference
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Testing: A hypothesis test evaluating evidence against a particular value for a parameter.
Statistical methods:
• Hypothesis test for one proportion
• Randomization test to compare the values of a parameter across two groups
Estimation: Confidence interval estimating a parameter (gives a range of plausible values for a parameter)
Statistical method:
• Bootstrap confidence interval
Prediction: Predict value of a variable for an observation using a statistical model based on other variables.
Statistical methods:
• Simple linear regression (one predictor) – last week
• Multiple linear regression (multiple predictors) – this week
• Classification trees – next week
Using data to make predictions
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◦ Using apartment rental data for the past several years, can we predict the average
rental price for one-bedroom apartments in a given year?
◦ Using weather data, can we build a model to predict which days would be good days
to go to the beach?
Types of variables
The x variables are often called predictors, covariates, independent variables,
explanatory variables, inputs, or features.
The y variables is often called response, output, outcome, or dependent variable.
Types of models for prediction
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There are many types of models to choose from to make predictions. In this
course, we’ll look at two types of models:
◦ Linear regression: Useful when the response y is numerical
◦ Classification trees: Useful when the response y is categorical