Scope and Method Exam 2

how do we assess a country’s economic activity

  we often want to measure its gross domestic product

Predictors, X

variables that we use as the basis for our predictors

Outcome variables, Y

variables that we are trying to predict based on the values of the predictors

Predicted outcomes Y-hat

the values of Y we predict based on the fitted model that summarizes the relationship between X and Y in a dataset where we observe both X and Y for each observation and the observed values of X

Prediction error is E-hat

which measures how far our prediction is from the observed value; it is the difference between the observed outcome and the predicted outcome

The theoretical model for the true relationship between X and Y

Yi = α+βXi +ϵi

Yi

is the outcome for observation i

a

is the intercept coefficient

β

is the slope coefficient

Xi

is the observed value of the predictor for observation i

ϵi

is the error (residual) for observation i

estimate the relationship between X and Y

ˆ Yi = ˆα+ ˆβXi

ˆYi

is the predicted value of Y for observation i

ˆa

is the estimated intercept coefficient

ˆβ

is the estimated slope coefficient

Xi

is the observed value of the predictor for observation i

Intercept

Y-hat when X=0

Slope

change in Y-hat divided by change in X between two points on the line

lm()

fits a linear model requiring the formula of the type Y~X where Y identifies the outcome variable and X identifies the predictor

log()

computes a natural logarithm of the argument specified inside the parentheses

Log-log linear model

is a fitted linear model in which both Y and X have been log-transformed

R-squared also known as the coefficient of determination

ranges from 0-1 and measures the proportion of the variation of the outcome variable explained by the model, the higher the R-squared the better the model fits the data

confounding variable

is a variable that affects both (i) the likelihood of receiving treatment X and (iii) the outcome Y

Post-treatment variables

are variables affected by the treatment

Internal validity of a study

refers to the extent to which its causal conclusions are valid for the sample of observations in the study

The external validity of a study

  refers to the extent to which its causal conclusions can be generated