PLCY460

dependent variable

the outcome of interest, usually denoted as Y

independent variable

a variable that possibly influences the value of the dependent variable

slope coefficient

the coefficient on an independent variable. It reflects how much the dependent variable increases when the independent variable increases by one. categorises relationship between X and Y

constant

the value that represents the intercept in a regression equation, indicating the dependent variable's expected value when all independent variables are zero - β0

error term

term associated with unmeasured factors in a regression model - greek letter epsilon

endogenous

An independent variable is endogenous if changes in it are related to factors in the error term.

exogenous

an independent var is exogenous if changes in it are unrelated to factors in the error term

correlation

measures the extent to which two variables are linearly related to each other. from -1 to 1, where correlations close to 0 indicate weak relationships between two variables.

randomisation

the process of determining the experimental value of the key independent variable based on a random process, so the treatment is exogenous.

internal validity

based on a process that is free from systematic error

external validity

research finding is externally valid when applied beyond the context in which analysis was conducted

standard deviation

describes how widely dispersed the values of observation are

replication

research that meets a replication standard can be duplicated based on the information provided at the time of publication

codebook

a file that describes sources for variables and any adjustments made

robust

statistical results that do not change when the model changes

Bivariate OLS

technique used to estimate a model with two variables: a dependent var and an independent var. Yi = β0 +β1Xi +i

fitted value

Value of Y predicted by estimated equation. also called predicted value

regression line

fitted line from a regression

residual

distance measured between the fitted value and observed value

sampling randomness

variation in estimates that is seen in a subset of an entire population. A sample with a dif. selection of people would observe a different estimated coefficient.

modeled randomness

variation attributable to inherent variation in the data-generation process. source of randomness when data is observed for an entire population

random variable

variable that takes values in a range and with the probabibilities defined by a distribution

distribution

range of possible values for a random variable and the assoc. relative probabilities for each value

continuous variable

variable that takes on any possible over some range

unbiased estimator

an estimator that produces estimates that are on average equal to the true value of the parameter of interest

bias

biased coefficient estimate will systematically be higher or lower than the true value

variance

a measure of how much a random variable varies

standard error

the square root of the variance - precision of a parameter estimate. Measures how much ˆ β1 will vary and large standard error indicates its distribution is very wide

variance of the regression

measures how well the model explains variation in the dependent variable

degrees of freedom

sample size minus number of parameters = N-K

Amount of info we have available to use in the estimation process

probability limit

value to which a distribution converges as the sample size gets very large

consistency

a consistent estimator is one for which the distribution of the estimate gets closer and closer to the true value as the sample size increases.

homoscedastic

error or random variable has the same variance for all observations

heteroscedastic

Variance of error term differs for some observations. Doesn’t cause OLS ˆ β1 estimates to be biased.

goodness of fit

how well a model fits the data

standard error of regression

Square root of variance of regression, and a measurement of goodness of fit

R²

Measure of the squared correlation of the fitted values and actual values

outliers

observations that are extremely different from those in the rest of the sample.

Hypothesis testing

a process assessing whether the observed data is or is not consistent with a claim of interest

null hypothesis

a hypothesis of no effect

Type 1 error

hypothesis testing error that occurs when we reject a null hypothesis that is in fact true. “False positive”

Type 2 error

a hypothesis testing error that occurs when we fail to reject a H^0 that is in fact false. “False negative

significance level

probability of committing a Type 1 error for a hypothesis test.

critical value

a value above which a βˆ1 would be so unlikely that we reject the null

p value

the probability of observing a coefficient as extreme as we actually observed if the null hypothesis were true.

power

Ability of our data to reject the null. A high-powered statistical test will reject the null with a very high probability when the null is false

substantive significance

reasonable change in the independent variable is associated with a meaningful change in the dependent variable, some statistically signficant is not substantively sig.

confidence interval

Defines range of true values that are consistent with observed coefficient estimate