Video Notes: Regression Hypothesis Testing – Vocabulary

Vocabulary flashcards covering regression coefficients, standard errors, hypothesis testing concepts, and a sample example from the lecture notes.

Slope (β1)

The rate of change in the dependent variable y for a one-unit change in the independent variable x; in a sample regression, the slope is estimated as β̂1.

Intercept (β0)

The predicted value of y when x = 0; the constant term in the regression equation y = β0 + β1 x.

Beta hat (β̂)

The estimated regression coefficient(s) obtained from sample data (e.g., β̂0 and β̂1).

Beta hat one (β̂1)

The estimated slope coefficient representing the effect of x on y in the regression.

Standard error (SE) of β̂1

The standard deviation of the sampling distribution of β̂1; measures the precision of the estimated slope.

Test statistic for slope

The value (β̂1 − 0) / SE(β̂1) used to test whether the slope differs from zero.

Null hypothesis (H0)

There is no relationship between x and y (β1 = 0).

Alternative hypothesis (H1)

There is a relationship between x and y (β1 ≠ 0); typically two-sided in this context.

Two-sided test

A hypothesis test that checks for any departure from the null value in either direction (positive or negative).

Regression equation

y = β0 + β1 x; the linear model relating y to x plus an error term.

Difference in means

The difference between the average outcomes of two groups; used to test whether group means differ.

Sample size (n)

The number of observations in a sample; affects precision of estimates and standard errors.

Sampling distribution of β̂

The distribution of the estimated slope β̂ across repeated samples from the population.

Mean reservation wage

The average wage a worker would accept to take a job; used as the dependent variable in the notes' example.