Multiple Regression Analysis: Inference

These flashcards cover essential vocabulary related to the key concepts discussed in the lecture on Multiple Regression Analysis and Inference.

OLS Estimator

Ordinary Least Squares estimator, used in linear regression to minimize the sum of the squares of the residuals.

Sampling Distribution

The probability distribution of a statistic obtained through a large number of samples drawn from a specific population.

Normality Assumption

The assumption that the error term in a regression model is normally distributed, which is crucial for inference.

Hypothesis Testing

A statistical method used to make decisions about the value of a parameter based on sample data.

t-test

A statistical test used to determine if there is a significant difference between the means of two groups.

p-value

The probability of observing test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is true.

Confidence Intervals

A range of values that is likely to contain the population parameter with a specified level of confidence.

Homoscedasticity

The property of having a constant variance across all levels of the independent variable(s).

Degrees of Freedom

The number of values in a calculation that are free to vary, which affects the critical values in hypothesis testing.

Gauss-Markov Theorem

States that the OLS estimators are the best linear unbiased estimators (BLUE) under the assumption of homoscedasticity.

Significance Level

The threshold at which the null hypothesis is rejected, often denoted by alpha (α).

One-sided Alternative

A hypothesis test that determines if a parameter is either greater than or less than a specified value, but not both.

Two-sided Alternative

A hypothesis test that determines if a parameter is different from a specified value, meaning it can be either greater or less.

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis.

Standard Error

An estimate of the standard deviation of the sampling distribution of a statistic, commonly used in hypothesis testing.

Residuals

The differences between observed and predicted values in a regression model.

Null Hypothesis (H0)

The default assumption that there is no effect or no difference; it is tested against an alternative hypothesis.

Alternative Hypothesis (H1)

The hypothesis that contrasts with the null hypothesis and represents the outcome that the test seeks to provide evidence for.

Minimum Variance Unbiased Estimator (MVUE)

An estimator that has the smallest variance among all unbiased estimators.

Linear Combination

An expression constructed from a set of terms by multiplying each term by a constant and adding the results together.

Statistical Insignificance

A result is considered statistically insignificant if the p-value is greater than the predetermined significance level.