Module 6

Linear Regression

A statistical method for predicting the value of a dependent variable based on one or more independent variables.

Correlation Coefficient

A measure that indicates the extent to which two variables fluctuate together.

Dependent Variable

The outcome variable that is predicted in a regression analysis, often referred to as variable Y.

Independent Variable

The predictor variable(s) used to predict the value of the dependent variable, often referred to as variable X.

Regression Line

A straight line that best fits the data in a scatter plot, minimizing the distance between the points and the line.

Residuals

The differences between the observed values and the values predicted by a regression model.

Least Squares Regression

A method that minimizes the sum of the squared residuals to find the best fitting line.

B0 (Beta 0)

The y-intercept of the regression line, indicating the predicted value of Y when X equals zero.

B1 (Beta 1)

The slope of the regression line, indicating the change in the predicted value of Y for each one-unit increase in X.

Simple Linear Regression

Regression analysis with one independent variable predicting a dependent variable.

Multiple Linear Regression

Regression analysis using two or more independent variables to predict a dependent variable.

Quantitative Variable

A variable that can be measured on a numerical scale, such as height or weight.

Qualitative Variable

A categorical variable that can be divided into groups, such as gender or color.

Binary Variable

A qualitative variable with only two categories, such as yes or no.

Hypothesis Testing

A statistical method that uses sample data to evaluate a hypothesis about a population parameter.

Null Hypothesis

The hypothesis stating that there is no effect or no relationship, often denoted as H0.

Alternative Hypothesis

The hypothesis that contradicts the null hypothesis, suggesting that there is an effect or relationship.

P Value

The probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.

Significance Level (Alpha)

The threshold for rejecting the null hypothesis, commonly set at 0.05.

R Square

A statistical measure representing the proportion of variance for the dependent variable that is explained by the independent variable(s).

Adjusted R Square

An adjusted version of R square that accounts for the number of predictors in a model.

Confidence Interval

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

Homoscedasticity

The assumption that the residuals of a regression model are equally distributed across all levels of the independent variables.

Multicollinearity

The presence of high correlations among independent variables in a regression model.

Dummy Variable

A binary variable created to represent categorical variables in regression analysis.

Type I Error

The error of rejecting the null hypothesis when it is actually true.

Type II Error

The error of not rejecting the null hypothesis when it is actually false.

Line of Best Fit

The regression line that minimizes the sum of the squares of the residuals.

Scatter Plot

A graphical representation of the relationship between two quantitative variables.

Causation vs. Correlation

Causation implies that one variable influences another, while correlation indicates that two variables are related without implying a direct cause.

Statistical Significance

A determination of whether the results of a statistical test are unlikely to have occurred under the null hypothesis.

Prediction

The use of a regression model to estimate unknown values of the dependent variable based on known values of the independent variable(s).

Standardized Coefficients

Coefficients that measure the effect of predictors in terms of standard deviations, allowing for direct comparison across variables.

ANOVA Table

A table showing the analysis of variance for testing whether there are significant differences among group means.

Durbin-Watson Test

A test used to detect the presence of autocorrelation in the residuals from a regression analysis.

Normal Distribution

A probability distribution where most values cluster around a central peak and the probabilities for values taper off symmetrically on both sides.

Kolmogorov-Smirnov Test

A nonparametric test used to determine if a sample comes from a specified distribution.

Shapiro-Wilk Test

A statistical test used to assess the normality of data.

Prediction Equation

An equation used to predict the dependent variable, formulated based on the regression coefficients.

Residual Plot

A scatter plot of residuals on the vertical axis and fitted values (or another variable) on the horizontal axis.

Coefficient of Determination

Another term for R square, indicating the proportion of variability in the dependent variable that is explained by the independent variable(s).

Research Question

A question that guides the direction of an analysis or study, often centered around the relationship between variables.

Statistical Model

A mathematical representation of observed data showcasing the relationship between variables, often used for prediction.

Regression Diagnostics

Tests and plots used to assess the validity and appropriateness of a regression model.

Independent Sample

Samples that are collected independently of each other, not affecting the outcome of each other.

Linear Relationship

A relationship between two variables that can be graphically represented as a straight line.

Parameter Estimates

The values of coefficients (like B0 and B1) obtained from a regression analysis, estimating the effects of independent variables on the dependent variable.

Model Fit

A measure of how well the regression model explains the data it is applied to.

Explanatory Variable

Another term for independent variable, indicating its role in explaining variations in the dependent variable.

Response Variable

Another term for dependent variable, indicating its role in responding to changes in independent variable(s).