What are the differences between joint relative frequency and marginal relative frequency?
Joint Relative Frequency: Proportion of observations in a specific cell. | Marginal Relative Frequency: Proportion of observations in each category of a single variable.
What are the differences between correlation and causation?
Correlation: Measures the strength and direction of a linear relationship. | Causation: Indicates that one variable directly causes a change in another variable.
What are the differences between slope and y-intercept in a regression line?
Slope: The change in the predicted y-value for every one-unit increase in x. | Y-intercept: The predicted value of y when x is zero.
What are the differences between r and R²?
r: Correlation coefficient, measures the strength and direction of a linear relationship. | R²: Coefficient of determination, represents the proportion of variance in the dependent variable explained by the independent variable.
What is the definition of Bivariate Data?
Data involving two variables analyzed simultaneously to explore their relationship.
What is the definition of Joint Relative Frequency?
The proportion of observations that fall into a specific cell in a two-way table.
What is the definition of Marginal Relative Frequency?
The proportion of observations in each category of a single variable.
What is the definition of Conditional Relative Frequency?
The proportion of observations in a specific category of one variable, given a specific category of the other variable.
What is the definition of Correlation Coefficient (r)?
A measure of the strength and direction of a linear relationship between two quantitative variables, ranging from -1 to 1.
What is the definition of Coefficient of Determination (R²)?
The proportion of variation in the dependent variable that is predictable from the independent variable.
What are residuals?
The difference between the actual and predicted y-values in a regression analysis.
Explain the concept of a two-way table.
A table that organizes categorical data to show the relationships between two categorical variables. It displays frequencies for each combination of categories.
Explain the concept of a scatterplot.
A graph that displays the relationship between two quantitative variables. Each point on the scatterplot represents a pair of values for the two variables.
Explain the concept of linear regression.
A statistical method used to model the relationship between two variables by fitting a linear equation to the observed data. It aims to find the line of best fit that minimizes the sum of squared residuals.
Explain what a strong correlation indicates.
A strong correlation (close to -1 or 1) indicates that the points on a scatterplot cluster closely around a line. It suggests a strong linear relationship between the variables.
Explain the meaning of R² (Coefficient of Determination).
R² represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It indicates the goodness of fit of the regression model.
Explain why correlation does not imply causation.
Just because two variables are related doesn't mean one causes the other. There could be lurking variables influencing both, leading to a spurious correlation.
