Stats Topic 6

Question 1

Simple linear regression

Answer 1

• is a statistical method used to describe the relationship between two continuous variables.
• It extends correlational analysis by allowing predictions of one variable (dependent variable, Y) based on another (independent variable, X)

Question 2

Simple Linear Regression key difference from correlation

Answer 2

While correlation shows the strength and direction of a relationship, regression quantifies how much Y changes when X changes.

Question 3

Regression Equation

Answer 3

• a (Intercept): The value of Y when X = 0.
• b (Slope): The amount Y changes for a one-unit increase in X.
• Example: If 𝑏 =−0.5, for each 1-hour increase in social media use, wellbeing decreases by 0.5 points.

Question 4

Regression Line

Answer 4

A real line (not imaginary like in correlation) that best fits the data and helps predict values.

Question 5

Key statistical measures

Answer 5

• R-value: Strength of the relationship between X and Y.
• R-Square (R²): Percentage of variance in Y explained by X.
• P-value: Determines statistical significance (typically p<0.05 means significant).

Question 6

Using Simple Linear Regression to Describe and Report Linear Relationships

Answer 6

• A numerical estimate of how much Y changes with X.
• A visual representation through a scatterplot with a regression line.
• Statistical insights into the strength, direction, and significance of the relationship.

Question 7

Drawing Conclusions from Simple Linear Regression

Answer 7

• Confidence intervals for the regression slope help assess precision.
• Causation warning: Regression shows association, not causation