Regression Analysis Concepts Quiz

Regression Analysis

• Regression analysis examines the relationship between variables.
• It builds on correlation analysis to understand how one variable affects another.
• Correlations examine the association between two variables, whilst regression analysis describes the characteristics of the relationship between these variables.
• Regression analysis includes the slope of the relationship and the point where the line intercepts the y-axis.
• Regression uses the same data as correlation, but describes the characteristics of the line of best fit.
• Regression allows the prediction of y-values based on x-values.
• Outcome variable is the variable being predicted.
• Predictor variable is the variable used to predict the outcome variable.
• Multiple regression analysis is used when more than one predictor variable is used.

Correlation

• Correlation analysis examines the association (or relationship) between two variables.
• Correlation coefficients are used to describe the strength and direction of this association.
• Coefficients, which can be positive or negative, assess the relationship between variables.
• Positive correlation: If variable X increases, variable Y also increases.
• Negative correlation: If variable X increases, variable Y decreases.
• The line of best fit describes the association (relationship).
• Magnitude reflects how well the line describes the association and explains how much variance of Y is explained by X (R²).
• Different types of correlation coefficients exist: Spearman coefficient, used for ordinal data, and Pearson correlation coefficient, used for continuous data.
• Correlation analysis produces a magnitude, If the observations are far from the line it means the magnitude will be small.
• If the observations are close to the line, the magnitude will be large.

Regression in SPSS

• To conduct regression analysis, select 'Analyze', 'Regression', and 'Linear...'.
• Move the dependent variable (outcome variable) to the 'Dependent' box.
• Move the independent variable (predictor variable) to the 'Independent(s)' box.
• Check confidence intervals in the 'Statistics' option.
• Interpreting the SPSS Output:
  • Model Summary: Measures how much variance of the outcome variable is explained by the predictor variable (R squared).
  • ANOVA: Assesses the significance of the model.
  • Coefficients: Shows the intercept and the slope of the regression equation. Indicates the significance of the slope (p-value).

Multiple Regression in SPSS

• Multiple regression analyses are used with multiple independent variables.
• SPSS output shows how each independent variable influences the dependent variable.
• The output shows the standardized coefficients that show the strength of the relationship (magnitude).
• The equation calculates the value of Z based on the variables X and Y, along with a constant. The equation is written as Z = aX + bY + c (Where a and b represent the regression coefficients).
• A higher R² reflects a stronger relationship between predictor (independent) variables and the outcome (dependent) variable.
• Multiple regression assesses the significance of the model and output shows the contribution and influence of each predictor variable to the dependent variable.