Misconceptions in bivariate analysis problems: Guidelines for teaching first year undergraduate students

Background: Many students struggle with bivariate analysis, especially where digital tools are lacking and manual methods dominate learning.Aim: This study seeks to uncover the types of conceptual misunderstandings and procedural errors that first-year undergraduate students encounter when solving problems related to correlation and regression. It also aims to explore the underlying factors contributing to these difficulties.Method: A qualitative analysis was conducted using examination scripts from 120 first-year students enrolled in a Descriptive Statistics and Probability module at a South African open distance learning university. The students’ responses to questions on linear correlation, regression fitting, and prediction were examined through a combination of descriptive statistics and deductive content analysis.Results: The analysis revealed a wide range of misconceptions. While 80% of students could correctly identify variables, only 41.7% computed the correlation coefficient accurately, 36.7% fitted the regression line correctly, and 33.3% predicted y-values properly. Frequent errors included misusing formulas, confusing statistical terms, and failing to check the plausibility of results. Manual methods, in particular, increased the risk of computational and interpretative mistakes.Conclusion: The findings point to substantial gaps in both conceptual understanding and procedural fluency among novice statistics students. To support better learning outcomes, educators should prioritize teaching strategies that integrate conceptual clarity, multiple solution paths, and routine validation practices, especially in contexts where digital tools are not widely available.