Predicting Father’s Education Level from Mother’s Using Simple Linear Regression

 

Introduction

Educational attainment frequently reflects intergenerational and spousal educational alignment. Simple linear regression provides a formal statistical framework for examining the predictive relationship between two continuous variables. The present analysis uses General Social Survey (GSS) data to determine whether mother’s years of education (maeduc) significantly predict father’s years of education (paeduc). This paper reports the regression equation, proportion of variance explained, prediction for a 16-year maternal education level, graphical results, and interpretation of the fitted regression line. This study examined whether mother’s education predicts father’s education using simple linear regression. The model accounted for 40.8% of the variance in father’s education (R² = .408). The final regression equation and prediction are reported below using proper statistical notation.

Method

Simple linear regression was conducted in IBM SPSS Statistics using paeduc as the dependent variable and maeduc as the independent variable. Missing values were managed using listwise deletion. Of 1,419 working dataset cases, 907 cases contained complete information and were retained for analysis.

Assumption Testing

Several assumptions underline ordinary least squares regression. First, linearity assumes a straight-line relationship between predictor and outcome variables. Visual inspection of the scatterplot indicated a clear positive linear trend. Second, homoscedasticity requires constant variance of residuals across predictor levels. The residual distribution appeared evenly dispersed around the fitted line without systematic funneling patterns. Third, independence of observations assumes that each case is statistically independent. Because the GSS sampling framework collects individual-level responses, independence is reasonably satisfied. Finally, normality of residuals was assessed visually and did not reveal severe deviations. Collectively, these diagnostics support the appropriateness of linear regression modeling for this dataset.

Visual inspection of the scatterplot supported linearity. Residual dispersion indicated homoscedasticity. Independence of observations was satisfied based on individual-level survey sampling. Residuals approximated normal distribution patterns.

Limitations

Although the model explains a meaningful proportion of variance, regression analysis reflects association rather than causation. Self-reported parental education may introduce measurement error. Additional demographic variables may account for remaining unexplained variance.

Results

The regression model was statistically significant, F(1, 905) = 617.245, p < .001. The correlation between variables was R = 0.637, and the model explained R² = 0.405 of the variances in father’s education (Adjusted R² = 0.405). The standard error of the estimate was 3.166. Thus, mother’s education accounted for 40.5% of the total variance in father’s education. In this equation, 2.607 represents the intercept, which is the predicted value of father’s education when mother’s education equals zero years. The slope coefficient of 0.757 represents the expected increase in father’s years of education for every one additional year of mother’s education. This positive slope indicates a direct and positive relationship between the two variables.

The unstandardized regression equation was: Ŷ = 2.607 + 0.757X

In this equation, 2.607 represents the intercept, or the predicted value of father’s education when mother’s education equals zero years. The slope coefficient of 0.757 indicates that each additional year of mother’s education is associated with an average increase of 0.757 years in father’s education.

Table 1 - Regression Coefficients for Predicting Father’s Education from Mother’s Education

Prediction at 16 Years of Mother’s Education

For a mother with 16 years of education, the predicted father education level is: Ŷ = 2.607 + 0.757(16) = 14.72 years. This value is obtained by substituting X = 16 into the regression equation.

Scatterplot with Line of Best Fit

The scatterplot below displays the individual data points representing observed values of mother’s and father’s education levels. The solid line represents the Line of Best Fit, calculated using the least-squares method. The upward slope visually confirms the positive predictive relationship between the variables.

Figure 1 - Scatterplot of Father’s Education by Mother’s Education with Line of Best Fit

Table 2 – ANOVA

Table 3 – Model Summary

Discussion

 The scatterplot displays individual observations and the solid least-squares Line of Best Fit, which minimizes the sum of squared residuals between observed and predicted values. The positive slope (.757) indicates that each additional year of mother’s education corresponds to an average increase of approximately 0.76 years in father’s education. Points above the line represent cases where fathers exceeded predicted education levels, whereas points below the line represent lower-than-predicted values. The standardized coefficient (β = .637) reflects a strong positive relationship. With R² = .405, the effect size is substantial within social science research contexts. However, regression modeling reflects predictive association rather than causal inference. These results align with research on educational assortative mating and intergenerational educational continuity.

The findings demonstrate a strong positive predictive relationship between mother’s and father’s education levels. With R² = .405, the model explains a substantial portion of variance in father’s education. However, regression indicates association rather than causation. Other social, cohort, and structural variables likely account for the remaining unexplained variance. The analysis satisfies all assumptions for basic linear modeling and provides a clear predictive framework for interpreting educational pairing patterns.

Conclusion

The regression equation Ŷ = 2.607 + 0.757X explained 40.5% of variance in father’s education. When mother’s education was 16 years, predicted father’s education was 14.72 years. The statistical and graphical evidence demonstrates a strong positive predictive relationship between parental education levels.

 

 

References

Shatz, I. (2024). Assumption-checking rather than (just) testing: Visualization and effect size in regression diagnostics. Behavior Research Methods, 56(2), 826–845. https://doi.org/10.3758/s13428-023-02072-x

Zapf, A., Wiessner, C., & König, I. R. (2024). Regression analyses in observational studies. Deutsches Ärzteblatt International, 121(4), 128–134. https://doi.org/10.3238/arztebl.m2023.0278