import numpy as np
import pandas as pd
import statsmodels.formula.api as smf

df = pd.read_csv("dataset.csv")

mediator_formula = (
    "G2 ~ G1 + studytime + failures + absences + age + Medu"
    " + C(school) + C(sex) + C(address)"
)
total_formula = (
    "G3 ~ G1 + studytime + failures + absences + age + Medu"
    " + C(school) + C(sex) + C(address)"
)
outcome_formula = (
    "G3 ~ G1 + G2 + studytime + failures + absences + age + Medu"
    " + C(school) + C(sex) + C(address)"
)

m_a = smf.ols(mediator_formula, data=df).fit()
m_total = smf.ols(total_formula, data=df).fit()
m_outcome = smf.ols(outcome_formula, data=df).fit()

a = m_a.params["G1"]
b = m_outcome.params["G2"]
c = m_total.params["G1"]
c_prime = m_outcome.params["G1"]
indirect = a * b

rng = np.random.default_rng(42)
boot = []

for _ in range(1000):
    indices = rng.integers(0, len(df), len(df))
    sample = df.iloc[indices].copy()
    try:
        a_star = smf.ols(mediator_formula, data=sample).fit().params["G1"]
        b_star = smf.ols(outcome_formula, data=sample).fit().params["G2"]
        boot.append(a_star * b_star)
    except Exception:
        continue

lower, upper = np.percentile(boot, [2.5, 97.5])

print(a, b, c, c_prime, indirect)
print(lower, upper)

df <- read.csv("dataset.csv", stringsAsFactors = TRUE)

mediator_formula <- G2 ~ G1 + studytime + failures +
  absences + age + Medu + school + sex + address

total_formula <- G3 ~ G1 + studytime + failures +
  absences + age + Medu + school + sex + address

outcome_formula <- G3 ~ G1 + G2 + studytime + failures +
  absences + age + Medu + school + sex + address

m_a <- lm(mediator_formula, data = df)
m_total <- lm(total_formula, data = df)
m_outcome <- lm(outcome_formula, data = df)

a <- coef(m_a)[["G1"]]
b <- coef(m_outcome)[["G2"]]
c_total <- coef(m_total)[["G1"]]
c_prime <- coef(m_outcome)[["G1"]]
indirect <- a * b

set.seed(42)
boot_indirect <- replicate(1000, {
  ids <- sample(seq_len(nrow(df)), replace = TRUE)
  d <- df[ids, ]
  a_star <- coef(lm(mediator_formula, data = d))[["G1"]]
  b_star <- coef(lm(outcome_formula, data = d))[["G2"]]
  a_star * b_star
})

quantile(boot_indirect, c(.025, .975), na.rm = TRUE)

* Path a: mediator model.
REGRESSION
 /DEPENDENT G2
 /METHOD=ENTER G1 studytime failures age absences
   school_MS sex_M address_U higher_yes internet_yes
 /STATISTICS COEFF OUTS R ANOVA CI(95) COLLIN TOL.

* Total-effect model.
REGRESSION
 /DEPENDENT G3
 /METHOD=ENTER G1 studytime failures age absences
   school_MS sex_M address_U higher_yes internet_yes
 /STATISTICS COEFF OUTS R ANOVA CI(95) COLLIN TOL.

* Direct and mediator outcome model.
REGRESSION
 /DEPENDENT G3
 /METHOD=ENTER G1 G2 studytime failures age absences
   school_MS sex_M address_U higher_yes internet_yes
 /STATISTICS COEFF OUTS R ANOVA CI(95) COLLIN TOL
 /SAVE PRED RESID ZPRED ZRESID COOK LEVER.

OUTPUT SAVE
 /OUTFILE='D:\DATA ANALYSIS\H Regression Tests and Models\Mediated Regression\SPSS_Output\spv\Mediated-Regression.spv'.

OUTPUT EXPORT
 /CONTENTS EXPORT=ALL LAYERS=PRINTSETTING MODELVIEWS=PRINTSETTING
 /PDF DOCUMENTFILE='D:\DATA ANALYSIS\H Regression Tests and Models\Mediated Regression\SPSS_Output\pdf\Mediated-Regression-SPSS-Output.pdf'.

Indirect effect:
=Path_A_Cell*Path_B_Cell

Proportion mediated:
=Indirect_Effect_Cell/Total_Effect_Cell

Sobel standard error:
=SQRT((Path_B^2*SE_A^2)+(Path_A^2*SE_B^2))

Sobel z:
=Indirect_Effect/Sobel_SE

Bootstrap CI lower:
=PERCENTILE.INC(Bootstrap_Indirect_Range,0.025)

Bootstrap CI upper:
=PERCENTILE.INC(Bootstrap_Indirect_Range,0.975)

Decision:
=IF(OR(CI_Lower>0,CI_Upper<0),
 "Indirect effect supported",
 "Interval includes zero")

• A single observed-variable mediator can be estimated with ordinary regression equations.
• Path analysis generalizes the structure to several simultaneous observed pathways.
• Structural equation modeling adds latent variables, measurement models and global fit.

• Mediation asks how or through what variable an association operates.
• Moderation asks when, for whom or at what level an association changes.
• Moderated mediation combines the two questions through conditional indirect effects.

• The decomposition holds for the same linear sample and compatible covariate specification.
• The reported values sum to 0.908578 after rounding.
• Different links, scales or samples can break the simple equality.

• Adding G2 raises outcome R² from 0.6991 to 0.8524.
• The increase reflects the strong conditional predictive contribution of G2.
• The fit increase supports the pathway description but is not itself the indirect-effect test.

• Python and R independently resample rows and refit both equations.
• Their intervals overlap strongly despite different random draws.
• Independent replication reduces concern that one software implementation or seed drives the decision.

• Write p < .001 rather than p = .000.
• R may display scientific notation for extremely small probabilities.
• The confidence interval and effect magnitude remain more informative than a very small p-value alone.

• Large samples make formal tests sensitive to minor departures.
• Bounded integer grades are not expected to be perfectly normal.
• Focus on residual behavior, model form and bootstrap robustness.

• A causal indirect effect compares potential mediator and outcome values under different exposures.
• Regression products equal causal effects only under identification assumptions.
• Observational results should use cautious language unless those assumptions are defended.

• A variable caused by X that also affects M and Y creates a difficult post-treatment confounding problem.
• Simply controlling it can introduce bias.
• Study design and causal diagrams should guide adjustment.

• One assumption concerns exposure assignment given baseline covariates.
• A second concerns mediator assignment given exposure and covariates.
• These assumptions are strong and cannot be verified solely from the observed regression tables.

• When students are sampled within schools, resampling individual rows may understate uncertainty.
• A cluster bootstrap resamples schools and retains students within selected schools.
• The appropriate resampling unit follows the independent sampling unit.

• An alternative simulates a and b from their estimated joint distribution.
• The product is calculated in every simulation.
• Bootstrap intervals remain more direct when row-level data and computing resources are available.

• The joint-significance approach requires significant a and b paths.
• It has reasonable power but does not directly produce an interval for a×b.
• Use the bootstrap product interval as the main result.

• Direct and indirect effects can have opposite signs.
• The total effect may then be smaller than either component or close to zero.
• Proportion-mediated ratios are inappropriate in inconsistent mediation.

• All focal grades use the same 0–19 scale, making unstandardized coefficients especially interpretable.
• One G1 point predicts about 0.879 G2 points, and one G2 point predicts about 0.881 G3 points conditional on G1.
• The indirect product is expressed in G3 points per one G1 point.

• Heteroskedasticity-consistent standard errors can be applied to each regression equation.
• A bootstrap that refits the equations can also reflect some non-normal sampling behavior.
• Use both as sensitivity analyses when residual variance changes substantially.

• A linear product can miss threshold, ceiling or curved relationships.
• Polynomial or spline terms may be included with careful effect definition.
• The indirect effect can become conditional on the value of X.

• If G1 changes the effect of G2 on G3, the indirect effect varies with G1.
• The outcome equation must include the G1×G2 interaction.
• Report conditional indirect effects rather than one constant product.

• G1 precedes G2 and G2 precedes G3 in the school-year sequence.
• This temporal order is stronger than measuring all three simultaneously.
• Unmeasured academic ability, motivation and classroom factors can still confound the pathways.

• The direct coefficient 0.1337 represents the adjusted G1–G3 association not represented by the included G2 pathway.
• It can reflect other mechanisms, measurement overlap or omitted mediators.
• It should not be interpreted as a single known direct process.

• Path a converts a one-unit X difference into an expected M difference.
• Path b converts a one-unit M difference into an expected Y difference while X is controlled.
• Multiplying the two coefficients places the pathway on the Y scale per one-unit X difference.

• The product of two approximately normal coefficients is not generally normal.
• Percentile resampling estimates the empirical shape without relying on a symmetric Sobel interval.
• Report the resampling unit, number of successful samples and interval method.

• The direct effect remains positive and significant in this analysis.
• The term partial mediation describes coexistence of indirect and direct components.
• Avoid treating a non-significant direct effect as proof that no direct pathway exists.

• A positive and negative pathway can cancel in the total effect.
• Modern indirect-effect testing does not require a significant c path as a preliminary gate.
• Theory and bootstrap evidence should guide the pathway conclusion.

• The ratio is about 0.8528 in this analysis.
• It is most stable when direct and indirect effects have the same sign.
• It should not be interpreted as a literal causal percentage without stronger assumptions.

• Unstandardized effects retain grade-point units and satisfy the simple c = c′ + a×b decomposition.
• Standardized effects depend on variable variances and may not decompose identically under every convention.
• Use unstandardized bootstrap effects as the primary report.

• Include variables that confound focal paths rather than every available variable automatically.
• Post-treatment covariates can distort the mediated pathway.
• State why each covariate belongs in the mediator and outcome equations.

• A defensible sequence requires G1 before G2 before G3 in time.
• Temporal order strengthens interpretation but does not remove all confounding.
• Repeated measurement designs are stronger than one-time cross-sectional data.

• Measurement error in G2 can attenuate path b and distort the indirect effect.
• Reliability should be reported for latent or multi-item mediators.
• Structural equation modeling can represent measurement error explicitly.

• Parallel mediators estimate several indirect effects without ordering the mediators.
• Serial mediators impose an ordered chain.
• Shared mediator variance makes individual indirect effects conditional on the other mediators.

• A pathway may vary across levels of another variable.
• Conditional indirect effects require interaction terms in path a, path b or both.
• Report index-of-moderated-mediation intervals rather than separate subgroup significance claims.

• Binary or count variables require generalized models rather than ordinary Gaussian equations.
• Products from nonlinear models need scale-aware interpretation.
• Natural-effect or simulation approaches may be preferable for causal interpretation.

• Students nested within schools can violate independence.
• Within-school and between-school indirect effects are different quantities.
• Use multilevel mediation when the sampling and pathway structure are clustered.

• Measure X before M and M before Y when possible.
• Control prior levels of M and Y to distinguish change from stable differences.
• Cross-lagged or latent-change models can address more complex temporal processes.

• A positive bootstrap interval does not test the no-unmeasured-confounding assumptions.
• Sensitivity analysis can quantify how strong an omitted confounder would need to be.
• State this limitation explicitly in observational research.

• Each equation assumes a linear conditional mean unless nonlinear terms are added.
• Grade ceiling and floor effects may create curvature.
• Use partial-residual plots, polynomial terms or splines when justified.

• Constant residual variance supports classical standard errors in each equation.
• Bootstrap inference for a×b does not automatically fix every model misspecification.
• Review residual plots and robust-standard-error sensitivity.

• The strong a path implies substantial shared variation.
• Path b and c′ remain conditional coefficients in the presence of that overlap.
• Report VIF or tolerance and avoid interpreting c′ as a simple G1–G3 association.

• An observation can affect a, b or both and therefore have a multiplied effect on a×b.
• Inspect influence in both equations.
• Bootstrap distributions may reveal instability when influential cases are repeatedly selected.

• All equations should use the same analysis sample.
• Listwise deletion can change the target population and reduce precision.
• Multiple imputation should preserve the mediation structure and combine indirect effects appropriately.

• One thousand samples provide a useful worked analysis.
• Five thousand or more may stabilize tail percentiles for publication.
• More resamples reduce Monte Carlo error but do not correct model bias.

• This analysis reports percentile endpoints.
• Bias-corrected methods adjust for bias and acceleration but may behave differently in small samples.
• Name the interval method so results can be reproduced.

• The Sobel test uses a normal approximation for a×b.
• It can be conservative or inaccurate when the product distribution is asymmetric.
• Use it as a supplementary calculation rather than the primary decision.

• The outcome model R² increases strongly when G2 enters.
• High prediction fit does not by itself prove the proposed mechanism.
• Pathway claims require theory, timing and confounding control in addition to fit.

• The Python lower and upper limits are 0.6792 and 0.8715.
• The R limits are 0.6766 and 0.8643.
• The small difference is consistent with independent random resamples and both intervals support the same decision.

• SPSS adds higher and internet covariates, while Python and R use Medu.
• The rounded SPSS paths remain close: a ≈ 0.877, b ≈ 0.877, c ≈ 0.899 and c′ ≈ 0.130.
• Compare scientific conclusions rather than demanding identical numbers from different specifications.

• Python and R show identical fitted coefficients and R² but AIC/BIC differ by small constants.
• Software can define likelihood constants and parameter counts differently.
• Compare information criteria within one software implementation and identical data specification.

• The observed values satisfy 0.133732 + 0.774846 ≈ 0.908578.
• This arithmetic check helps identify coding or extraction errors.
• Rounding can create tiny discrepancies.

• Power depends on both a and b, their uncertainty and sample size.
• A weak link can make the product difficult to detect even when the other path is strong.
• Simulation-based planning is more informative than planning from one coefficient alone.

• Use ‘indirect association’ or ‘statistically supported indirect effect’ for observational designs.
• Use causal terms only with appropriate identification assumptions and design.
• Distinguish statistical mediation from a proven mechanism.

• Save formulas, covariate lists, factor references, seed and bootstrap indices.
• Export the complete path and model-fit tables.
• Regenerate charts and reports directly from code.