Regression analysis is the most widely used inferential statistical technique in Kenyan postgraduate research. At universities including Kenyatta University, the University of Nairobi, JKUAT, Mount Kenya University, Strathmore, Moi, Egerton, and Laikipia, the vast majority of Masters and PhD dissertations in Business, Education, Public Health, Social Sciences, Agriculture, and Economics include at least one form of regression analysis in Chapter 4. Yet regression is also one of the most frequently misapplied techniques in Kenyan postgraduate work — not because it is inherently difficult, but because students often run it without first testing whether their data meets its requirements, interpret its output without understanding what each statistic means, and report it without the level of detail that panel examiners require.
This guide covers the full range of regression techniques you are likely to encounter or need in a Kenyan postgraduate study — from the foundations of multiple OLS regression through hierarchical and stepwise approaches, binary logistic regression, and the increasingly common use of moderation and mediation analysis. For each technique, we explain when to use it, how to run it in SPSS, how to interpret every component of the output, and how to write it up in a way that satisfies both your supervisory panel and the academic standards your institution requires.
Table of Contents
- The Regression Landscape: Choosing the Right Model for Your Research Questions
- The Seven Assumptions of OLS Multiple Regression — and How to Test Them in SPSS
- Standard Multiple Regression: Running, Reading, and Reporting the Output
- Hierarchical Regression: Testing the Incremental Contribution of Variable Blocks
- Stepwise Regression: What It Is, When to Use It, and Why Panels Are Suspicious of It
- Logistic Regression: When Your Dependent Variable Is Categorical
- Moderation Analysis: Testing Whether a Third Variable Changes the Relationship
- Mediation Analysis: Testing the Mechanism Through Which an Effect Operates
- Reporting Regression Results in APA 7th Edition — Templates for Every Model Type
- Panel Questions on Regression Analysis — and How to Answer Each One
- How Tobit Research Consulting Can Help
1. The Regression Landscape: Choosing the Right Model for Your Research Questions
The first decision in regression analysis is not how to run the model — it is which model to run. This choice must be driven by two things: the nature of your dependent variable and the research question you are asking. A panel at any Kenyan university will ask why you chose your regression approach. “I used multiple regression because it is common” is not a defensible answer. “I used binary logistic regression because my dependent variable — loan default — is dichotomous (defaulted / did not default), which violates the continuous-variable requirement of OLS regression” is. Every model choice must be theoretically and methodologically justified.
| Regression Type | Use When | Dependent Variable Type | Typical Research Example in Kenya |
|---|---|---|---|
| Standard Multiple OLS Regression | You have one continuous dependent variable and two or more independent variables, and you want to assess their combined and individual effects | Continuous (interval or ratio scale) | Effect of strategic planning, employee training, and organisational culture on firm performance (measured on a composite Likert scale) |
| Hierarchical Multiple Regression | You want to test variables in a theoretically specified order — controlling for some predictors while examining the unique contribution of others | Continuous | Testing whether corporate governance practices predict financial performance, after controlling for firm size and age |
| Stepwise Regression | You are in exploratory mode with many predictors and limited theoretical basis for ordering them — you want SPSS to identify the strongest predictors statistically | Continuous | Identifying which of 12 supply chain factors most strongly predict delivery performance among Nairobi SMEs |
| Binary Logistic Regression | Your dependent variable has exactly two categories (yes/no, default/no default, adopted/not adopted) | Dichotomous (binary categorical) | Factors influencing whether smallholder farmers in Nakuru County adopted drought-resistant seed varieties |
| Multinomial Logistic Regression | Your dependent variable has three or more unordered categories | Nominal categorical with 3+ groups | Factors predicting which of three mobile payment platforms (M-Pesa, Airtel Money, Equity EazzyPay) a business owner uses as their primary transaction method |
| Moderation (Interaction) Analysis | You hypothesise that the relationship between X and Y differs depending on the level of a third variable (the moderator) | Continuous or categorical | Testing whether gender moderates the relationship between financial literacy and investment behaviour among Nairobi County residents |
| Mediation Analysis | You hypothesise that X affects Y through an intervening variable M — the mediator carries (partially or fully) the effect of X on Y | Continuous or categorical | Testing whether employee motivation mediates the relationship between transformational leadership and organisational performance |
2. The Seven Assumptions of OLS Multiple Regression — and How to Test Them in SPSS
OLS regression produces estimates that are unbiased, efficient, and consistent only when a set of underlying assumptions hold. These assumptions are not administrative formalities — they are the mathematical conditions under which the regression results mean what you say they mean. Running regression without testing assumptions and reporting violations is one of the most common methodological weaknesses panels identify in Kenyan postgraduate Chapter 4 analyses. Every assumption must be tested, the results must be reported, and any violations must be addressed before presenting your regression findings.
How to test: Create scatter plots of each independent variable against the dependent variable in SPSS via Graphs → Legacy Dialogs → Scatter/Dot → Simple Scatter. A roughly linear cloud of points indicates the assumption is met. Also inspect the partial regression plots produced alongside the main regression output (request these via the Plots dialog in the regression procedure). Systematic curves, S-shapes, or other non-linear patterns indicate the linearity assumption is violated — consider polynomial terms or variable transformation.
How to report: “Linearity was assessed through inspection of scatter plots and partial regression plots. The relationships between each independent variable and the dependent variable appeared approximately linear, satisfying this assumption.”
How to test: The Durbin-Watson statistic tests for first-order autocorrelation among residuals and is produced automatically in the SPSS regression Model Summary output when you request it via the Statistics dialog. A value between 1.5 and 2.5 confirms no significant autocorrelation. Values below 1.5 indicate positive autocorrelation (common in time-series data); values above 2.5 indicate negative autocorrelation. Autocorrelation inflates t-statistics by underestimating standard errors, leading to falsely significant findings.
How to report: “Independence of residuals was confirmed by the Durbin-Watson statistic (d = 1.94), which falls within the acceptable range of 1.5 to 2.5, indicating no significant first-order autocorrelation (Field, 2018).”
How to test: After running the regression, request that SPSS save the standardised residuals and standardised predicted values (via the Save dialog). Then create a scatter plot of standardised residuals (Y-axis) against standardised predicted values (X-axis). A random cloud of points with no systematic pattern confirms homoscedasticity. A funnel shape — where the spread of residuals increases or decreases as predicted values increase — indicates heteroscedasticity, which requires remediation (log transformation of the DV, or use of heteroscedasticity-robust standard errors in Stata).
How to report: “Homoscedasticity was assessed via a scatter plot of standardised residuals against standardised predicted values. The residuals displayed a random, roughly uniform scatter around zero with no discernible pattern, indicating that the homoscedasticity assumption was satisfied.”
How to test: This is not the same as requiring that each variable is normally distributed — it is the residuals (prediction errors) of the model that must be normal. In SPSS, request a Normal P-P Plot of regression standardised residuals via the Plots dialog in the regression procedure. If residuals are normally distributed, the points will fall approximately along the diagonal reference line. Also inspect the histogram of residuals. The Kolmogorov-Smirnov test can be applied to saved residuals for a formal test, though for large samples visual inspection is more informative.
How to report: “The normality of residuals was evaluated using a Normal P-P Plot and a histogram of standardised residuals. Both indicated that residuals were approximately normally distributed, satisfying this assumption.”
How to test: Multicollinearity is assessed using two statistics available in the SPSS Coefficients table when you tick Collinearity Diagnostics in the Statistics dialog: Tolerance (the proportion of variance in a predictor not explained by other predictors) and VIF (Variance Inflation Factor, equal to 1/Tolerance). Tolerance values below 0.10 and VIF values above 10 indicate problematic multicollinearity. Some researchers apply a stricter threshold of VIF > 5 for concern. A preliminary check can also be done via a Pearson correlation matrix: predictors correlating above r = .80 with each other suggest multicollinearity. Where multicollinearity is identified, consider removing one of the correlated variables, creating a composite index, or using ridge regression.
How to report: “Multicollinearity was assessed using Tolerance and Variance Inflation Factor (VIF) statistics. All Tolerance values exceeded .10 (range: .31–.82) and all VIF values were below 10 (range: 1.22–3.24), indicating no significant multicollinearity among the predictors (Hair et al., 2010).”
How to test: Request Cook’s Distance in the SPSS regression Save dialog. Cases with Cook’s Distance greater than 1.0 are considered influential and warrant investigation. Standardised residuals beyond ±3 are considered outliers. Also inspect leverage values (hat values): cases with leverage above 2(k+1)/n (where k = number of predictors and n = sample size) have high leverage. Review flagged cases to determine whether they represent genuine data points or data entry errors. If genuine, they should be retained but reported; if they represent errors, they should be corrected or excluded with justification.
How to report: “Outliers and influential points were assessed using Cook’s Distance and standardised residuals. No cases had Cook’s Distance greater than 1.0, and all standardised residuals fell within ±3, indicating no problematic outliers or influential cases.”
How to assess: OLS regression is sensitive to the ratio of observations to predictors. The minimum widely cited rule of thumb is 10 to 20 observations per predictor variable in the model. For example, a model with five independent variables requires at least 50 to 100 usable observations for reliable estimation. Some methodologists (including Green, 1991, as cited by Field, 2018) recommend a minimum sample size of N ≥ 50 + 8m (for testing overall model fit) and N ≥ 104 + m (for testing individual predictors), where m = number of independent variables. Where your sample size is a concern relative to the number of predictors, consider reducing the number of variables in the model or combining related predictors through factor analysis or index construction.
How to report: “The study included [n] usable observations and [k] predictor variables, yielding a cases-to-variables ratio of [n/k]:1, which exceeds the minimum threshold of 10:1 recommended by Field (2018) for reliable OLS estimation.”
3. Standard Multiple Regression: Running, Reading, and Reporting the Output
Standard multiple regression (the Enter method in SPSS) enters all specified independent variables into the model simultaneously and estimates their individual and combined contributions to variance in the dependent variable. It is the most common regression approach in Kenyan postgraduate research and the one whose output you must be able to interpret in its entirety.
Running Multiple Regression in SPSS
- Go to Analyze → Regression → Linear. Move your dependent variable into the Dependent box and all independent variables into the Independent(s) box.
- Under Method, ensure “Enter” is selected (this is the simultaneous entry method).
- Click Statistics: tick Estimates, Model fit, R squared change, Descriptives, Part and Partial correlations, and Collinearity diagnostics. Click Continue.
- Click Plots: move *ZRESID to the Y-axis and *ZPRED to the X-axis. Tick “Normal probability plot.” Click Continue.
- Click Save: tick Standardised residuals, Cook’s Distance, and Leverage values. Click Continue. Then click OK.
Reading the SPSS Multiple Regression Output: Table by Table
R is the multiple correlation coefficient — the correlation between your observed and model-predicted values of the dependent variable. R² (R-squared, the coefficient of determination) tells you the proportion of variance in the dependent variable explained by all the independent variables together. For example, R² = .42 means the independent variables collectively explain 42% of the variance in the dependent variable. Adjusted R² is a more conservative estimate that penalises for the number of predictors in the model — use this in your reporting, especially when comparing models or when your predictor-to-sample ratio is not large. Standard Error of the Estimate indicates how far the predicted values typically deviate from actual values in the original scale.
The ANOVA table tests whether the overall regression model explains significantly more variance than a model with no predictors (the intercept-only model). The F-statistic and its associated p-value (Sig.) in the ANOVA table answer the question: Is the regression model as a whole statistically significant? If p < .05, the model is significant and your predictors collectively explain a non-trivial amount of variance in Y. This is reported as: “The overall regression model was statistically significant, F(k, n–k–1) = [value], p = [value], R² = [value], adjusted R² = [value], indicating that the independent variables collectively accounted for [%] of the variance in [dependent variable].”
This is the table your entire regression discussion will be built from. For each predictor: B (unstandardised coefficient) tells you the change in Y for a one-unit increase in X, holding all other predictors constant — reported in the original measurement scale. Std. Error is the standard error of B. β (Beta, the standardised coefficient) tells you the change in Y (in standard deviation units) for a one-standard-deviation increase in X — allowing comparison of relative predictor strength across variables measured on different scales. t is the test statistic for the null hypothesis that B = 0. Sig. (p-value) tests whether the individual predictor makes a statistically significant unique contribution to explaining variance in Y. Tolerance and VIF assess multicollinearity for each predictor.
Model summary sentence: “Multiple regression analysis was conducted to examine the influence of credit risk management (CRM), interest rate policy (IRP), and loan monitoring practices (LMP) on loan repayment performance (LRP) among urban SACCOs in Nairobi County. The model was statistically significant, F(3, 196) = 47.23, p < .001, R² = .42, adjusted R² = .41, indicating that the three predictors collectively accounted for 42% of the variance in loan repayment performance.”
Individual predictor sentences: “Credit risk management was the strongest predictor (β = .48, t = 8.34, p < .001), followed by loan monitoring practices (β = .31, t = 5.12, p < .001). Interest rate policy did not significantly predict loan repayment performance (β = .07, t = 1.22, p = .224). Multicollinearity was not a concern, with all VIF values below 5 (range: 1.18–2.97) and Tolerance values above .10 (range: .34–.85).”
4. Hierarchical Regression: Testing the Incremental Contribution of Variable Blocks
Hierarchical regression — also called sequential or blocked regression — is a method of building a regression model in a theoretically specified order, entering predictors in blocks (steps) and assessing whether each new block adds a statistically significant increment of explained variance (ΔR²) beyond what was already explained by previous blocks. It is the appropriate approach when your research design involves control variables, when you want to test the unique contribution of a theoretically central variable after controlling for others, or when your conceptual framework specifies a specific causal ordering of predictors.
Hierarchical regression is especially common in Kenyan management, education, and public health dissertations where the researcher wants to: (1) enter demographic control variables (age, gender, experience, firm size) in Block 1 to account for their contribution before examining the main predictors; (2) enter the primary independent variables in Block 2 and test whether they explain variance beyond what demographics alone explain; and sometimes (3) enter interaction terms in Block 3 to test moderation effects. The key theoretical point — which panellists at KU, UoN, and JKUAT will probe — is that the order of entry must be driven by theory or logic, not convenience.
Interpreting the Hierarchical Regression Model Summary
The critical statistic in hierarchical regression is ΔR² (R-squared change) and its associated F-change significance test. ΔR² tells you how much additional variance in the dependent variable is explained by the new block of predictors, over and above the variance already explained by variables entered in earlier blocks. If adding Block 2 variables increases R² from .18 to .41, then ΔR² = .23: the Block 2 variables explain an additional 23% of variance in Y after controlling for the Block 1 variables.
Block 1 report: “In the first step, demographic control variables (gender, age, years of experience, and firm size) were entered. This model accounted for 9% of the variance in organisational performance, F(4, 195) = 4.83, p < .001, R² = .09, adjusted R² = .07.”
Block 2 report: “In the second step, the three strategic management variables (strategic planning, resource allocation, and performance monitoring) were entered. Adding these predictors significantly improved model fit, ΔR² = .27, F change(3, 192) = 28.41, p < .001, bringing the total explained variance to 36%, adjusted R² = .34. The beta coefficients indicated that strategic planning (β = .41, p < .001) and performance monitoring (β = .29, p = .002) were significant predictors of organisational performance after controlling for demographics, while resource allocation was not significant (β = .09, p = .183).”
5. Stepwise Regression: What It Is, When It Is Appropriate, and Why Panels Are Suspicious of It
Stepwise regression is a method in which SPSS itself determines which variables to include in the final regression model based on statistical criteria — specifically, whether a variable’s contribution is statistically significant at entry (Forward method) or whether removing it would significantly reduce model fit (Backward method). The combined Stepwise method enters variables forward and then removes those that become non-significant as new variables are added.
Why Kenyan university panels are sceptical of stepwise regression: Stepwise regression is an empirically driven method — the model is built by the data, not by the researcher’s theory. This is problematic in academic research because it can produce models that capitalise on chance patterns in the sample, do not replicate in new samples, and are difficult to justify theoretically. If you use stepwise regression in your dissertation, your panel will ask: “Why did you let SPSS decide which variables to include rather than your theoretical framework?” You must have a clear and defensible answer. Stepwise regression is most defensible when you are genuinely in an exploratory phase with no established theory to guide predictor selection, and when you acknowledge its limitations in your methodology section.
6. Logistic Regression: When Your Dependent Variable Is Categorical
When the dependent variable in your research is binary — a yes/no, presence/absence, adopted/not adopted, defaulted/not defaulted outcome — OLS regression is technically inappropriate because its assumptions require a continuous dependent variable and because OLS can produce predicted probabilities outside the 0–1 range. Binary logistic regression is the correct technique. It models the log-odds (logit) of the outcome as a linear function of the predictors and produces results expressed as odds ratios — a different and very specific form of interpretation that must be understood and reported correctly.
Key Output Components in Binary Logistic Regression (SPSS)
The Chi-square statistic in the Omnibus Tests table tests whether the model with predictors fits significantly better than the null model (intercept only). A significant result (p < .05) confirms that at least one predictor is meaningfully related to the outcome. Report as: “The overall logistic regression model was statistically significant, χ²(k) = [value], p = [value].”
Unlike OLS regression which has R², logistic regression uses the Hosmer-Lemeshow test to assess how well the model fits the data. Crucially, for this test you want a non-significant result (p > .05) — a significant Hosmer-Lemeshow result means the model does not fit the data well. Report as: “The Hosmer-Lemeshow test indicated adequate model fit, χ²(8) = [value], p = [value].” This is one of the most commonly misreported statistics in Kenyan logistic regression analyses — students often look for p < .05 everywhere and incorrectly flag a good-fitting model as a problem.
Because OLS R² is not computable for logistic regression, SPSS provides pseudo-R² measures including Cox & Snell R² and Nagelkerke R². Nagelkerke R² is the more commonly reported and is interpreted similarly to R² in OLS — it gives an approximate indication of the proportion of variance in the outcome explained by the model, though its calculation differs and it should always be labelled as a pseudo-R² measure. Report as: “The Nagelkerke R² was [value], indicating that the predictors explained approximately [%] of the variance in [outcome variable].”
The most important output for reporting individual predictor effects is the Exp(B) column, which gives the odds ratio for each predictor. An odds ratio of 1.0 means the predictor has no effect on the odds of the outcome. An odds ratio greater than 1.0 means that a one-unit increase in the predictor is associated with increased odds of the outcome; an odds ratio less than 1.0 means decreased odds. For example, Exp(B) = 2.34 for a predictor means that a one-unit increase in that predictor is associated with odds of the outcome that are 2.34 times higher (i.e., 134% higher), holding other predictors constant. The 95% confidence interval for Exp(B) is also reported — if the interval does not include 1.0, the odds ratio is statistically significant.
“Binary logistic regression was conducted to identify factors predicting SACCO loan default among youth borrowers (0 = no default, 1 = default). The overall model was statistically significant, χ²(5) = 62.4, p < .001, and the Hosmer-Lemeshow test confirmed adequate model fit, χ²(8) = 7.23, p = .512. The model explained 29% of the variance in loan default (Nagelkerke R² = .29) and correctly classified 78.4% of cases.”
“Financial literacy score was a significant negative predictor of loan default (B = −0.34, Exp(B) = 0.71, 95% CI [0.58, 0.87], p = .001), indicating that borrowers with higher financial literacy scores had 29% lower odds of defaulting on their loans. Loan amount was a significant positive predictor (B = 0.42, Exp(B) = 1.52, 95% CI [1.19, 1.94], p = .001), with each KES 10,000 increase in loan amount associated with 52% higher odds of default.”
7. Moderation Analysis: Testing Whether a Third Variable Changes the Relationship
Moderation analysis tests whether the strength or direction of the relationship between an independent variable (X) and a dependent variable (Y) differs depending on the level of a third variable — the moderator (W). A moderator variable changes when, for whom, or under what conditions X affects Y. In regression terms, moderation is tested by including an interaction term (the product of X and W) as an additional predictor in the model. If the interaction term is statistically significant, moderation is confirmed.
The moderation question: Does the effect of X on Y depend on W? For example: Does the effect of digital financial literacy on M-Pesa usage frequency depend on gender? Does the relationship between board independence and firm performance differ between family-owned and publicly listed companies? If your conceptual framework proposes a moderating variable, moderation analysis is the appropriate test.
Running Moderation Analysis in SPSS Using Hierarchical Regression
- Mean-centre your continuous predictors. Before creating the interaction term, subtract the mean from each continuous variable involved in the interaction. Mean-centring reduces multicollinearity between the main effects and the interaction term and improves the interpretability of the regression coefficients. Create new centred variables via Transform → Compute Variable:
X_centred = X - MEAN(X). - Create the interaction term. Compute a new variable that is the product of the centred X and centred W:
XW_interaction = X_centred * W_centred. For a categorical moderator (e.g., gender coded 0/1), centre only the continuous predictor and multiply by the dummy-coded moderator. - Run the hierarchical regression in three blocks. Block 1: control variables (if any). Block 2: main effects — X_centred and W_centred. Block 3: the interaction term XW_interaction.
- Interpret the result. If the interaction term in Block 3 is statistically significant (p < .05) and ΔR² for Block 3 is significant, moderation is confirmed. If the interaction term is not significant, the relationship between X and Y does not depend on W — moderation is not supported.
- Probe and visualise the interaction. A significant interaction should be followed by simple slopes analysis or graphing to show what the relationship between X and Y looks like at different levels of W (typically at low, medium, and high values of the moderator — often defined as ±1 SD from the mean). This visualisation is essential for a complete moderation analysis.
“To test the moderating role of gender on the relationship between financial literacy and investment behaviour, a hierarchical regression was conducted with mean-centred predictors. In Block 1, control variables were entered (F(2, 247) = 3.41, p = .034, R² = .027). In Block 2, the main effects of financial literacy (centred) and gender were entered (ΔR² = .18, F change(2, 245) = 27.22, p < .001). In Block 3, the interaction term (financial literacy × gender) was entered. The interaction term was statistically significant (β = .19, t = 3.02, p = .003), and the block accounted for a significant increment of variance (ΔR² = .03, F change(1, 244) = 9.12, p = .003), confirming that gender significantly moderated the relationship between financial literacy and investment behaviour.”
“Probing the interaction revealed that the positive relationship between financial literacy and investment behaviour was stronger for male respondents (b = 0.61, SE = 0.08, p < .001) than for female respondents (b = 0.28, SE = 0.09, p = .002).”
8. Mediation Analysis: Testing the Mechanism Through Which an Effect Operates
Mediation analysis tests whether the effect of an independent variable (X) on a dependent variable (Y) is transmitted — entirely or in part — through an intervening variable called the mediator (M). Where moderation asks when or for whom X affects Y, mediation asks how or why X affects Y. A classic mediation research question in Kenyan management research: Does transformational leadership (X) affect organisational performance (Y) directly, or does it work primarily through its effect on employee motivation (M) — with motivated employees then driving performance?
The modern standard for mediation analysis in postgraduate research is the PROCESS macro by Andrew Hayes, which is available as a free download for SPSS and uses bootstrapping to estimate the indirect effect and its confidence interval. The older Baron and Kenny (1986) four-step approach — once the standard in Kenyan university research — is now considered outdated because it relies on significance testing of individual paths rather than the indirect effect itself, and because it cannot produce confidence intervals for the indirect effect. Supervisors and panels at forward-looking Kenyan institutions increasingly expect the PROCESS approach.
The total effect (c) is the overall relationship between X and Y, ignoring M — the effect you would estimate from a simple regression of Y on X alone. The direct effect (c’) is the relationship between X and Y after controlling for M — the part of X’s effect on Y that does not go through the mediator. The indirect effect (a × b) is the product of the path from X to M (path a) and the path from M to Y (path b) — this is the mediated portion of the effect. Full mediation occurs when the indirect effect is significant and the direct effect (c’) becomes non-significant after M is included. Partial mediation occurs when both the direct and indirect effects remain significant, meaning X affects Y both directly and through M.
Mediation analysis is increasingly common in Kenyan Masters dissertations in the fields of Human Resource Management, Strategic Management, Education, and Public Health. Research questions involving mediating mechanisms — “Does employee engagement mediate the relationship between leadership style and retention?”; “Does perceived service quality mediate the relationship between staff competence and patient satisfaction?” — are particularly strong research designs because they address not just whether a relationship exists but through what process it operates. This adds theoretical depth that panels at KU Graduate School and UoN Faculty Postgraduate Committees specifically look for in PhD proposals and dissertations.
“Mediation analysis was conducted using the PROCESS macro (Hayes, 2018, Model 4) with 5,000 bootstrap samples and 95% bias-corrected confidence intervals to test whether employee motivation (M) mediated the relationship between transformational leadership (X) and organisational performance (Y).”
“The total effect of transformational leadership on organisational performance was significant (c = 0.54, SE = 0.08, p < .001). The effect of transformational leadership on employee motivation (path a) was also significant (a = 0.61, SE = 0.09, p < .001), as was the effect of employee motivation on organisational performance controlling for transformational leadership (path b = 0.38, SE = 0.07, p < .001). The direct effect of transformational leadership on performance after controlling for motivation was reduced and no longer statistically significant (c’ = 0.31, SE = 0.09, p = .072), suggesting full mediation. The indirect effect was 0.23 (SE = 0.06, 95% BC CI [0.12, 0.36]). Because the bootstrap confidence interval did not include zero, the indirect effect was statistically significant, confirming that employee motivation fully mediated the relationship between transformational leadership and organisational performance.”
9. Reporting Regression Results in APA 7th Edition — Summary Checklist
✅ Always Include in Regression Reporting
- State which type of regression was run and justify the choice
- Report that all OLS assumptions were tested — name the tests and state whether they were satisfied
- Report the F-statistic, degrees of freedom, p-value, R², and adjusted R² for the overall model
- Report B, SE, β (standardised), t, and p for every predictor in the Coefficients table
- Report VIF and Tolerance values as a multicollinearity check
- For hierarchical regression, report ΔR² and F change for each block
- For logistic regression, report χ², Hosmer-Lemeshow, Nagelkerke R², classification accuracy, and Exp(B) with 95% CI for each predictor
- For mediation, report total, direct, and indirect effects with bootstrap CIs
- Present results in a table for more than two predictors
❌ Common Regression Reporting Errors in Kenyan Dissertations
- Reporting only R² without adjusted R² — particularly problematic with small samples
- Omitting the F-statistic and model significance test entirely
- Reporting only p-values without coefficients — panels cannot evaluate effect size from p alone
- Describing a logistic regression Hosmer-Lemeshow p > .05 as “non-significant and therefore bad” — this is the reverse of the correct interpretation
- Interpreting logistic regression B coefficients as if they were OLS coefficients — they are log-odds, not unit effects
- Failing to report the Durbin-Watson statistic when independence of residuals was a relevant concern
- Not acknowledging violated assumptions — omitting a problem does not make it disappear; it makes you look like you did not test for it
- Concluding that a non-significant mediator means “no mediation” without testing the indirect effect
10. Panel Questions on Regression Analysis — and How to Answer Each One
| Panel Question | What They Are Testing | How to Prepare |
|---|---|---|
| “Why did you choose multiple regression for this study?” | Whether your model choice was driven by the nature of your variables and questions — not convention | State that you have one continuous dependent variable and multiple continuous/dummy-coded predictors, and that you wanted to assess their individual and collective contributions while controlling for confounds |
| “Did you test the assumptions of regression before running your model?” | Whether you understand that regression has conditions that must be met for results to be valid | Name all seven assumptions and state specifically how you tested each one in SPSS, what you found, and how you dealt with any violations |
| “What does R² mean in your study?” | Whether you can articulate what variance explained means in substantive terms | State the value and say: “This means that [X]% of the variation in [dependent variable] across the sampled [population] is accounted for by the combination of [list predictors], with the remaining [100−X]% attributable to variables not included in this model” |
| “How do you interpret the beta coefficient for your strongest predictor?” | Whether you can translate a statistical result into a meaningful substantive claim | For OLS: “A one-unit increase in [X] is associated with a [B]-unit increase in [Y], holding all other predictors in the model constant.” For standardised Beta: “[X] was the strongest predictor, with a one-standard-deviation increase in [X] associated with a [β]-standard-deviation increase in [Y].” |
| “What is multicollinearity and how did you check for it?” | Whether you understand a core regression problem and its consequences | Define it (high correlation between predictors inflates standard errors and makes coefficient estimates unstable), state that you used Tolerance and VIF statistics, give your values, and compare them to the accepted thresholds (Tolerance > .10, VIF < 10) |
| “Why did you use logistic regression instead of linear regression?” | Whether you understand the relationship between variable type and model choice | Explain that your dependent variable is binary (two categories), which violates OLS assumptions of continuous outcome and homoscedasticity, making logistic regression the methodologically appropriate choice |
| “What is an odds ratio and how do you interpret it?” | Whether you can explain the core output of logistic regression in plain terms | An odds ratio is the ratio of the probability of the outcome occurring to the probability of it not occurring, for a one-unit change in the predictor. An OR of 2.0 means the outcome is twice as likely; an OR of 0.5 means it is half as likely |
| “What is the difference between moderation and mediation?” | Whether you understand two commonly confused but fundamentally different analytical concepts | Moderation answers “under what conditions?” — a moderator changes the strength or direction of the X→Y relationship. Mediation answers “through what mechanism?” — a mediator is the intervening variable through which X affects Y |
| “How do you know your indirect effect in the mediation is significant?” | Whether you used a current, valid method for testing mediation | Reference the bootstrapped confidence interval from PROCESS (Hayes, 2018): if the 95% bias-corrected confidence interval for the indirect effect (a × b) does not include zero, the indirect effect is statistically significant |
Expert Regression Analysis Support for Kenyan Masters and PhD Students
At Tobit Research Consulting, our statisticians handle every aspect of advanced regression analysis — from assumption testing and model selection through running, interpreting, and writing up results in APA 7th edition format. We work with students at KU, UoN, JKUAT, MKU, Strathmore, Egerton, Moi, Laikipia, and all other Kenyan universities. Our regression analysis services include:
- Full OLS multiple regression with assumption testing (linearity, normality, homoscedasticity, independence, multicollinearity, outliers)
- Hierarchical (blocked) regression with ΔR² analysis and theoretically justified block ordering
- Stepwise regression with academic justification and limitation acknowledgement
- Binary and multinomial logistic regression with odds ratio tables, Hosmer-Lemeshow, and Nagelkerke R²
- Moderation (interaction) analysis with mean-centred predictors and interaction visualisation
- Mediation analysis using PROCESS macro with bootstrapped confidence intervals (Hayes, 2018)
- Complete Chapter 4 write-up with APA 7th edition tables, result paragraphs, and hypothesis outcome statements
- Analysis in SPSS, Stata, EViews, and R
- Panel preparation: coaching on how to answer examiner questions about your regression analysis
Whether you are just starting your Chapter 4 analysis or revising after a panel correction, we are here to ensure your regression results are technically sound, clearly reported, and fully defensible.
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This guide is part of Tobit Research Consulting’s Data Analysis Series for Kenyan postgraduate students. Key methodological sources include: Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.), SAGE; Hair, J.F. et al. (2010). Multivariate Data Analysis (7th ed.), Pearson; Hayes, A.F. (2018). Introduction to Mediation, Moderation, and Conditional Process Analysis (2nd ed.), Guilford Press; Baron, R.M. & Kenny, D.A. (1986). The moderator-mediator variable distinction in social psychological research, Journal of Personality and Social Psychology, 51(6), 1173–1182; Pallant, J. (2020). SPSS Survival Manual (7th ed.), McGraw-Hill; Green, S.B. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26(3), 499–510; and SPSS Statistics documentation, IBM Corporation.
