Non-linear Regression
Non-linear Regression is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Architecture, Planning & Design sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.
🎯 What is it for?
Non-linear Regression automatically performs, in the background, all the assumption checks required for the relevant data type (normality, homogeneity of variance, etc.) and presents the results with a clear table and chart. Automatic interpretation to the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.
📌 When is it used?
- Statistical analysis of measurements in the Architecture, Planning & Design domain
- To produce APA 7-compatible result tables for academic publications
- Hypothesis testing and decision-making processes
- Undergraduate / master’s / PhD theses after the appropriate method has been selected
📐 Assumptions
- Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
- Independent observations — Observations must come from individuals independent of one another
- Sufficient sample size — The minimum n requirement for the analysis must be met
- Outlier check — Outliers must be detected and evaluated
If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.
🛠 How to do it in MerQur
Load the data. Select the sample file from File → Open. MerQur auto-detects column types.
Select the analysis. From the left side select Non-linear Regression.
Panel assignments (form fields in the program):
- Y Sutunu:
boy_m - X Sutunu:
yas_yil - Fonksiyon preset:
gompertz
Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).
▶ Run — click the button. Results are produced automatically as a table + chart.
📄 Export to Word. APA 7-formatted report with italic statistical symbols.
📊 Sample Dataset — Architecture, Planning & Design
ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.
🎬 Example File
This analysis is demonstrated on the following example dataset for Architecture, Planning & Design:
Peyzaj_Mimarligi/48_nonlinear_gompertz_growth.xlsx
🎬 Scenario
Tree height-by-age is not linear but an S-curve saturating toward a ceiling; we use the Gompertz growth model.
⚙️ Variable Selection
- Target: height_m
- Predictor: age_year
- Function: gompertz
Data Preview (First 5 Rows)
| tree_id | age_year | height_m | type |
|---|---|---|---|
| 1 | 38.9 | 23.22 | plane_tree |
| 2 | 9.9 | 9.67 | plane_tree |
| 3 | 28.4 | 22.42 | plane_tree |
| 4 | 18.8 | 15.4 | plane_tree |
| 5 | 16.6 | 13.78 | plane_tree |
n = 80 · Columns: tree_id, age_year, height_m, type
📈 MerQur Output
💬 Interpretation
We modelled how tree height changes with age with the Gompertz growth model. Tree growth is not linear: it is slow when young, then fast, finally saturating toward a ceiling (a — the asymptotic maximum height) — an asymmetric S-curve. Gompertz captures exactly this form; the fit is excellent (R2 = 0.99). The curve gives three parameters: the ceiling (a), growth rate (c) and inflection (b). These are compared across species/conditions to answer “which tree grows faster/taller”. Nonlinear regression is the basic tool of growth-age modelling in landscape/forest mensuration; a straight line would misrepresent the nature of tree growth.
⚠ Common Mistakes
- Misidentifying the data type (e.g., loading a categorical variable as numeric)
- Skipping assumption checks and going straight to the p-value
- Failing to report effect size — APA 7 requires both p and effect size
- Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
- Not switching to a non-parametric alternative when n is insufficient
📹 Video Walkthrough
Watch the video below for an end-to-end walkthrough of this analysis on a Architecture, Planning & Design file.
▶ Non-linear Regression — video walkthrough
This section is part of the İleri Düzey I — Gelişmiş Regresyon Modelleri video (8 analyses in one video). The link below jumps straight to 3:38, where this analysis begins. Narration is in Turkish.
🎓 Education Sciences · 🧪 Natural Sciences & Mathematics · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🏃 Sport Sciences · 🌾 Agriculture, Forestry & Aquatic
📚 If You Used This Analysis, Cite MerQur
If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
For BibTeX, RIS, EndNote and the English citation form: all citation formats →
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
- Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.