Bayesian Linear Regression

Regresyon · Bayesian

Bayesian Linear Regression is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Natural Sciences & Mathematics 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?

Bayesian 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 Natural Sciences & Mathematics 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 Bayesian Linear Regression.

Panel assignments (form fields in the program):

y_col: verim
x_cols: ['deney_id', 'reagent_A_mM', 'reagent_B_mM']
prior_precision: 0.01

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 — Natural Sciences & Mathematics

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 Natural Sciences & Mathematics:

Fen_Matematik/47_bayesian_reagent_yield.xlsx

🎬 Scenario

We model yield with two reagent concentrations in a Bayesian framework. To express uncertainty probabilistically, Bayesian regression is appropriate.

⚙️ Variable Selection

Dependent variable: yield
Predictor(s): reagent_A_mM
Predictor(s): reagent_B_mM

Data Preview (First 5 Rows)

experiment_id	reagent_A_mM	reagent_B_mM	yield
1.0	13.59	14.01	28.23
2.0	61.33	47.19	31.48
3.0	33.79	0.79	28.31
4.0	48.97	3.0	25.94
5.0	24.01	8.8	23.61

n = 100 · Columns: experiment_id, reagent_A_mM, reagent_B_mM, yield

📈 MerQur Output

BAYESIAN LINEAR REGRESSION RESULT ───────────────────────────────────────────── sigma^2 posterior mean = 9.39 (sd = 1.34) outcome: yield predictors: reagent_A_mM, reagent_B_mM coefficient posteriors + P(beta>0) reported

💬 Interpretation

We modeled yield with two reagent concentrations in a Bayesian framework: instead of point estimates we obtained each coefficient’s full posterior distribution and the “probability the effect is positive”. The Bayesian approach expresses uncertainty directly in probability language and can incorporate prior knowledge. In the lab, when the sample is small or prior-experiment information is valuable, it offers intuitive interpretations like “the effect is probably positive”.

⚠ 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 Natural Sciences & Mathematics file.

▶ Bayesian Linear Regression — video walkthrough

This section is part of the İleri Düzey II — Bayesçi, Mekânsal ve Yol Modelleri video (8 analyses in one video). The link below jumps straight to 4:44, where this analysis begins. Narration is in Turkish.

▶ Watch this analysis (4:44) 📺 All videos

🔀 The same analysis in other disciplines:
🎓 Education Sciences · 🏛 Architecture, Planning & Design · ⚙ 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 →

Sources:

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.