What This App Does
The Trendline and Correlation app helps you study how one measured variable changes with another. You can enter your own paired data, test four common mathematical models, compare their goodness of fit, inspect residuals, and read a guided interpretation of the results.
The app is designed as a workflow. Start with data, move to visualization, review the automated analysis, then compare the result cards to decide which model best represents the pattern in your measurements.
Minimum data requirementYou need at least 4 valid paired points before the app generates graphs and analysis.
Supported modelsLinear, quadratic, exponential, and logarithmic trendlines are all evaluated from the same dataset.
Automatic updatesGraphs, residuals, and analysis refresh automatically as soon as your valid data changes.
ExportsYou can export the graph as an image, download the dataset as CSV, and copy the active equation.
Fast Workflow
1. Name variablesSet the X and Y column headers to match your experiment or dataset.
2. Enter dataType paired values manually or load a noisy demo dataset to explore quickly.
3. Inspect plotsSwitch models in Visualization to compare equations, R2, Pearson's r, and residual structure.
4. Interpret resultsReview the four model cards in Results and decide which explanation best matches the science.
Press Esc or click outside the modal to close this guide at any time.
๐งญ Layout and Navigation
The app uses a left-side navigation rail on desktop and a slide-out menu on mobile. Each section is focused on one stage of analysis so the interface stays readable while you work.
- Explore introduces the purpose of the app and the core question behind correlation studies.
- Learn explains background concepts such as variables, correlation, model types, and R2.
- Data is where you name variables, enter measurements, and load sample datasets.
- Visualization renders the scatter plot, selected trendline, metadata pills, and residual analysis.
- Analyze summarizes the fit quality across all available models after 4 valid points are present.
- Results lets you inspect each model one by one with an equation, fit score, and interpretation.
๐งช Data Section Controls
The Data section is where you define your variables and manage the paired table that drives the rest of the app.
- Independent Variable is the X-axis quantity, usually the one you control or choose.
- Dependent Variable is the Y-axis quantity, the one that responds to changes in X.
- Apply Headers updates the table labels and the graph axis titles to match your chosen names.
- Add Row appends a new empty pair so you can keep typing without rebuilding the table.
- Clear All removes current entries and resets the table to a clean starting state.
๐ฆ Demo Data Buttons
The demo buttons load example datasets that imitate common experimental patterns. These samples include realistic noise so the app behaves more like a real laboratory or field dataset.
- Linear Data gives a near-straight-line relationship with small deviations around the line.
- Quadratic creates a curved, parabola-like trend that is useful when the response bends.
- Exponential shows accelerating growth or decay where equal X changes do not add equal Y changes.
- Random produces varied points to test how the app behaves when no strong pattern exists.
๐ Visualization Controls
The Visualization section becomes active once there are at least 4 valid X-Y pairs. Until then, the app shows a feedback panel reminding you to add more data.
- Trendline selector lets you switch between linear, quadratic, exponential, and logarithmic fits.
- Show Equation displays the fitted model formula below the plot.
- Show R2 displays the coefficient of determination for the currently selected trendline.
- Show Pearson r appears only for a linear trendline because Pearson's r is specifically a linear correlation measure.
- Residual Analysis is always shown below the scatter plot when a graph exists so you can inspect model error structure.
๐ค Analyze Section
The Analyze section runs automatically when there are at least 4 valid points. You do not need to click a separate analyze button.
- The app calculates each available model from the same cleaned dataset.
- It compares fit quality using R2 and summarizes which model currently performs best.
- It reports Pearson's r as an additional linear summary, but that value should not be treated as evidence for non-linear models.
- If your table contains blank or incomplete rows, only rows with both valid X and Y numbers are used.
๐งพ Results and Interpretation
The Results section is designed for comparison rather than forcing you to focus only on one best-fit answer. You can switch among all four model options and inspect their individual details.
- Each model button opens a dedicated result view with that model's equation and fit quality.
- The interpretation text explains what the model shape suggests physically or experimentally.
- Pearson interpretation is shown only for the linear model so the language stays statistically correct.
- The reflection questions are included to support classroom discussion, reporting, or lab write-ups.
๐พ Export and Utility Actions
The bottom action buttons in Results help you take the analysis outside the app for reports or presentations.
- Export Graph saves the current main chart as an image file.
- Download CSV exports the table using your current header labels.
- Copy Equation copies the equation for the currently selected result model to the clipboard.
Statistical Concepts Used By The App
Scatter Plot
Each point represents one paired observation. The overall shape of the cloud is the first clue about whether the relationship is straight, curved, rapidly increasing, or weak.
Trendline
A trendline is a fitted mathematical model. The app compares four model families because different physical processes create different curve shapes.
R2
R2 measures how much of the variation in Y is explained by the model. Values closer to 1 indicate the model follows the observed data more closely.
Residuals
Residuals are the differences between observed Y values and the model's predicted Y values. A good model often produces residuals scattered around zero without a strong visible pattern.
Pearson's r
Pearson's r describes the direction and strength of a linear relationship, from negative to positive. It should not be used as the main interpretation tool for quadratic, exponential, or logarithmic behavior.
Best Fit Versus Best Science
The highest R2 is useful, but it is not the whole story. Choose the model that fits well and also makes scientific sense for the process you are studying.
Good Practice When Using This Analyzer
- Use consistent measurement units and make sure every X value is paired with the correct Y value.
- Look at the scatter plot before trusting the numerical summary. Shape matters.
- Use residuals to check whether a model is systematically missing part of the pattern.
- Interpret Pearson's r only when the relationship is plausibly linear.
- Do not assume correlation proves causation. Experimental design and scientific reasoning still matter.
- When reporting results, include the equation, R2, a short interpretation, and a note about why the chosen model makes sense.
Citation Recommendation
If you use this web application in academic work:
Olarve, J. S. L. (2026).
Trendline and Correlation. i-Nano Research Facility, De La Salle University Manila. Retrieved from
https://www.inanolab.com/trendline.html
Disclaimer
This web application is provided for educational, instructional, and research-support purposes. While reasonable effort has been made to produce correct calculations and clear interpretations, the developer and affiliated institution do not guarantee that the outputs are free from error, complete for every dataset, or appropriate for every scientific, technical, or academic context.
Users are responsible for checking their input data, verifying results independently, and applying appropriate statistical judgment and domain expertise. The app should not be used as the sole basis for high-stakes decisions, formal certification, medical conclusions, safety-critical analysis, regulatory submissions, or claims of causation.
