Regression Analysis
Regression models the linear relationship between a response and one or more predictors. This tutorial explains what a regression coefficient means, how RAISINS reports fit and significance, how to check every assumption, and how to run the whole analysis code-free… Read more …
Regression is the workhorse of applied statistics: it models how a response variable changes with one or more predictors, letting you both predict outcomes and isolate the unique effect of each factor. This tutorial starts from first principles, what a regression line really estimates, how to read a coefficient as a partial effect, and what R², the F-test and the p-values are actually telling you. It then walks through the complete workflow in RAISINS: preparing data, choosing the response and predictors, optional advanced model options (transformations, polynomial and interaction terms, stepwise selection), the coefficient/model-fit/ANOVA tables, the full battery of assumption checks and influence diagnostics, publication-ready plots, automatic interpretation, and the RA-One AI assistant, all without writing a single line of code.
1 What is regression?
Suppose you record, across 200 plots, the crop yield each plot produced and, alongside it, how much water it received, the fertiliser dose, the weed pressure and the harvest month. You suspect these factors drive yield, but by how much, and which ones actually matter once the others are accounted for?
A regression answers exactly this. It fits the straight line (or, with several predictors, the flat “plane”) that comes closest to all your data points, and from that fitted line it hands you two things at once:
- Prediction, given a plot’s irrigation, fertiliser and so on, what yield would we expect?
- Effect estimation, how much does yield change for a one-unit change in each predictor, holding the others fixed?
The line is chosen by Ordinary Least Squares (OLS): of all possible lines, RAISINS picks the one that makes the total of the squared vertical gaps between the points and the line as small as possible. Those gaps are the residuals, the part of the response the model could not explain.
Regression draws the best-fitting line through your data and reports, for each predictor, how strongly it moves the response, and whether that movement is larger than what random noise alone would produce.
1.1 Reading a coefficient
Every predictor gets a number, its coefficient (β). In a multiple regression this is a partial effect: the expected change in the response for a one-unit increase in that predictor while every other predictor is held constant. A positive β means the response rises with the predictor; a negative β means it falls. The intercept (β₀) is the model’s baseline, the predicted response when all predictors sit at zero (or, for categories, at their reference level).
\[Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_k X_k + \varepsilon\]
1.2 The p-value, in plain language
For each coefficient RAISINS runs a test of the claim “this predictor has no effect” (β = 0) and reports a p-value, which answers:
If this predictor truly had no effect, how often would I see a coefficient this far from zero purely by chance?
A p-value of 0.40 means “quite often, nothing to see here.” A p-value below 0.001 means “almost never, this predictor is doing real work.” Researchers conventionally treat p < 0.05 as evidence that a predictor genuinely matters.
A p-value is not the probability that the coefficient is correct, nor the size of the effect. A predictor can be highly significant yet tiny, or large yet non-significant in a small dataset. Always read the coefficient (the size) and its confidence interval next to the p-value, not the p-value alone.
1.3 The null and alternative hypotheses
Regression tests each coefficient against a starting assumption that nothing is happening:
- H₀ : βⱼ = 0, predictor j has no effect on the response.
- H₁ : βⱼ ≠ 0, predictor j does affect the response.
A small p-value makes H₀ hard to believe, so you reject it and call the predictor significant. A large p-value means the data are compatible with “no effect,” so you fail to reject H₀, which is not the same as proving the predictor is useless, only that this dataset did not show its effect.
A little history: from "regression to the mean" to least squares
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The word regression comes from Sir Francis Galton, who in the 1880s noticed that the children of exceptionally tall parents tended to be tall, but less tall than their parents, heights “regressed” toward the population average. Karl Pearson then turned Galton’s biological observation into the mathematics of correlation and the least-squares line we still use, while the least-squares principle itself traces back to Legendre and Gauss at the start of the nineteenth century. Ronald A. Fisher later fused regression with the analysis of variance, giving the F-test and ANOVA table that sit beside every modern regression output. From these roots, regression spread into agriculture, medicine, economics and engineering as the standard tool both for prediction and for isolating the effect of one factor from many.
2 Simple or multiple regression?
RAISINS fits both, and the only thing that changes is how many predictors you select.
| Model | Predictors | Typical question |
|---|---|---|
| Simple Linear Regression (SLR) | One predictor (X) | How does yield change with irrigation alone? |
| Multiple Linear Regression (MLR) | Two or more predictors | What is the effect of irrigation after accounting for fertiliser, weeds and harvest month? |
The power of MLR is that each coefficient is a partial effect: it separates the contribution of one predictor from all the others. But that power comes with one predictor-specific hazard: multicollinearity. When two predictors carry nearly the same information (say, two highly correlated soil measures), the model cannot decide which deserves the credit, and their individual coefficients become unstable, even though the model’s overall predictions stay fine. RAISINS flags this automatically with the Variance Inflation Factor (VIF/GVIF) in the Assumptions tab.
A predictor need not be numeric. A factor such as harvest (april, july, june, march in our dataset) is entered as plain text labels; RAISINS automatically dummy-codes it, choosing one level as the reference and reporting each remaining level as a contrast against it. The reference is the alphabetically first level, here april, so the coefficient for “july” reads as the difference in yield between a july harvest and an april harvest, holding everything else constant. There is no coefficient for april itself: it is absorbed into the intercept.
3 Beyond the straight line: advanced model options
A plain straight-line fit is not always the right model. RAISINS keeps the default simple, but tucks four powerful extensions behind an optional Enable advanced model options switch on the Analysis sidebar (Figure 1). When the switch is off, a standard model is fitted; when it is on, you can add any combination of the following. The intro paragraph on the results page always states which options were actually applied, so your write-up stays honest.
| Option | What it does | When to reach for it |
|---|---|---|
| Dependent-variable transformation | Fits the model on a transformed Y, log, log10, √, inverse (1/Y) or square (Y²) | Residuals are skewed, or the spread grows with the fitted value (heteroscedasticity) |
| Polynomial terms | Adds X², X³ … for chosen numeric predictors (degree 2 - 4) | The relationship curves rather than running straight |
| Two-way interactions | Adds Xᵢ·Xⱼ terms | The effect of one predictor depends on the level of another |
| Stepwise selection (AIC) | Automatically keeps/drops terms to minimise AIC (forward, backward, or both) | You have many candidate predictors and want a parsimonious model |
If you transform Y, RAISINS notes it on every table and plot, and, where it can, back-transforms fitted values to the original scale so the numbers remain interpretable. A log transform, for instance, is back-transformed to the median prediction (RAISINS says so explicitly).
3.1 Machine-learning mode (train/test validation)
Separate from the advanced options, the Analysis sidebar carries an Enable Machine Learning Approach switch. Turn it on and RAISINS randomly splits your data into a training set (default 80%, adjustable) and a held-out test set, fits the model on the training portion, then evaluates how well it predicts the unseen test rows. The Analysis Results tab then adds a Test Set Performance table, RMSE, MSE, test-set SSE, and a test-set R² (with an approximate adjusted R²), plus an optional Actual vs Predicted table. The split uses a fixed random seed so the result is reproducible. Leave the switch off to fit the model on the entire dataset in the usual way.
The ordinary R² and PRESS in the Model Statistics table describe fit on the data used to build the model; the machine-learning metrics describe prediction on rows the model never saw. When you transformed Y, the test-set metrics are computed on back-transformed predictions (original scale), so they are not directly comparable to the residual-based statistics on the transformed scale, RAISINS notes this too.
4 Assumptions of regression
OLS gives the “best linear unbiased” estimates only when a set of classical assumptions hold. RAISINS provides a formal test and a diagnostic plot for each, so you never have to take the model on faith.
| Assumption | What it means | RAISINS check | What if it fails? |
|---|---|---|---|
| Linearity | The relationship is genuinely linear (in the parameters) | Residuals vs Fitted plot | Add polynomial/interaction terms, or transform |
| Independence | Errors are uncorrelated across observations | Durbin - Watson test; ACF plot | Serious for time/space-ordered data; needs design-level fixes |
| Homoscedasticity | Residual variance is constant across fitted values | Non-constant variance (Breusch - Pagan) test; Scale-Location plot | Transform Y, or use robust standard errors |
| Normality of residuals | Residuals are approximately normal | Shapiro - Wilk test; Normal Q-Q plot | Matters most in small samples; try a transformation |
| No multicollinearity (MLR) | Predictors are not near-duplicates | VIF / GVIF table | Drop or combine redundant predictors |
Heteroscedasticity and non-linearity are the dangerous ones: they distort standard errors and can bias the coefficients. Normality matters mainly in small samples; once n is large, the Central Limit Theorem protects the tests. Independence is critical only when data are ordered in time or space. Multicollinearity never harms prediction; it only muddies the interpretation of individual coefficients, which matters when your goal is to understand each predictor’s unique effect.
5 Getting to the module
Visit the RAISINS home page at www.raisins.live and open Data Analysis. Select the Regression Analysis module (Figure 2). No programming is required: upload your data, choose the response and predictor columns, and RAISINS handles everything from computation to publication-ready output.
5.1 Citing RAISINS, and the record behind this module
To cite the platform in a paper, thesis or report, use the RAISINS citation (APA, Harvard and BibTeX) at www.raisins.live/citation.html. That is the primary reference.
Alongside it, each module has a CPRR, a Computational Provenance & Reproducibility Record, which answers the reviewer’s fair question, what exactly did the software do to my data? It states the R version and the exact version of every package, names the specific function behind each result (stats::lm() for the model fit, car::vif() for multicollinearity, car::ncvTest() for non-constant variance, lmtest::dwtest() for autocorrelation, stats::shapiro.test() (or moments::jarque.test() for large samples) for normality, DAAG::press() for the PRESS statistic, and MASS::stepAIC() when stepwise selection is used), lists every default and decision rule, and includes runnable R code reproducing each step on a public dataset. It carries its own DOI.
Cite the RAISINS paper as your primary reference for the platform, and add the CPRR as supporting documentation when a journal asks for computing details or when you want a precise methods section. The record supports the citation; it does not replace it.
6 Preview mode and Quick Tour
Before subscribing, explore the whole module using Preview mode from the Welcome page. It loads built-in datasets so you can try every feature, the analysis, assumption checks, plots and the RA-One assistant, without uploading your own data. First-time users are greeted with a Quick Tour: an interactive, step-by-step walkthrough that highlights each tab and control and explains what it does. You can replay it any time from the Quick Tour tab in the top navigation.
7 A working example
Throughout this tutorial we use an agricultural dataset of 200 plots (dataset1.csv, also available from the Datasets tab). The response variable (Y) is yield (kg/plot), and the four predictors are:
- irrigation (litres/plot), a continuous measure of water applied
- NPK (kg/ha), the fertiliser dose
- weedgrowth, a continuous weed-pressure score
- harvest, a categorical factor with four levels (april, july, june, march)
The question is which of these agronomic factors drive yield, and by how much, once the others are accounted for. Note the mix of variable types: three numeric predictors and one categorical predictor, which RAISINS dummy-codes automatically. The data layout is shown in Figure 4.
8 How to prepare your data
Your analysis is only as good as your data. Feed RAISINS clean data and it delivers powerful insight; feed it messy data and the results cannot be trusted. You have four routes:
- Create your dataset in MS Excel
- Build it directly within the RAISINS app (Create Data)
- Use a built-in Model dataset as a reference
- Create it through the RA-One chat assistant
9 Preparing data in MS Excel
Open a new blank Excel workbook with a single sheet and no stray content. Use a column-based layout: one column for the response variable (Y) and one column for each predictor (X), with one row per observation. Numeric predictors must be purely numeric; categorical predictors (such as harvest month) are entered as consistent text labels and RAISINS dummy-codes them automatically. Save as CSV, XLS or XLSX; CSV is recommended as it is lighter and loads faster. Avoid blank rows above the data and stray spaces in column names. For reference, see Figure 4.
Dataset creation rules
- Column naming, no spaces; use underscores (
_) or dots (.); avoid symbols such as %, #. Always start a column name with a letter. - Data arrangement, start at the upper-left corner; the row above the data must not be blank.
- Cell management, do not type or delete in empty cells; if needed, select them, right-click and choose Clear Contents.
- Column relevance, name every column meaningfully and drop columns you will not analyse.
- Numeric vs categorical, measurement columns (the response and numeric predictors) must be purely numeric; entries like “NA” or ” - ” cause errors. Categorical predictors should use consistent text labels (e.g., “april”, “july”) with no trailing spaces.
How to save as CSV in MS Excel
- Open your workbook, data on a single sheet, correctly arranged.
- File → Save As / Save a Copy, choose a location.
- Save as type → CSV (Comma delimited) (*.csv).
- Name the file without spaces (use underscores).
- Save.
💡 Tip: before saving, confirm the data is on the first sheet, numeric columns are clean, and categorical labels are consistent.
10 Prepare using Create Data in RAISINS
Unsure about the format? RAISINS can build the template for you:
- Navigate to the Create Data tab
- Select the number of Variables (1 response + all predictors)
- Select the number of Observations (rows)
- Click Create
The layout appears as in Figure 5. Enter your values into the downloaded CSV (or paste them in), then upload it under Analysis.
11 Download Model Datasets
To explore the module before using your own data, download a ready-made example:
- Navigate to the Datasets tab
- Click the Download CSV link for the dataset you want
- Use it as a formatting reference, or upload it directly to try the analysis
12 Creating a dataset using RA-One chat
RA-One, the built-in chat assistant, can create a correctly formatted dataset through a simple conversation. Open RA-One from its navigation tab or the floating chat bubble, tell it how many observations and which variables you need, and it generates a template in the required format. Review it in the chat, download the CSV, and upload it under Analysis (Figure 7).
13 The Analysis tab
Figure 8 shows the Analysis tab. Click Browse in the sidebar to upload your CSV or Excel file. Selectors then appear: use Dependent variable (Y) to pick the response column, and Independent variable(s) (X) to choose one predictor (SLR) or several (MLR). Optionally open Advanced model options (Section 3) to add a transformation, polynomial or interaction terms, or stepwise selection. Click Run Analysis and every output appears instantly across the sub-tabs: Analysis Results, Assumptions, Plots & Graphs, Interpretation, FAQs and View Data. On the results panel you can also set the number of decimal digits and the font used in the tables.
14 Analysis results
The Analysis Results sub-tab presents three tables that together describe the fitted model: the Model Coefficients, the Model Statistics, and the ANOVA table for Regression.
Table 1: Model Coefficients
For every term this table reports the estimated coefficient (β), its Std. Error, the t-value, and the p-value for the test that the true coefficient is zero. Significance stars appear beside each estimate, and very small p-values are shown as “< 0.001” rather than a rounded “0.000”.
Understanding the coefficients table
| Column | Meaning |
|---|---|
| Estimate (β) | Partial regression coefficient, the change in Y per one-unit rise in the predictor, holding the others fixed |
| Std. Error | Precision of the estimate; smaller is better |
| t Value | Estimate ÷ Std. Error, tests whether β differs from zero |
| P Value | Probability of a t this extreme if β were truly zero |
| Significance | *** p < 0.001 · ** p < 0.01 · * p < 0.05 · (blank) not significant |
Interpretation from Figure 9
In the working example the fitted model is
\[\widehat{\text{yield}} = 4.085 + 0.046\,(\text{irrigation}) + 0.187\,(\text{NPK}) - 0.001\,(\text{weedgrowth}) + \text{harvest contrasts}\]
irrigation is the strongest predictor (β = 0.046, SE = 0.001, t = 32.81, p < 0.001): every extra litre/plot of water is associated with about 0.046 kg/plot more yield, so an additional 100 litres buys roughly 4.6 kg. NPK is also highly significant (β = 0.187, SE = 0.009, t = 21.53, p < 0.001): each extra kg/ha of fertiliser adds about 0.19 kg/plot. weedgrowth is not significant (β = -0.001, t = -0.17, p = 0.864): once water and fertiliser are accounted for, weed pressure shows no independent effect in these data. The harvest contrasts are measured against april (the reference level, chosen alphabetically): july (β = -0.70, p = 0.092), june (β = -0.71, p = 0.081) and march (β = -0.69, p = 0.091) all sit just outside the 5% threshold, so there is only weak, non-significant evidence that harvest month shifts yield. The intercept (4.085, p < 0.001) is the baseline yield for an april plot with zero irrigation, zero NPK and zero weed growth.
Each β is a partial effect: read it as “the change in yield for a one-unit change in this predictor, with the others held constant.”
A predictor can be statistically significant yet agronomically trivial, or practically important yet non-significant in a small trial. Read the size of each coefficient and its confidence interval alongside the p-value.
Table 2: Model Statistics
Understanding model statistics
| Statistic | Meaning |
|---|---|
| R² | Proportion of variance in Y explained by the model (0 - 1; higher is better) |
| Adjusted R² | R² penalised for the number of predictors; the fairer index when comparing models |
| Residual Std. Error | Typical size of a prediction error, in the units of Y |
| PRESS | Leave-one-out prediction error sum of squares; lower means better out-of-sample prediction |
Interpretation from Figure 10
Here the model explains about 90% of the variation in yield (R² = 0.8995), and the Adjusted R² of 0.8964 is barely lower, confirming the fit is genuine rather than an artefact of adding predictors. The residual standard error is 2.015 kg/plot on 193 degrees of freedom: that is the typical size of a prediction miss, which is small against a mean yield of roughly 16.8 kg/plot. A high R² is encouraging, but it never certifies that the model is correct. That is what the Assumptions tab is for, and in this example it has something important to say.
Table 3: ANOVA table for Regression
The ANOVA table splits total variation into the part explained by the model and the unexplained residual, and its overall F-test asks whether the model as a whole beats an intercept-only model. Below the table a footnote reminds you that per-term rows use sequential (Type I) sums of squares, so a predictor’s individual contribution depends on the order in which terms entered the model.
Interpretation from Figure 11
The overall model is highly significant (F₆,₁₉₃ = 287.96, p < 0.001), so the four predictors jointly explain a meaningful share of the variation in yield. Read sequentially, irrigation takes the largest share (SS = 4773.05, F = 1175.25, p < 0.001), followed by NPK (SS = 2225.69, F = 548.02, p < 0.001). weedgrowth adds essentially nothing once those two are in the model (SS = 0.13, F = 0.03, p = 0.859), and harvest is likewise non-significant (SS = 18.00 on 3 df, F = 1.48, p = 0.222). The residual mean square (4.06 on 193 df) is the baseline variance behind every standard error and F-ratio in the analysis. This mirrors the coefficient table exactly: water and fertiliser drive yield; weeds and harvest month do not.
15 Assumptions
The Assumptions sub-tab gathers the formal statistical tests that validate your model, each with a plain-language interpretation. The matching diagnostic plots (Residuals vs Fitted, Normal Q-Q, Scale-Location, Residuals vs Leverage, and the ACF) now live in the Plots & Graphs tab (Section 16), where they share the same customization and export tools as every other plot.
Multicollinearity, VIF / GVIF
RAISINS reports the Variance Inflation Factor, generalised to GVIF for categorical predictors with several dummy codes. For a predictor \(X_j\),
\[VIF_j = \frac{1}{1 - R_j^2},\]
where \(R_j^2\) is the R² from regressing \(X_j\) on all other predictors. As a rule of thumb, VIF > 5 (or Standard GVIF > ≈ 2.24) signals troublesome collinearity. When any predictor is categorical, RAISINS reports the generalized form, and the Assumptions tab shows three columns: the raw GVIF, its Df, and the Standard GVIF (GVIF^(1/(2·Df))), which rescales the value so a single threshold works whatever the degrees of freedom. Compare the Standard GVIF against ≈ 2.24, or square it and compare against the familiar 5. The downloadable report prints only the Standard GVIF column, so its numbers are the square roots of the raw GVIFs you see on screen; they are the same result on two scales, not a disagreement. In the working example every value sits essentially at 1 (raw GVIF: irrigation 1.02, NPK 1.17, weedgrowth 1.16, harvest 1.05 on 3 df; Standard GVIF: 1.008, 1.081, 1.076 and 1.009 respectively), so the four predictors carry independent information and multicollinearity is not a concern. This also means we can trust the individual coefficients: the model has no trouble deciding which predictor deserves the credit.
Homoscedasticity, non-constant variance test
The non-constant variance (NCV / Breusch - Pagan) test checks whether residual variance is constant. A p-value below 0.05 indicates heteroscedasticity, non-constant spread, which distorts standard errors even when the coefficients themselves are unbiased. In the working example the test returns χ²(1) = 5.51, p = 0.019, which is below 0.05: this model does show heteroscedasticity. The usual remedy is a variance-stabilising transformation of Y (log or square root) from Advanced model options (Section 3); re-run the analysis with the transformation and check whether the test clears.
Normality of residuals, Shapiro - Wilk
The Shapiro - Wilk test assesses whether the residuals are approximately normal (it is used for samples of 3 to 5000 observations; for larger samples RAISINS automatically switches to the Jarque - Bera test, which serves the same purpose). In the working example it returns W = 0.922, p < 0.001, so the residuals depart from normality. Before you panic: with n = 200 the Central Limit Theorem largely protects the coefficient tests, and these tests are so powerful at this sample size that they flag departures which are practically harmless. Read the verdict alongside the Normal Q-Q plot in Plots & Graphs, which is the more forgiving visual check, and note that the same transformation that fixes the heteroscedasticity above will often improve normality too.
Independence, Durbin - Watson
The Durbin - Watson statistic tests for serial autocorrelation in the residuals. It ranges from 0 to 4: a value near 2 indicates independence; below ~1.5 suggests positive autocorrelation; above ~2.5 suggests negative. RAISINS reports a p-value alongside the statistic, and its written verdict follows that p-value rather than the rule of thumb alone. In the working example DW = 2.13, p = 0.472, comfortably in the clear, so the independence assumption holds. For cross-sectional field data such as these plots this is usually a confirmatory check.
Influence & Outlier Diagnostics
The Assumptions tab also reports an Influence & Outlier Diagnostics table (Figure 16). It separates three distinct kinds of unusual point: an outlier (large residual, unusual in Y), a high-leverage point (unusual in the predictor space), and an influential point (one that actually moves the fitted model). For each observation it lists the fitted value, raw and standardized/studentized residuals, leverage (\(h_{ii}\)), Cook’s distance, and DFFITS, and adds a plain-language Flag (e.g., “Potential outlier”, “High leverage”, “Influential”). The cutoffs used are shown in a note above the table (leverage > 2p/n; Cook’s D > 4/n). The whole table is downloadable as CSV.
In the working example, with n = 200 and p = 7, the cutoffs are leverage > 0.07 and Cook’s D > 0.02, and 16 of the 200 plots are flagged: 7 influential outliers, 5 influential, 2 extreme outliers and 2 high-leverage points. That sounds alarming until you notice the 4/n rule is deliberately sensitive; the largest Cook’s D is only 0.21, far below the classical danger mark of 1, so no single plot is dictating the model. The flags are telling you where to look, not that the analysis is broken.
A flagged point may be a data-entry error (fix or remove it) or a genuine, important extreme case (keep it). Never delete points just because they are flagged; investigate, and where it matters, report the model with and without the point.
16 Plots & Graphs
The Plots & Graphs tab holds the full visualisation suite. Plots are selected from a row of icon buttons; the active plot appears below with a gear (Plot Settings) button in its corner. Every plot is fully customizable, title, axis labels, colours, point size, theme and more, and every plot can be downloaded in PNG, JPEG, TIFF, PDF and SVG at a chosen resolution. Defaults are publication-grade and colourblind-safe (an Okabe - Ito palette), so figures look consistent and are readable by everyone straight out of the box.
Two families of plots live here. The relationship / model plots help you understand the fitted model; the diagnostic plots (moved here from the Assumptions tab) help you check the assumptions from Section 15. Hover over any thumbnail below to read what it shows.
Regression line, a scatter of Y against a chosen predictor with the fitted line and confidence band; the quickest read on the direction and strength of a relationship.
Coefficient plot, each coefficient as a point with its 95% confidence interval; bars crossing zero are non-significant. A compact summary of effect sizes and significance.
Observed vs Predicted, actual Y against the model’s predictions; points hugging the 45° line indicate a well-fitting model.
Residuals vs Fitted (diagnostic), checks linearity and constant variance. Look for a flat, patternless cloud around zero; curves or fans signal a problem.
Normal Q-Q (diagnostic), residual quantiles against normal quantiles; points on the diagonal support the normality assumption.
Correlation heatmap, pairwise correlations among the numeric variables; a fast way to spot predictors that may be collinear.
The tab also offers a facet plot (the response against each predictor in its own panel), a Pareto chart ranking predictors by the size of their standardized effect, added-variable (partial-regression) plots, a residual distribution histogram, a pair plot (scatter-plot matrix), and the remaining diagnostics, Scale-Location, Residuals vs Leverage, and the ACF of residuals.
17 Interpretation
The Interpretation sub-tab gives a clear, plain-language write-up of your results (Figure 24): which predictors are significant and in which direction (with the size of each coefficient), the overall model fit (R², adjusted R² and the F-test), any assumption violations detected, and practical suggestions (a transformation, dropping a redundant predictor, and so on). The narrative also states which advanced options and which mode (standard vs machine-learning split) were used, so it reads like a ready-to-adapt methods paragraph. The text is revealed with a short typing animation; a Stop button reveals the full write-up at once, and a Copy button places the plain-text version on your clipboard for pasting into a manuscript.
18 RA-One Chat
RA-One is the built-in conversational assistant, reachable from its own navigation tab or the floating chat bubble. Ask questions in plain language and it answers using your analysis, never generic advice and never invented numbers; if a value is not available it says so. Every reply is in plain English, with no code.
RA-One draws on the full set of results the app produces, the coefficient table (with confidence intervals and standardized betas), every model-fit statistic (R², adjusted R², F-test, AIC, BIC, RMSE, MAE, PRESS), the ANOVA table, all assumption tests, the influence and outlier diagnostics, and the machine-learning test-set metrics when that mode is on. It can explain what a coefficient, p-value, R² or confidence interval means for your specific model, walk you through why an assumption passed or failed, and answer general concept questions (partial effects, multicollinearity, when to transform) so you build understanding alongside your results. If a value is not part of your current results, it tells you so rather than inventing one.
The same chat window can also prepare your data, build a correctly formatted template (Section 12) or fetch a model dataset (Section 11), and, most usefully, generate plots on request. Ask for “residuals vs fitted”, “the coefficient plot”, a “scatter of yield vs irrigation” or a “correlation heatmap” and RA-One renders the figure directly in the chat. Each chat plot comes with a plot-type toolbar to switch graphics and a Plot Settings panel to pick the predictor and restyle it, and a one-click high-resolution download.
In a single conversation RA-One can interpret your results, build a data template, fetch a model dataset, and draw customizable plots; so much of a routine regression session can happen without ever leaving the chat.
19 FAQs
A dedicated FAQs tab answers common questions, how to read R² correctly, what to do when an assumption is violated, how categorical predictors are handled, and when to prefer multiple over simple regression, with clear explanations and practical tips. If you are ever unsure how something works, start here.
20 View data
View Data is the first line of defence for data integrity. On upload, RAISINS runs an automated Health Check that validates column types and formatting: it flags any predictor or response column containing non-numeric values, missing entries or formatting inconsistencies that would compromise the fit. Resolving these before you click Run Analysis ensures every output rests on clean, correctly typed data.
21 Wrapping up
Regression rests on one honest question: once the noise is accounted for, how much does each factor really move the response? Everything else, the ANOVA F-test, the assumption checks, the influence diagnostics, the transformations, exists to make sure that question is answered fairly. RAISINS automates the machinery so you can concentrate on what the answer means for your research.
If you get stuck at any point, RA-One is available 24 × 7, or write to us at [email protected].