Regression Scatter

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status="ready" · linear least squares over 44 load-test runs — 95% confidence band, two runs flagged and named on the plot

p95 latency vs. concurrency

y = 1.84x + 62.3 · fitted on 44 of 44 observations

R²: 0.968
Slope: +1.84
Points: 44
Band: 95% confidence

ObservationOutlier · |σ| ≥ 2Least-squares fit95% confidence band

p95 latency vs. concurrency: 44 observations of p95 latency (ms) against Concurrent requests. linear least-squares fit y = 1.84x + 62.3, R² 0.968, 44 points fitted, 95% confidence band drawn. 2 flagged beyond 2 standard errors: Run 13, Run 34.
Observation	Concurrent requests	p95 latency (ms)	Fitted	Residual in standard errors	Flag
Run 01	11	93.4	82.5	+0.654	Within range
Run 02	16	98.1	91.7	+0.383	Within range
Run 03	21	82.2	101	-1.12	Within range
Run 04	25	118	108	+0.605	Within range
Run 05	28	94.6	114	-1.14	Within range
Run 06	33	107	123	-0.938	Within range
Run 07	35	130	127	+0.177	Within range
Run 08	40	150	136	+0.851	Within range
Run 09	44	152	143	+0.522	Within range
Run 10	47	144	149	-0.285	Within range
Run 11	53	145	160	-0.843	Within range
Run 12	57	157	167	-0.569	Within range
Run 13	59	246	171	+4.4	Outlier
Run 14	63	161	178	-0.989	Within range
Run 15	67	188	185	+0.153	Within range
Run 16	74	198	198	+0.0102	Within range
Run 17	75	197	200	-0.196	Within range
Run 18	82	202	213	-0.635	Within range
Run 19	84	234	217	+1.02	Within range
Run 20	87	213	222	-0.541	Within range
Run 21	93	223	233	-0.617	Within range
Run 22	94	227	235	-0.462	Within range
Run 23	101	259	248	+0.645	Within range
Run 24	106	246	257	-0.621	Within range
Run 25	108	272	261	+0.636	Within range
Run 26	113	279	270	+0.509	Within range
Run 27	117	270	277	-0.442	Within range
Run 28	120	279	283	-0.227	Within range
Run 29	125	285	292	-0.419	Within range
Run 30	128	285	297	-0.723	Within range
Run 31	134	300	308	-0.486	Within range
Run 32	136	302	312	-0.584	Within range
Run 33	141	329	321	+0.465	Within range
Run 34	146	288	330	-2.5	Outlier
Run 35	148	353	334	+1.13	Within range
Run 36	152	340	341	-0.11	Within range
Run 37	155	340	347	-0.417	Within range
Run 38	161	371	358	+0.758	Within range
Run 39	163	368	362	+0.358	Within range
Run 40	168	369	371	-0.133	Within range
Run 41	174	405	382	+1.38	Within range
Run 42	175	375	384	-0.495	Within range
Run 43	181	411	395	+0.947	Within range
Run 44	183	397	398	-0.0713	Within range

band="prediction" level={0.99} · same 44 runs — the ribbon now covers where a single new run should land, which is far wider than where the line is

p95 latency vs. concurrency

y = 1.84x + 62.3 · fitted on 44 of 44 observations

R²: 0.968
Slope: +1.84
Points: 44
Band: 99% prediction

ObservationOutlier · |σ| ≥ 2Least-squares fit99% prediction band

p95 latency vs. concurrency: 44 observations of p95 latency (ms) against Concurrent requests. linear least-squares fit y = 1.84x + 62.3, R² 0.968, 44 points fitted, 99% prediction band drawn. 2 flagged beyond 2 standard errors: Run 13, Run 34.
Observation	Concurrent requests	p95 latency (ms)	Fitted	Residual in standard errors	Flag
Run 01	11	93.4	82.5	+0.654	Within range
Run 02	16	98.1	91.7	+0.383	Within range
Run 03	21	82.2	101	-1.12	Within range
Run 04	25	118	108	+0.605	Within range
Run 05	28	94.6	114	-1.14	Within range
Run 06	33	107	123	-0.938	Within range
Run 07	35	130	127	+0.177	Within range
Run 08	40	150	136	+0.851	Within range
Run 09	44	152	143	+0.522	Within range
Run 10	47	144	149	-0.285	Within range
Run 11	53	145	160	-0.843	Within range
Run 12	57	157	167	-0.569	Within range
Run 13	59	246	171	+4.4	Outlier
Run 14	63	161	178	-0.989	Within range
Run 15	67	188	185	+0.153	Within range
Run 16	74	198	198	+0.0102	Within range
Run 17	75	197	200	-0.196	Within range
Run 18	82	202	213	-0.635	Within range
Run 19	84	234	217	+1.02	Within range
Run 20	87	213	222	-0.541	Within range
Run 21	93	223	233	-0.617	Within range
Run 22	94	227	235	-0.462	Within range
Run 23	101	259	248	+0.645	Within range
Run 24	106	246	257	-0.621	Within range
Run 25	108	272	261	+0.636	Within range
Run 26	113	279	270	+0.509	Within range
Run 27	117	270	277	-0.442	Within range
Run 28	120	279	283	-0.227	Within range
Run 29	125	285	292	-0.419	Within range
Run 30	128	285	297	-0.723	Within range
Run 31	134	300	308	-0.486	Within range
Run 32	136	302	312	-0.584	Within range
Run 33	141	329	321	+0.465	Within range
Run 34	146	288	330	-2.5	Outlier
Run 35	148	353	334	+1.13	Within range
Run 36	152	340	341	-0.11	Within range
Run 37	155	340	347	-0.417	Within range
Run 38	161	371	358	+0.758	Within range
Run 39	163	368	362	+0.358	Within range
Run 40	168	369	371	-0.133	Within range
Run 41	174	405	382	+1.38	Within range
Run 42	175	375	384	-0.495	Within range
Run 43	181	411	395	+0.947	Within range
Run 44	183	397	398	-0.0713	Within range

model="exponential" · least squares runs on ln y, so the R² tile names the scale it describes and the curve is drawn back in user units

Weekly active users since launch

y = 1,190·e^(0.0934x) · fitted on 26 of 26 observations

R² (on ln y): 0.994
Rate (ln y per x): +0.0934
Points: 26
Band: 95% confidence

ObservationOutlier · |σ| ≥ 2Least-squares fit95% confidence band

Weekly active users since launch: 26 observations of Weekly active users against Week. exponential least-squares fit y = 1,190·e^(0.0934x), R² 0.994, 26 points fitted, 95% confidence band drawn. 1 flagged beyond 2 standard errors: W4.
Observation	Week	Weekly active users	Fitted	Residual in standard errors	Flag
W1	1	1,240	1,310	-1.02	Within range
W2	2	1,410	1,440	-0.39	Within range
W3	3	1,570	1,580	-0.103	Within range
W4	4	2,020	1,730	+2.77	Outlier
W5	5	1,810	1,900	-0.867	Within range
W6	6	2,020	2,090	-0.59	Within range
W7	7	2,320	2,290	+0.162	Within range
W8	8	2,780	2,520	+1.73	Within range
W9	9	2,650	2,770	-0.736	Within range
W10	10	3,150	3,040	+0.651	Within range
W11	11	3,440	3,330	+0.535	Within range
W12	12	3,740	3,660	+0.396	Within range
W13	13	4,010	4,020	-0.0403	Within range
W14	14	4,490	4,410	+0.322	Within range
W15	15	4,590	4,840	-0.959	Within range
W16	16	4,910	5,320	-1.4	Within range
W17	17	5,540	5,840	-0.919	Within range
W18	18	6,210	6,410	-0.574	Within range
W19	19	7,270	7,040	+0.58	Within range
W20	20	7,610	7,730	-0.275	Within range
W21	21	7,930	8,480	-1.21	Within range
W22	22	8,800	9,310	-1.03	Within range
W23	23	9,970	10,200	-0.46	Within range
W24	24	12,100	11,200	+1.38	Within range
W25	25	12,800	12,300	+0.637	Within range
W26	26	14,700	13,500	+1.51	Within range

model="logarithmic" · a learning curve; the slope tile reads "per ln x" because that is what the coefficient means here

Time on task by repetition

y = -12.9·ln(x) + 93.5 · fitted on 32 of 32 observations

R²: 0.955
Slope per ln x: -12.9
Points: 32
Band: 95% confidence

ObservationOutlier · |σ| ≥ 2Least-squares fit95% confidence band

Time on task by repetition: 32 observations of Seconds to complete against Repetition. logarithmic least-squares fit y = -12.9·ln(x) + 93.5, R² 0.955, 32 points fitted, 95% confidence band drawn. 1 flagged beyond 2 standard errors: #4.
Observation	Repetition	Seconds to complete	Fitted	Residual in standard errors	Flag
#1	1	92	93.5	-0.76	Within range
#2	2	84	84.6	-0.267	Within range
#3	3	79.2	79.4	-0.0687	Within range
#4	4	82.2	75.6	+2.82	Outlier
#5	5	70.8	72.8	-0.838	Within range
#6	6	69	70.4	-0.598	Within range
#7	7	68.6	68.4	+0.0733	Within range
#8	8	70.6	66.7	+1.64	Within range
#9	9	63.3	65.2	-0.789	Within range
#10	10	65.1	63.8	+0.533	Within range
#11	11	63.6	62.6	+0.42	Within range
#12	12	62.2	61.5	+0.304	Within range
#13	13	60.1	60.4	-0.142	Within range
#14	14	60	59.5	+0.215	Within range
#15	15	56.2	58.6	-1	Within range
#16	16	54.5	57.8	-1.36	Within range
#17	17	54.8	57	-0.912	Within range
#18	18	54.8	56.2	-0.604	Within range
#19	19	56.8	55.5	+0.526	Within range
#20	20	54.2	54.9	-0.286	Within range
#21	21	51.5	54.3	-1.16	Within range
#22	22	51.3	53.7	-0.989	Within range
#23	23	52.1	53.1	-0.412	Within range
#24	24	55.8	52.5	+1.38	Within range
#25	25	53.5	52	+0.631	Within range
#26	26	55.1	51.5	+1.52	Within range
#27	27	47.7	51	-1.4	Within range
#28	28	50.4	50.5	-0.0603	Within range
#29	29	46.8	50.1	-1.39	Within range
#30	30	51.5	49.7	+0.784	Within range
#31	31	51.2	49.2	+0.838	Within range
#32	32	51.9	48.8	+1.31	Within range

outlierThreshold={1.5} · no real relationship — R² near zero, a nearly flat line and a band wide enough to admit it

No relationship to find

y = 0.186x + 71 · fitted on 30 of 30 observations

R²: 0.022
Slope: +0.186
Points: 30
Band: 95% confidence

ObservationOutlier · |σ| ≥ 1.5Least-squares fit95% confidence band

No relationship to find: 30 observations of Satisfaction score against Ticket age (days). linear least-squares fit y = 0.186x + 71, R² 0.022, 30 points fitted, 95% confidence band drawn. 3 flagged beyond 1.5 standard errors: T4, T18, T28.
Observation	Ticket age (days)	Satisfaction score	Fitted	Residual in standard errors	Flag
T1	0.5	57	71.1	-1.05	Within range
T2	1.9	70.2	71.4	-0.0851	Within range
T3	3.2	72.8	71.6	+0.0879	Within range
T4	4.4	92.9	71.8	+1.53	Outlier
T5	6.7	55.1	72.2	-1.24	Within range
T6	7.3	77.7	72.4	+0.384	Within range
T7	8.1	93.3	72.5	+1.49	Within range
T8	10	84.7	72.9	+0.844	Within range
T9	12	65.9	73.2	-0.521	Within range
T10	12.5	75.7	73.3	+0.168	Within range
T11	14.5	58.3	73.7	-1.09	Within range
T12	14.9	79.5	73.8	+0.404	Within range
T13	16.6	57.9	74.1	-1.14	Within range
T14	17.7	58.8	74.3	-1.09	Within range
T15	19.3	86.6	74.6	+0.845	Within range
T16	19.9	92.1	74.7	+1.22	Within range
T17	21.7	72.2	75	-0.2	Within range
T18	23.1	50.7	75.3	-1.74	Outlier
T19	24.9	93.7	75.6	+1.28	Within range
T20	25	55.6	75.7	-1.42	Within range
T21	26.7	80.5	76	+0.321	Within range
T22	27.3	66.2	76.1	-0.702	Within range
T23	28.7	84.7	76.3	+0.594	Within range
T24	30.6	80.9	76.7	+0.3	Within range
T25	32.2	92.8	77	+1.14	Within range
T26	34.2	76.9	77.4	-0.0344	Within range
T27	34.9	93.9	77.5	+1.19	Within range
T28	35.6	50.6	77.6	-1.97	Outlier
T29	36.6	91.3	77.8	+0.988	Within range
T30	39.6	71.6	78.4	-0.505	Within range

band="none" · the same runs with the ribbon switched off, when only the trend and R² are wanted

p95 latency vs. concurrency

y = 1.84x + 62.3 · fitted on 44 of 44 observations

R²: 0.968
Slope: +1.84
Points: 44
Band: off

ObservationOutlier · |σ| ≥ 2Least-squares fit

p95 latency vs. concurrency: 44 observations of p95 latency (ms) against Concurrent requests. linear least-squares fit y = 1.84x + 62.3, R² 0.968, 44 points fitted, no band drawn. 2 flagged beyond 2 standard errors: Run 13, Run 34.
Observation	Concurrent requests	p95 latency (ms)	Fitted	Residual in standard errors	Flag
Run 01	11	93.4	82.5	+0.654	Within range
Run 02	16	98.1	91.7	+0.383	Within range
Run 03	21	82.2	101	-1.12	Within range
Run 04	25	118	108	+0.605	Within range
Run 05	28	94.6	114	-1.14	Within range
Run 06	33	107	123	-0.938	Within range
Run 07	35	130	127	+0.177	Within range
Run 08	40	150	136	+0.851	Within range
Run 09	44	152	143	+0.522	Within range
Run 10	47	144	149	-0.285	Within range
Run 11	53	145	160	-0.843	Within range
Run 12	57	157	167	-0.569	Within range
Run 13	59	246	171	+4.4	Outlier
Run 14	63	161	178	-0.989	Within range
Run 15	67	188	185	+0.153	Within range
Run 16	74	198	198	+0.0102	Within range
Run 17	75	197	200	-0.196	Within range
Run 18	82	202	213	-0.635	Within range
Run 19	84	234	217	+1.02	Within range
Run 20	87	213	222	-0.541	Within range
Run 21	93	223	233	-0.617	Within range
Run 22	94	227	235	-0.462	Within range
Run 23	101	259	248	+0.645	Within range
Run 24	106	246	257	-0.621	Within range
Run 25	108	272	261	+0.636	Within range
Run 26	113	279	270	+0.509	Within range
Run 27	117	270	277	-0.442	Within range
Run 28	120	279	283	-0.227	Within range
Run 29	125	285	292	-0.419	Within range
Run 30	128	285	297	-0.723	Within range
Run 31	134	300	308	-0.486	Within range
Run 32	136	302	312	-0.584	Within range
Run 33	141	329	321	+0.465	Within range
Run 34	146	288	330	-2.5	Outlier
Run 35	148	353	334	+1.13	Within range
Run 36	152	340	341	-0.11	Within range
Run 37	155	340	347	-0.417	Within range
Run 38	161	371	358	+0.758	Within range
Run 39	163	368	362	+0.358	Within range
Run 40	168	369	371	-0.133	Within range
Run 41	174	405	382	+1.38	Within range
Run 42	175	375	384	-0.495	Within range
Run 43	181	411	395	+0.947	Within range
Run 44	183	397	398	-0.0713	Within range

status="loading" · skeleton keeps the stat row and the 300px plot box, so nothing shifts when the numbers land

p95 latency vs. concurrency

p95 latency (ms) against Concurrent requests · linear least squares

status="empty" · items=[]

p95 latency vs. concurrency

p95 latency (ms) against Concurrent requests · linear least squares

Nothing to fit yet

A trend line appears once observations carry both Concurrent requests and p95 latency (ms).

status="error" · onRetry provided — click Try again

p95 latency vs. concurrency

p95 latency (ms) against Concurrent requests · linear least squares

Couldn't load these observations

The data source didn't respond.

n = 2 — a line through two points is interpolation, not a fit; the card says so

Two observations

Throughput (rps) against Batch size · linear least squares

R²: —
Slope: —
Points: 2
Band: —

A least-squares fit needs at least 3 points and 2 were supplied. The points are plotted without a trend.

Observation

Two observations: 2 observations of Throughput (rps) against Batch size. No fit could be computed. No observation exceeds the outlier threshold. A least-squares fit needs at least 3 points and 2 were supplied. The points are plotted without a trend.
Observation	Batch size	Throughput (rps)	Fitted	Residual in standard errors	Flag
A	8	240	—	—	Within range
B	32	610	—	—	Within range

zero variance in x — the slope would be vertical, so no line is drawn

One predictor value, six responses

Error rate (%) against Replica count · linear least squares

R²: —
Slope: —
Points: 6
Band: —

Every fitted point shares one Replica count value, so the line would be vertical and the slope undefined. The points are plotted without a trend.

Observation

One predictor value, six responses: 6 observations of Error rate (%) against Replica count. No fit could be computed. No observation exceeds the outlier threshold. Every fitted point shares one Replica count value, so the line would be vertical and the slope undefined. The points are plotted without a trend.
Observation	Replica count	Error rate (%)	Fitted	Residual in standard errors	Flag
Probe 1	4	1.02	—	—	Within range
Probe 2	4	0.85	—	—	Within range
Probe 3	4	1.04	—	—	Within range
Probe 4	4	1.33	—	—	Within range
Probe 5	4	1.11	—	—	Within range
Probe 6	4	1.43	—	—	Within range

zero variance in y — the fit is flat and R² is undefined, not 0 and not 1

Response never moves

y = 0x + 3 · fitted on 7 of 7 observations

R²: —
Slope: 0
Points: 7
Band: 95% confidence

Retries never varies, so there is no variation for a fit to explain: R² is undefined and the band collapses onto the flat line.

ObservationLeast-squares fit95% confidence band

Response never moves: 7 observations of Retries against Payload (KB). linear least-squares fit y = 0x + 3, R² undefined, 7 points fitted, 95% confidence band drawn. No observation exceeds the outlier threshold. Retries never varies, so there is no variation for a fit to explain: R² is undefined and the band collapses onto the flat line.
Observation	Payload (KB)	Retries	Fitted	Flag
Call 1	4	3	3	Within range
Call 2	13	3	3	Within range
Call 3	22	3	3	Within range
Call 4	31	3	3	Within range
Call 5	40	3	3	Within range
Call 6	49	3	3	Within range
Call 7	58	3	3	Within range

a perfect fit — R² 1, zero residuals, a band with no width

Exactly on the line

y = 3x + 5 · fitted on 6 of 6 observations

R²: 1.000
Slope: +3
Points: 6
Band: 95% confidence

The fitted points are exactly collinear: R² is 1, every residual is zero and the band has no width.

ObservationLeast-squares fit95% confidence band

Exactly on the line: 6 observations of Cost against Units. linear least-squares fit y = 3x + 5, R² 1.000, 6 points fitted, 95% confidence band drawn. No observation exceeds the outlier threshold. The fitted points are exactly collinear: R² is 1, every residual is zero and the band has no width.
Observation	Units	Cost	Fitted	Flag
L1	0	5	5	Within range
L2	5	20	20	Within range
L3	10	35	35	Within range
L4	15	50	50	Within range
L5	20	65	65	Within range
L6	25	80	80	Within range

model="logarithmic" with x ≤ 0 — those points are plotted as crosses, not fitted

Log model, values it cannot take

y = 10.2·ln(x) + 32.3 · fitted on 5 of 7 observations

R²: 0.990
Slope per ln x: +10.2
Points: 5 of 7
Band: 95% confidence

2 observations fall outside this model's domain (x > 0): drawn as crosses and left out of the fit.

ObservationNot fittedLeast-squares fit95% confidence band

Log model, values it cannot take: 7 observations of Settle time (s) against Signed drift. logarithmic least-squares fit y = 10.2·ln(x) + 32.3, R² 0.990, 5 points fitted, 95% confidence band drawn. No observation exceeds the outlier threshold. 2 observations fall outside this model's domain (x > 0): drawn as crosses and left out of the fit.
Observation	Signed drift	Settle time (s)	Fitted	Residual in standard errors	Flag
−4	-4	21	—	—	Outside the model domain, not fitted
0	0	26	—	—	Outside the model domain, not fitted
1	1	31	32.3	-1.22	Within range
3	3	44	43.5	+0.342	Within range
8	8	55	53.5	+0.947	Within range
18	18	63	61.8	+0.823	Within range
40	40	68	69.9	-1.65	Within range

Loading preview…

"use client"

import * as React from "react"
import {
  Area,
  CartesianGrid,
  ComposedChart,
  Line,
  Scatter,
  XAxis,
  YAxis,
  ZAxis,
} from "recharts"

Installation

npx shadcn@latest add https://ui.zyeon.ai/r/chart-regression-scatter.json

Prompt

Build a React + TypeScript + Tailwind "ChartRegressionScatter" card on the
shadcn chart primitives (ChartContainer / ChartTooltip over a recharts
ComposedChart) with zod. Every statistic is computed inside the component —
there is no statistics dependency, because simple least squares is about forty
lines plus one table of t values.

Contract
- One zod schema is the single source of truth:
  { status: "loading" | "empty" | "error" | "ready"; title; xLabel; yLabel;
    model?: "linear" | "logarithmic" | "exponential";
    items: { id, label, x: number, y: number }[] }.
  Refine that "ready" carries at least one item.
- Component props = z.infer of the schema plus band?: "confidence" |
  "prediction" | "none" (default "confidence"), level?: 0.9 | 0.95 | 0.99
  (default 0.95), outlierThreshold?: number (default 2), onRetry?: () => void
  and className. No hand-written parallel interface.
- xLabel / yLabel are used verbatim by the axis titles, the caption, the
  tooltip, the aria summary and the data table, so one rename moves everything.

Behavior - the fit
- All three models are ordinary least squares over a linearised pair, so one
  set of sums serves them all: linear fits (x, y); logarithmic fits (ln x, y)
  and needs x > 0; exponential fits (x, ln y) and needs y > 0. The inverse
  transform maps the fitted curve and both band edges back into user units, and
  because exp() is monotone the two edges stay in order.
- Sums are taken in two passes (mean first, then deviations), never as
  Sxx = Sum(x^2) - (Sum x)^2 / n. The one-pass form subtracts two large nearly
  equal numbers and on data like epoch timestamps it returns a negative Sxx,
  which becomes a NaN slope and a blank chart.
- SSE is accumulated from the residuals directly rather than as
  Syy - slope*Sxy: that subtraction goes slightly negative on a perfect fit,
  and sqrt() of it is NaN.
- Print R^2, the slope, how many points were fitted and what the band means as
  four labelled figures above the plot. For the exponential model least squares
  minimised ln y, so the tile reads "R^2 (on ln y)" - quoting it as an R^2 on y
  would be a lie. The slope tile is relabelled per model too ("Slope", "Slope
  per ln x", "Rate (ln y per x)"), because the coefficient means a different
  thing in each.
- Band half-width at x is t * s * sqrt(k + 1/n + (x - xbar)^2 / Sxx), where s
  is the residual standard error, k = 0 for a confidence band (where the line
  is) and k = 1 for a prediction band (where one new observation lands). That
  is what makes a confidence band a hyperbola pinched at xbar. Sample it at
  ~72 x positions across the padded domain and render it as a range Area with
  the fitted curve as a Line on top.
- t comes from a small table of two-sided critical values at 90 / 95 / 99 % by
  degrees of freedom, not from a library. Lookup takes the largest tabulated df
  at or below the real one, so an in-between sample size errs wide, never
  narrow.
- Outliers are flagged by studentised residual: e / (s * sqrt(1 - h)) with
  leverage h = 1/n + (x - xbar)^2 / Sxx. Dividing by sqrt(1 - h) is the point -
  the raw residual beside a high-leverage observation is small precisely
  because the line chased it. Flag, never drop: excluding a point silently
  changes the very numbers the card reports, and that decision belongs to the
  reader.

Behavior - the inputs that break naive regression charts
Each of these plots the observations and prints a sentence saying what
happened. None of them may produce NaN geometry or an empty rectangle.
- non-finite x or y: dropped before anything is measured; "ready" with nothing
  left renders the empty branch.
- fewer than 3 usable points: no fit at all. Two points determine a line
  exactly, which leaves zero degrees of freedom, an undefined residual variance
  and a band of width NaN - a line through two points is interpolation, not
  evidence.
- zero variance in x (Sxx = 0): the slope is a division by zero, so no line is
  drawn.
- zero variance in y (Syy = 0): the flat line IS the fit, but R^2 = 1 - SSE/SST
  is 0/0, so R^2 prints an em dash and says why. Not 0, not 1.
- an exact fit (SSE = 0): R^2 is 1, the band collapses onto the line, and the
  studentised residuals are 0 by definition rather than 0/0.
- values outside the model's domain (x <= 0 under log, y <= 0 under
  exponential): plotted as crosses, excluded from the fit, and counted in the
  "Points" tile as "5 of 7".
- numeric props are clamped: an outlierThreshold below 0.5 or non-finite falls
  back to 2 (0 would flag every point, NaN would flag none), and an unknown
  band or level falls back to a 95% confidence band.
- the y domain grows at most one full data span past the observations and the
  axis clips the rest, so an exponential band on weak evidence cannot squash
  every point onto one row.

Rendering & styling
- Semantic tokens only. Observations are var(--chart-2) at 45% fill with a
  full-opacity stroke; outliers are var(--chart-5); the fit line and its band
  are var(--primary) (line at 2px, band at 14% opacity). The data gets a chart
  hue and the model gets the theme's foreground pair: neighbouring chart tokens
  sit only about 1.3:1 apart, so a fit line inside that ramp can land a step
  away from the dots it has to be read against, while --primary flips with the
  theme and is always the strongest mark on the card.
- Colour is never the only channel. Outliers are diamonds carrying their own
  label, out-of-domain points are crosses, and a drawn (not coloured-text)
  legend keys all four marks. --chart-N is never used as a text colour.
- Draw the outlier marker and its name in one custom Scatter `shape`, not with
  a LabelList: a LabelList label inherits the symbol's own width as its wrap
  width, so "Run 34" comes out stacked two lines high on a 10px dot.
- Guard every Scatter behind a non-empty length check. recharts reads an empty
  `data` array as "no data of my own" and falls back to the chart-level
  dataset, minting one phantom symbol per curve sample.
- Axis ticks are snapped to a 1/2/5x10^n step, because padding the domain for
  clearance pushes the ends onto values like -0.5 or 107. Notation is then
  chosen once per axis from those ticks, and compact is only used if it still
  tells them apart: picking it from the magnitude alone renders an axis of
  epoch seconds as four ticks that all read "1.7B" - they do not overlap, they
  are not clipped, and they say nothing. Always an explicit "en-US" locale,
  never Intl(undefined).
- No animation anywhere: isAnimationActive={false}. A regression line drawing
  itself in tells nobody anything, and it makes prefers-reduced-motion a
  non-issue; only the loading skeleton pulses, under motion-reduce:animate-none.
- Four first-class branches inside one bg-card panel: loading (skeleton stat
  row plus a tilted ribbon silhouette in the same 300px box), empty (dashed
  frame with a rising dotted line), error (message plus a "Try again" button
  only when onRetry exists), ready.
- Accessibility: the chart is one role="img" whose aria-label states n, the
  equation, R^2, the band, the outliers by name and every degeneracy notice.
  Because role="img" makes its subtree presentational, give the recharts svg
  tabIndex={-1} so it is not a tab stop that announces nothing, and put the
  real numbers in a table rendered as a SIBLING of it, one row per observation
  (x, y, fitted, residual in standard errors, flag). Wrap that table in a div
  carrying sr-only: a bare table is display:table and ignores the 1px width.

Customization levers
- Band: "confidence" answers "where is the line", "prediction" answers "where
  will the next observation land" (much wider - measured 9x at n = 44), "none"
  drops the ribbon when only the trend and R^2 are wanted. level picks
  90 / 95 / 99 %; extending the t table is how you add another level.
- Model: "linear" for a constant rate, "logarithmic" for diminishing returns
  and learning curves, "exponential" for compounding growth. A power law (fit
  ln y on ln x) is one more entry in the MODELS map - the fitting code does not
  change.
- outlierThreshold: 2 standard errors is the usual first cut; 3 for noisy
  telemetry where only the screaming ones matter; 1.5 when the point of the
  chart is to surface candidates for review.
- Density: the plot is h-[300px] with 7% / 9% domain padding. A shorter plot
  wants more y padding, because the outlier labels live in that band.
- Palette: swap the observation hue to another var(--chart-N) to match a host
  palette, but keep the fit on a theme-flipping token - a fixed chart token is
  exactly what makes a line vanish against its own dots in one of the themes.
- Interaction: dots are inert by design. Give Scatter an onClick and route it
  to the item id if a point should open a record; the tooltip payload already
  carries the whole contract item plus its fitted value and residual.

Concepts

Least squares, computed here — the slope, intercept, R², residual standard error and every band edge come out of about forty lines of arithmetic plus one table of Student's t values. The table is read conservatively: a sample size between two rows takes the lower degrees of freedom, so the band errs wide rather than narrow.
Confidence band vs prediction band — both are t·s·sqrt(k + 1/n + (x−x̄)²/Sxx) and the only difference is k. With k = 0 the ribbon says where the line is; with k = 1 it also carries a new observation's own scatter and says where the next point will land. On the 44-run demo the second is 9× taller — same data, a completely different promise.
The pinch at x̄ — a confidence band is a hyperbola, narrowest at the mean of x and flaring at both ends, because the further you extrapolate the more the uncertainty in the slope costs. Measured on the demo: 2.15× wider at the domain edge than at x̄.
Studentised, not raw, residuals — an observation with high leverage drags the line toward itself, which shrinks its own residual and hides it. Dividing by sqrt(1 − h) puts every point on one scale before the threshold is applied, so an outlier at the edge of the range is as visible as one in the middle.
Flag, never drop — a point past the threshold gets a diamond and its name, and stays in the fit. Excluding it would silently change the very numbers the card reports; deciding to exclude an observation belongs to the person reading the chart.
R² describes the scale it was fitted on — the exponential model minimises squared error in ln y, so its R² is an R² of ln y. The tile says so instead of quietly presenting it as fit quality on y.
Degeneracy is a rendered sentence, not a blank rectangle — fewer than three points, a constant x, a constant y and an exact fit each hit a named branch that still plots the observations and explains what could not be computed. R² prints an em dash where 1 − SSE/SST is 0/0; it never prints NaN and never quietly prints 0.

Regression Scatter

p95 latency vs. concurrency

p95 latency vs. concurrency

Weekly active users since launch

Time on task by repetition

No relationship to find

p95 latency vs. concurrency

p95 latency vs. concurrency

p95 latency vs. concurrency

p95 latency vs. concurrency

Two observations

One predictor value, six responses

Response never moves

Exactly on the line

Log model, values it cannot take

Installation

Prompt

Concepts

On This Page

p95 latency vs. concurrency

p95 latency vs. concurrency

Weekly active users since launch

Time on task by repetition

No relationship to find

p95 latency vs. concurrency

p95 latency vs. concurrency

p95 latency vs. concurrency

p95 latency vs. concurrency

Two observations

One predictor value, six responses

Response never moves

Exactly on the line

Log model, values it cannot take