Domain: Natural Science — Statistics & Data Science
Target concept: Autocorrelation: The residuals exhibit a continuous positive-negative pattern along the time axis.

Video generation prompt: The figure shows a coordinate axis, with the horizontal axis representing time and the vertical axis representing the metric. A set of residual points related to autocorrelation is plotted on this coordinate axis.

Evaluation guide:
(i) Target concept: Autocorrelation in regression residuals manifested as deterministic sign alternation over time.
Minimum mechanism: Residuals must be modeled as a first-order autoregressive process (AR(1)) with negative coefficient near −1, producing near-perfect oscillatory behavior; visual alternation is sufficient proxy under pedagogical constraints.
(ii)Storyline: Frame 1–2: Clean coordinate system appears, axes labeled correctly. Frame 3–4: First residual point appears on upper half-plane. Frame 5–6: Second point appears on lower half-plane, strictly right of first. Frame 7–8: Third point appears upper, fourth lower, fifth upper; each new point emerges left-to-right without overlap or erasure. Perspective is fixed front-facing 2D graph view; no camera movement, zoom, or rotation; all elements remain fully within frame boundaries at all times.

Manual:
Experimental Procedure
1. Display a clean 2D coordinate axis with horizontal axis labeled "Time" and vertical axis labeled "Residual".
2. Plot five distinct dot-shaped points left-to-right in chronological order along the axis.
3. Alternate point positions strictly above and below the horizontal axis (e.g., +, −, +, −, +).
Observation of Experimental Phenomena
Five points appear sequentially left-to-right; each adjacent pair lies on opposite sides of the horizontal axis; no point lies on the axis; all points are equally legible and unoccluded.
Summary of Experimental Principles
Autocorrelation is indicated by systematic sign alternation in residuals over time — a continuous positive-negative pattern along the time axis reflects lag-1 dependence in error terms.

Prompt Grounding rubric:
level_1: No coordinate axis is shown; the horizontal axis is not labeled as time and the vertical axis is not labeled as the residual/metric value; no residual points are plotted; there is no sense of a time-ordered sequence.
level_2: A coordinate axis appears, but it is oriented incorrectly (e.g., time runs vertically and the metric runs horizontally) or its labels are missing/swapped; alternatively, residual points appear but are scattered without any left-to-right time ordering (e.g., a later point sits to the left of an earlier one).
level_3: A 2D coordinate axis is present with the horizontal axis labeled as time and the vertical axis labeled as the residual/metric value; at least three residual points (dots) are plotted, positioned left-to-right in increasing time order; there is no requirement yet on whether points sit above or below the horizontal axis.
level_4: All conditions for score 3 are met; in addition, at least five distinct residual points are plotted left-to-right in strictly increasing time order, each rendered as a single clearly visible dot sitting either above or below the horizontal axis line (never touching the axis itself), with no two points overlapping and no extraneous labels, arrows, or shapes added to the plot.
level_5: All conditions for score 4 are met; in addition, exactly five residual points are shown, spaced along the time axis clearly enough that their left-to-right order is unambiguous at a glance, the full axis and every point remain inside the frame at all times with no cropping, and nothing besides the axis, its two labels, and the five points is drawn on the chart.

Scientific and Causal Correctness rubric:
level_1: The plotted points show no sign-based structure consistent with autocorrelation: all points fall on the same side of the horizontal axis, or their above/below placement looks randomly scattered with no alternating pattern; or the axes are mislabeled so the horizontal axis no longer represents time (e.g., labeled 'iteration' or 'frequency').
level_2: Axis labels correctly represent time (horizontal) and residual/metric (vertical), but the above/below sign sequence shows no consistent alternation (for example two points above followed by two below followed by one above), so at least three consecutive points share the same sign.
level_3: Axis labels are correct; at least four residual points are plotted in time order; among these, sign alternation (a point above the axis followed by one below, or vice versa) is visible in at least three adjacent pairs, giving clear visual evidence of the oscillating positive/negative pattern associated with negative-lag autocorrelation.
level_4: All conditions for score 3 are met; in addition, no point breaks the alternating sign pattern anywhere in the visible sequence, no point sits exactly on the horizontal axis (which would make its sign ambiguous), and all points remain distinct and non-overlapping so the alternation is unambiguous to a viewer.
level_5: All conditions for score 4 are met; in addition, every adjacent pair among all five points shows a sign reversal (a complete +,−,+,−,+ or −,+,−,+,− run with zero exceptions), matching the near-perfect oscillation expected from an AR(1) process with a coefficient near −1; the distances of the points from the axis are visually comparable in scale, with no single point so much larger than the others that it reads as an outlier rather than part of the oscillating pattern.

Spatiotemporal Consistency rubric:
level_1: The axis disappears and reappears, or residual points jump directly from one location to another without ever appearing in between; the axis rotates, stretches, or changes scale partway through the clip; or the overall lighting/perspective of the scene changes abruptly.
level_2: The axis stays visible but is stretched, skewed, or rescaled unevenly over time; residual points flicker, vanish and reappear, or change size/opacity inconsistently between frames; or a later point in time visibly appears on screen before an earlier one.
level_3: The axis stays fixed in position, orientation, and scale for the whole clip; all five residual points appear one at a time in left-to-right order with no point popping in out of sequence and no point hidden behind another; there is no visible scene cut or re-rendering jump partway through.
level_4: All conditions for score 3 are met; in addition, each new point's appearance (if animated) moves smoothly and only in the left-to-right direction consistent with time order, no point enters from an unexpected direction or angle, and there is no visible pop in brightness or shadow as each new point appears.
level_5: All conditions for score 4 are met; in addition, every point appears fully formed at its final position with no visible growing, stretching, or morphing beforehand; the axis lines look consistently straight and steady with no visible wobble; and the appearance of each new point looks smooth to the eye with no visible stutter or flicker.