Kwik Plot

This program computes the Pearson correlation coefficient (R) for a user-supplied dataset of up to 100 (X, Y) pairs and then renders a scatter plot using a 17×25 character array. It calculates means (MX, MY), standard deviations (SX, SY), and the cross-product mean to derive R, guarding against division by zero when either standard deviation is zero. The scatter plot maps data points into a 17×24 grid stored in the string array A$, using a sequence of characters (“*”, “2”–”9″) to represent overplotted points at the same cell. The Y-axis is drawn with block-graphic vertical bar characters, and the X-axis labels are printed using TAB positioning with calculated interval values.

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Program Analysis

Program Structure

The program is divided into four logical phases:

1. Initialisation (lines 10–90): Prints a title in inverse video, dimensions the string array A$(17,25) and numeric arrays X(100), Y(100), and zeroes the accumulators.
2. Data entry (lines 100–180): Prompts the user for a sample size N and then collects each X/Y pair in a loop, clearing the screen between entries.
3. Statistics computation (lines 190–340): Accumulates sums to compute means MX, MY, standard deviations SX, SY, and the Pearson correlation coefficient R.
4. Scatter plot (lines 350–720): Finds the data range, normalises coordinates into the 17×24 grid, populates A$ with overplot symbols, and prints the chart with axis labels.

Statistical Computation

The program uses the computational form of variance and covariance. The mean-of-squares minus the square-of-means formula is used for standard deviations:

• SX = SQR((MSQX/N) - MX^2)
• SY = SQR((MSQY/N) - MY^2)
• R = ((CROSS/N) - (MX*MY)) / (SX*SY)

A guard at line 300 skips the R calculation if either standard deviation is zero (constant data), and line 330 prints an appropriate message. Note that ABS is applied before squaring at lines 230–240, which is mathematically redundant since squaring always yields a non-negative result, but causes no harm.

Overplot Symbol Encoding

Rather than using a simple presence/absence marker, the program encodes point density in the character stored at each grid cell. The cascade of IF tests at lines 560–640 must be evaluated top-to-bottom (highest to lowest) to correctly increment the count without skipping values:

Cell contents	Meaning
" "	No data point
"*"	1 point
"2"–"9"	2–9 overlapping points

The sequence saturates at 9; any additional points beyond 9 at the same cell are silently ignored because no IF branch matches "9" to increment it further.

Coordinate Normalisation

Data values are scaled to fit the grid using the formulae at lines 470–480:

• X(I) = INT(((X(I)/XRANGE)*16) + 1.5) — maps to rows 1–17
• Y(I) = INT(((Y(I)/YRANGE)*24) + 1.5) — maps to columns 1–24

The +1.5 offset effectively rounds to the nearest integer while shifting the origin from 0 to 1. This assumes all data values are non-negative; negative X or Y values would produce out-of-bounds indices and likely cause an error.

Bugs and Anomalies

• Loop variable mismatch (lines 660–700): The outer loop uses L as the control variable (FOR L=17 TO 1 STEP -1), but the loop body references I in the IF conditions and PRINT statements at lines 670–680. Since I was last set to N at the end of the normalisation loop, the axis labels and row selection are essentially broken. The variable should be L throughout.
• Only positive data supported: The range-finding loop (lines 350–400) only tracks the maximum values (XH, YH), and the normalisation divides by these maxima, so datasets containing zero or negative values will produce incorrect or erroneous results.
• A$ column dimension: A$ is dimensioned as (17,25) but only columns 1–24 are used; column 25 is never written, leaving one unused column per row.
• Unused variables: XRANGE and YRANGE are assigned the same values as XH and YH respectively (lines 410–420) and P is computed at line 440 for axis labelling, but Z is initialised to XH (line 450) and decremented by IX — the X-axis labels are thus printed in descending order, which is unusual for a scatter plot.
• Lines 950–970: A CLEAR / SAVE / RUN sequence follows the STOP at line 900 and is unreachable during normal execution; it serves as a manual save utility if entered directly.

Notable BASIC Idioms

• The title at line 10 uses inverse-video character escapes (%K%W%I%K%P%L%O%T) to display “KWIKPLOT” in reverse highlight.
• The horizontal axis border at line 710 is constructed from ZX81 block-graphic characters to draw a continuous double-width line across the chart.
• The TAB keyword is used at line 720 to position four numeric axis labels at evenly-spaced column positions in a single PRINT statement.