Statistics

This program performs statistical analysis including standard deviation, mean, linear regression, and trend line calculation on paired X/Y data sets. The user selects one of three modes — Statistics (X only), Regression, or Trend — before entering data values one at a time. Running totals for sums, sums of squares, and cross-products (SXTY) are accumulated incrementally, allowing standard deviation and mean to be updated after each entry using the computational formula SDX = SQR((E – N*CMX²)/(N-1)). Entering X = -9999 halts input cleanly, while a value where A – P < -10000 triggers the final regression/trend output at line 500. The slope and Y-intercept are computed from the accumulated sums using the standard least-squares formulas.

Program Analysis

Program Structure

The program is organized into four logical phases:

1. Initialization (lines 3–11): All accumulators are zeroed and mode variable P is prepared.
2. Menu and mode selection (lines 10–20): The user chooses between Statistics (1), Regression (2), or Trend (3) via INPUT P.
3. Data entry loop (lines 96–310): Repeated INPUT of X (and conditionally Y) values with live display of running statistics.
4. Final output (lines 500–530): Full regression results printed after the sentinel value triggers exit from the loop.

Accumulator Variables

Data Entry and Sentinel Logic

The data entry loop begins at line 96. Two sentinel mechanisms are used. Entering -9999 at line 102 triggers STOP, aborting the program entirely. The more interesting mechanism at line 101 checks IF A-P<-10000: because P is 1, 2, or 3, subtracting it from a large negative value like -9999 gives approximately -10000 or slightly less, so an input of -9999 is intended to route to the output section at line 500. However, the STOP at line 102 intercepts -9999 first, meaning line 101’s branch to line 500 would only activate for values below roughly -10001 + P — a subtle ordering issue. In practice, entering a value such as -10002 would correctly route to line 500 without stopping.

Standard Deviation Formula

The program uses the computational (single-pass) formula for sample standard deviation: SDX = SQR((E - N*CMX²) / (N-1)), which avoids storing all individual values. This is memory-efficient and well-suited to the constrained environment. Guards at lines 165 and 245 skip the calculation when N=1 to avoid division by zero.

Regression Calculation

At line 500, the least-squares slope is computed as B = (SXTY - N*CMX*CMY) / (E - N*CMX²), which is the standard formula expressed in terms of accumulated sums. The Y-intercept follows as C = CMY - B*CMX. These are algebraically equivalent to the textbook formulas using raw sums of deviations. Line 530 conditionally prints the trend line equation in the form Y = C + B*X only when mode 3 (Trend) is selected.

Display Techniques

The program makes extensive use of PRINT AT for precise screen positioning, overlaying live-updating statistics (mean and standard deviation) at fixed screen coordinates during Statistics mode. In Regression/Trend modes, the row variable R is incremented at line 216 after each Y entry to scroll data down the screen, providing a running table of entered X/Y pairs. The column positions (3, 12, 16) give a rough tabular layout without using TAB in the loop.

Notable Anomalies

• In Statistics mode (P=1), the Y input section (lines 200–260) is bypassed by the GOTO 300 at line 180, but SDY and CMY are never initialized, which would produce an error if they were accidentally referenced — they are not, so this is harmless.
• The row counter R is initialized to 1 at line 6 and never reset, so entering more than roughly 18 data pairs in Regression/Trend mode would cause PRINT AT R,... to wrap or error.
• In Statistics mode the live display at line 300 updates SDX and CMX on screen after each X entry, providing immediate feedback, which is a useful interactive design choice.

   3 LET TX=0
   4 LET TY=0
   5 LET N=0
   6 LET R=1
   7 LET E=0
   8 LET D=0
   9 LET SXTY=0
  10 PRINT AT 4,10;"[C][H][O][O][S][E]█[T][E][S][T]";AT 7,8;"1. STATISTICS";AT 9,8;"2. REGRESSION";AT 11,8;"3. TREND"
  11 LET SDX=0
  20 INPUT P
  50 CLS
  60 IF P=1 THEN PRINT AT 4,2;"[S][T][A][N][.]█[D][E][V][.][=]";AT 5,8;"[M][E][A][N][=]"
  85 IF P=1 THEN GOTO 96
  90 PRINT "    X","  Y"
  96 PRINT AT 20,1;"TYPE ONE X-VALUE-[X][=][-][9][9][9][9]█[T][O]█[R][U][N]"
 100 INPUT A
 101 IF A-P<-10000 THEN GOTO 500
 102 IF A=-9999 THEN STOP
 105 IF P<>1 THEN PRINT AT R,3;A;AT R,12;"█"
 130 LET TX=TX+A
 140 LET E=E+A**2
 150 LET N=N+1
 160 LET CMX=TX/N
 165 IF N=1 THEN GOTO 180
 170 LET SDX=SQR ((E-N*CMX**2)/(N-1))
 180 IF P=1 THEN GOTO 300
 200 PRINT AT 10,20;"[Y]"
 210 INPUT Y
 215 PRINT AT R,16;Y
 216 LET R=R+1
 220 LET TY=TY+Y
 230 LET D=D+Y**2
 240 LET CMY=TY/N
 245 IF N=1 THEN GOTO 260
 250 LET SDY=SQR ((D-N*CMY**2)/(N-1))
 260 LET SXTY=SXTY+A*Y
 270 GOTO 96
 300 PRINT AT 4,13;SDX;AT 5,13;CMX
 310 GOTO 96
 500 LET B=(SXTY-N*CMX*CMY)/(E-N*CMX**2)
 501 LET C=CMY-B*CMX
 505 CLS
 510 PRINT "STAN DEV X=";SDX
 511 PRINT TAB 9;"Y=";SDY
 512 PRINT "CUR MEAN X=";CMX
 513 PRINT TAB 9;"Y=";CMY
 520 PRINT "Y-INTCPT= ";C
 525 PRINT "SLOPE= ";B
 530 IF P=3 THEN PRINT AT 9,0;"TREND LINE EQ> Y=";C;"+";B;"X"