World of Ham Radio 1997/WOHR97_AmSoft_(1997-02-01).iso/antenna/ant_21/prog/linreg.bas

BASIC Source File | 1997-02-01 | 5KB | 171 lines

     REM   LINREG.BAS
         cls: PRINT : PRINT " This program fits a straight line to a given set of coordinates"
     PRINT " using the method of least squares.  The equation of the line,"
     PRINT " coefficient of determination, coefficient of correlation and standard"
     PRINT " error of estimate are printed.  Once the line has been fitted, you may"
     PRINT " predict values of y for given values of x."
     PRINT
     PRINT " From SOME COMMON BASIC PROGRAMS, 3rd edition, by Lon Poole and"
     PRINT " Mary Borchers, Osborne/McGraw-Hill, Berkeley CA, 1979.  The authors"
     PRINT " state that the programs had been tested on a Wang 2200 and the"
     PRINT " Commodore PET (ancient history!).  Adapted where necessary to"
     PRINT " Microsoft QuickBasic 4.5, and modified for more aesthetic and useful"
     PRINT " output (with attention to curve-fitting for programmers) and compiled"
     PRINT " by Orrin C. Winton WN1Z, 11/94 and 11/95."
     PRINT
     PRINT " The plot routine came from PROGRAMMING WITH BASIC 3rd ed., by"
     PRINT " Byron S. Gottfried, McGraw-Hill, NY, 1986, extensively modified by"
     PRINT " O.C. Winton.  The menu program is from ADVANCED QuickBASIC, by Ken"
     PRINT " Knecht, Scott, Foresman and Company, Glenview, Illinois, 1989"
     PRINT " and is modified only slightly."

     PRINT
     PRINT " linear regression"
     PRINT
     PRINT " number of known points:  ";
     INPUT n
     DIM x(30)
     DIM y(30)
     DIM o(30)
     DIM p(30)
     j = 0
     k = 0
     l = 0
     m = 0
     r2 = 0

     REM   loop to enter coordinates of points
     FOR i = 1 TO n
         PRINT " x,y of point"; i;
         INPUT x(i), y(i)
         REM   accumulate intermediate sums
         j = j + x(i)
         k = k + y(i)
         l = l + x(i) ^ 2
         m = m + y(i) ^ 2
         r2 = r2 + x(i) * y(i)
     NEXT i

     REM   compute curve coefficient
     b = (n * r2 - k * j) / (n * l - j ^ 2)
     a = (k - b * j) / n
     PRINT
     PRINT " f(x) = ("; b; "* x) + "; a

     REM   compute regression analysis
     j = b * (r2 - j * k / n)
     m = m - k ^ 2 / n
     k = m - j
     PRINT
     r2 = j / m
     PRINT " coefficient of determination (r^2) = "; r2
     PRINT " coefficient of correlation         = "; SQR(r2)
     IF k < 0 OR (n - 2) <= 0 THEN GOTO d
     PRINT " standard error of estimate         = "; SQR(k / (n - 2)): GOTO e
d:       PRINT " standard error of estimate         = "
e:       PRINT

     REM   estimate y-coordinates of points with entered x-coordinates
     INPUT " do you wish to do interpolation?  enter 'y' for yes"; y$
     IF y$ = "y" THEN
         PRINT " enter -999 to quit interpolation"
         GOTO b
     ELSE GOTO c
     END IF

b:       PRINT " x = ";
     INPUT x
     IF x = -999 THEN GOTO c
     REM   restart or end program?
     PRINT " y = "; a + b * x
     PRINT
     GOTO b
c:       REM


2115 ' ******* Prepare to plot regression-equation y-values against
2116 '         user-input x-values.  Not user-input y-values.
2117 '
2120 FOR i = 1 TO n
2122     o(i) = x(i)
2124 NEXT i

2126 FOR i = 1 TO n
2128     p(i) = b * (o(i)) + a
2130 NEXT i

2270 ' ******* Find Largest and Smallest X and Y (the user-input x,y values)
2280 '
2290 XMAX = -100000!: YMAX = -100000!: XMIN = 100000!: YMIN = 100000!
2300 FOR i = 1 TO n
2310    IF x(i) > XMAX THEN XMAX = x(i)
2320    IF y(i) > YMAX THEN YMAX = y(i)
2330    IF x(i) < XMIN THEN XMIN = x(i)
2340    IF y(i) < YMIN THEN YMIN = y(i)
2350 NEXT i
2360
2370 ' ******* Scale the Xs and Ys
2380 '
2390 FOR i = 1 TO n
2400     x(i) = 29 + INT(280 * (x(i) - XMIN) / (XMAX - XMIN))
2410     y(i) = 189 - INT(150 * (y(i) - YMIN) / (YMAX - YMIN))
2420 NEXT i

2470 ' ******* Plot the Graphical Display of user-input x and y values
2480 '
2490 SCREEN 9
2500 LINE (19, 29)-(19, 199): LINE -(319, 199)
2510 FOR IY = 59 TO 179 STEP 20: LINE (19, IY)-(23, IY): NEXT IY
2520 FOR IX = 39 TO 299 STEP 20: LINE (IX, 199)-(IX, 195): NEXT IX
2530 '
2540 FOR i = 1 TO n
2550     PSET (x(i), y(i)): LINE (x(i), y(i) - 2)-(x(i) - 4, y(i) + 2)
2560     LINE -(x(i) + 4, y(i) + 2): LINE -(x(i), y(i) - 2)
2570 NEXT i
2580 '
2590 FOR i = 1 TO n - 1
2600     LINE (x(i), y(i))-(x(i + 1), y(i + 1))
2610 NEXT i

2770 ' ******* Find Largest and Smallest o and p
2780 '
2790 OMAX = -100000!: PMAX = -100000!: OMIN = 100000!: PMIN = 100000!
2800 FOR i = 1 TO n
2810    IF o(i) > OMAX THEN OMAX = o(i)
2820    IF p(i) > PMAX THEN PMAX = p(i)
2830    IF o(i) < OMIN THEN OMIN = o(i)
2840    IF p(i) < PMIN THEN PMIN = p(i)
2850 NEXT i
2860
2870 ' ******* Scale the Os and Ps
2880 '
2890 FOR i = 1 TO n
2900     o(i) = 29 + INT(280 * (o(i) - OMIN) / (OMAX - OMIN))
2910     p(i) = 189 - INT(150 * (p(i) - PMIN) / (PMAX - PMIN))
2920 NEXT i

3000 ' ******* Plot the regression equation y-values against
3002 '         user-input x values.  Not user-input y values.
3010 '
3015 COLOR 4
3020 FOR i = 1 TO (n - 1)
3030     LINE (o(i), p(i))-(o(i + 1), p(i + 1))
3040 NEXT i

3045 COLOR 7
3050 PRINT " f(x) = ("; b; "* x) + "; a
3060 PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT : PRINT
3064 PRINT " White curve w/markers: your x,y inputs."
3066 COLOR 4: PRINT " Red curve is eqn's y based on your x-inputs."
3068 PRINT " Eqn's fit is close to perfect if red line overwrites white line."
3069 COLOR 2
3070 INPUT " hit any key to end LINEAR REGRESSION sub-program", dummy
3080 RUN "menu"
3099 END