Fits a line to a set of data points using least squares.

Required Arguments

XDATA — Vector of length NOBS containing the x-values.   (Input)

YDATA — Vector of length NOBS containing the y-values.   (Input)

B0 — Estimated intercept of the fitted line.   (Output)

B1 — Estimated slope of the fitted line.   (Output)

Optional Arguments

NOBS — Number of observations.   (Input)
Default: NOBS = size (XDATA,1).

STAT — Vector of length 12 containing the statistics described below.   (Output)

I           ISTAT(I)

                                           1                                                                    Mean of XDATA

                                           2                                                                    Mean of YDATA

                                           3                                                                    Sample variance of XDATA

                                           4                                                                    Sample variance of YDATA

                                           5                                                                    Correlation

                                           6                                                                    Estimated standard error of B0

                                           7                                                                    Estimated standard error of B1

                                           8                                                                    Degrees of freedom for regression

                                           9                                                                    Sum of squares for regression

                                           10                                                                  Degrees of freedom for error

                                           11                                                                  Sum of squares for error

                                           12                                                                  Number of (x, y) points containing NaN (not a number) as either the x or  y value

FORTRAN 90 Interface

Generic:          CALL RLINE (XDATA, YDATA, B0, B1 [,…])

Specific:         The specific interface names are S_RLINE and D_RLINE.

FORTRAN 77 Interface

Single:            CALL RLINE (NOBS, XDATA, YDATA, B0, B1, STAT)

Double:          The double precision name is DRLINE.

Description

Routine RLINE fits a line to a set of (x, y) data points using the method of least squares. Draper and Smith (1981, pages 1− 69) discuss the method. The fitted model is

where (stored in B0) is the estimated intercept and (stored in B1) is the estimated slope. In addition to the fit, RLINE produces some summary statistics, including the means, sample variances, correlation, and the error (residual) sum of squares. The estimated standard errors of  are computed under the simple linear regression model. The errors in the model are assumed to be uncorrelated and with constant variance.

If the x values are all equal, the model is degenerate. In this case, RLINE sets
to zero and  to the mean of the y values.

Comments

Informational error

Type           Code

4                   1          Each (x, y) point contains NaN (not a number). There are no valid data.

Example

This example fits a line to a set of data discussed by Draper and Smith (1981, Table 1.1, pages 9− 33). The response y is the amount of steam used per month (in pounds), and the independent variable x is the average atmospheric temperature (in degrees Fahrenheit).

 

      USE RLINE_INT

      USE UMACH_INT

      USE WRRRL_INT

 

      IMPLICIT   NONE

      INTEGER    NOBS

      PARAMETER  (NOBS=25)

!

      INTEGER    NOUT

      REAL       B0, B1, STAT(12), XDATA(NOBS), YDATA(NOBS)

      CHARACTER  CLABEL(13)*15, RLABEL(1)*4

!

      DATA XDATA/35.3, 29.7, 30.8, 58.8, 61.4, 71.3, 74.4, 76.7, 70.7,&

           57.5, 46.4, 28.9, 28.1, 39.1, 46.8, 48.5, 59.3, 70.0, 70.0,&

           74.5, 72.1, 58.1, 44.6, 33.4, 28.6/

      DATA YDATA/10.98, 11.13, 12.51, 8.4, 9.27, 8.73, 6.36, 8.5,&

           7.82, 9.14, 8.24, 12.19, 11.88, 9.57, 10.94, 9.58, 10.09,&

           8.11, 6.83, 8.88, 7.68, 8.47, 8.86, 10.36, 11.08/

      DATA RLABEL/'NONE'/, CLABEL/' ', 'Mean of X', 'Mean of Y',&

           'Variance X', 'Variance Y', 'Corr.', 'Std. Err. B0',&

           'Std. Err. B1', 'DF Reg.', 'SS Reg.', 'DF Error',&

           'SS Error', 'Pts. with NaN'/

!

      CALL RLINE (XDATA, YDATA, B0, B1, STAT=STAT)

!

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) B0, B1

99999 FORMAT (' B0 = ', F7.2, '  B1 = ', F9.5)

      CALL WRRRL ('%/STAT', STAT, RLABEL, CLABEL, 1, 12, 1, &

                  FMT = '(12W10.4)')

!

      END

Output

 

B0 =   13.62  B1 =  -0.07983

                                STAT
Mean of X   Mean of Y  Variance X  Variance Y       Corr.  Std. Err. B0
      52.6          9.424       298.1       2.659     -0.8452         0.5815

Std. Err. B1     DF Reg.     SS Reg.    DF Error    SS Error  Pts. with NaN
0.01052           1       45.59          23       18.22              0

Figure 3- 5  Plot of the Data and the Least Squares Line

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