Fits a line to a set of data points using least squares.
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)
NOBS — Number of
observations. (Input)
Default: NOBS = size (XDATA,1).
STAT — Vector of length 12 containing the statistics described below. (Output)
I |
STAT(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 |
Generic: CALL RLINE (XDATA, YDATA, B0, B1 [,…])
Specific: The specific interface names are S_RLINE and D_RLINE.
Single: CALL RLINE (NOBS, XDATA, YDATA, B0, B1, STAT)
Double: The double precision name is DRLINE.
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.
Informational error
Type Code
4 1 Each (x, y) point contains NaN (not a number). There are no valid data.
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
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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