(maxima.info)Functions and Variables for stats
83.3 Functions and Variables for stats
======================================
-- Option variable: stats_numer
Default value: 'true'
If 'stats_numer' is 'true', inference statistical functions return
their results in floating point numbers. If it is 'false', results
are given in symbolic and rational format.
-- Function: test_mean
test_mean (<x>)
test_mean (<x>, <options> ...)
This is the mean <t>-test. Argument <x> is a list or a column
matrix containing a one dimensional sample. It also performs an
asymptotic test based on the Central Limit Theorem if option
''asymptotic' is 'true'.
Options:
* ''mean', default '0', is the mean value to be checked.
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
* ''dev', default ''unknown', this is the value of the standard
deviation when it is known; valid values are: ''unknown' or a
positive expression.
* ''conflevel', default '95/100', confidence level for the
confidence interval; it must be an expression which takes a
value in (0,1).
* ''asymptotic', default 'false', indicates whether it performs
an exact <t>-test or an asymptotic one based on the Central
Limit Theorem; valid values are 'true' and 'false'.
The output of function 'test_mean' is an 'inference_result' Maxima
object showing the following results:
1. ''mean_estimate': the sample mean.
2. ''conf_level': confidence level selected by the user.
3. ''conf_interval': confidence interval for the population mean.
4. ''method': inference procedure.
5. ''hypotheses': null and alternative hypotheses to be tested.
6. ''statistic': value of the sample statistic used for testing
the null hypothesis.
7. ''distribution': distribution of the sample statistic,
together with its parameter(s).
8. ''p_value': p-value of the test.
Examples:
Performs an exact <t>-test with unknown variance. The null
hypothesis is H_0: mean=50 against the one sided alternative H_1:
mean<50; according to the results, the p-value is too great, there
are no evidence for rejecting H_0.
(%i1) load("stats")$
(%i2) data: [78,64,35,45,45,75,43,74,42,42]$
(%i3) test_mean(data,'conflevel=0.9,'alternative='less,'mean=50);
| MEAN TEST
|
| mean_estimate = 54.3
|
| conf_level = 0.9
|
| conf_interval = [minf, 61.51314273502712]
|
(%o3) | method = Exact t-test. Unknown variance.
|
| hypotheses = H0: mean = 50 , H1: mean < 50
|
| statistic = .8244705235071678
|
| distribution = [student_t, 9]
|
| p_value = .7845100411786889
This time Maxima performs an asymptotic test, based on the Central
Limit Theorem. The null hypothesis is H_0: equal(mean, 50) against
the two sided alternative H_1: not equal(mean, 50); according to
the results, the p-value is very small, H_0 should be rejected in
favor of the alternative H_1. Note that, as indicated by the
'Method' component, this procedure should be applied to large
samples.
(%i1) load("stats")$
(%i2) test_mean([36,118,52,87,35,256,56,178,57,57,89,34,25,98,35,
98,41,45,198,54,79,63,35,45,44,75,42,75,45,45,
45,51,123,54,151],
'asymptotic=true,'mean=50);
| MEAN TEST
|
| mean_estimate = 74.88571428571429
|
| conf_level = 0.95
|
| conf_interval = [57.72848600856194, 92.04294256286663]
|
(%o2) | method = Large sample z-test. Unknown variance.
|
| hypotheses = H0: mean = 50 , H1: mean # 50
|
| statistic = 2.842831192874313
|
| distribution = [normal, 0, 1]
|
| p_value = .004471474652002261
-- Function: test_means_difference
test_means_difference (<x1>, <x2>)
test_means_difference (<x1>, <x2>, <options> ...)
This is the difference of means <t>-test for two samples.
Arguments <x1> and <x2> are lists or column matrices containing two
independent samples. In case of different unknown variances (see
options ''dev1', ''dev2' and ''varequal' bellow), the degrees of
freedom are computed by means of the Welch approximation. It also
performs an asymptotic test based on the Central Limit Theorem if
option ''asymptotic' is set to 'true'.
Options:
*
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
* ''dev1', default ''unknown', this is the value of the standard
deviation of the <x1> sample when it is known; valid values
are: ''unknown' or a positive expression.
* ''dev2', default ''unknown', this is the value of the standard
deviation of the <x2> sample when it is known; valid values
are: ''unknown' or a positive expression.
* ''varequal', default 'false', whether variances should be
considered to be equal or not; this option takes effect only
when ''dev1' and/or ''dev2' are ''unknown'.
* ''conflevel', default '95/100', confidence level for the
confidence interval; it must be an expression which takes a
value in (0,1).
* ''asymptotic', default 'false', indicates whether it performs
an exact <t>-test or an asymptotic one based on the Central
Limit Theorem; valid values are 'true' and 'false'.
The output of function 'test_means_difference' is an
'inference_result' Maxima object showing the following results:
1. ''diff_estimate': the difference of means estimate.
2. ''conf_level': confidence level selected by the user.
3. ''conf_interval': confidence interval for the difference of
means.
4. ''method': inference procedure.
5. ''hypotheses': null and alternative hypotheses to be tested.
6. ''statistic': value of the sample statistic used for testing
the null hypothesis.
7. ''distribution': distribution of the sample statistic,
together with its parameter(s).
8. ''p_value': p-value of the test.
Examples:
The equality of means is tested with two small samples <x> and <y>,
against the alternative H_1: m_1>m_2, being m_1 and m_2 the
populations means; variances are unknown and supposed to be
different.
(%i1) load("stats")$
(%i2) x: [20.4,62.5,61.3,44.2,11.1,23.7]$
(%i3) y: [1.2,6.9,38.7,20.4,17.2]$
(%i4) test_means_difference(x,y,'alternative='greater);
| DIFFERENCE OF MEANS TEST
|
| diff_estimate = 20.31999999999999
|
| conf_level = 0.95
|
| conf_interval = [- .04597417812882298, inf]
|
(%o4) | method = Exact t-test. Welch approx.
|
| hypotheses = H0: mean1 = mean2 , H1: mean1 > mean2
|
| statistic = 1.838004300728477
|
| distribution = [student_t, 8.62758740184604]
|
| p_value = .05032746527991905
The same test as before, but now variances are supposed to be
equal.
(%i1) load("stats")$
(%i2) x: [20.4,62.5,61.3,44.2,11.1,23.7]$
(%i3) y: matrix([1.2],[6.9],[38.7],[20.4],[17.2])$
(%i4) test_means_difference(x,y,'alternative='greater,
'varequal=true);
| DIFFERENCE OF MEANS TEST
|
| diff_estimate = 20.31999999999999
|
| conf_level = 0.95
|
| conf_interval = [- .7722627696897568, inf]
|
(%o4) | method = Exact t-test. Unknown equal variances
|
| hypotheses = H0: mean1 = mean2 , H1: mean1 > mean2
|
| statistic = 1.765996124515009
|
| distribution = [student_t, 9]
|
| p_value = .05560320992529344
-- Function: test_variance
test_variance (<x>)
test_variance (<x>, <options>, ...)
This is the variance <chi^2>-test. Argument <x> is a list or a
column matrix containing a one dimensional sample taken from a
normal population.
Options:
* ''mean', default ''unknown', is the population's mean, when it
is known.
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
* ''variance', default '1', this is the variance value
(positive) to be checked.
* ''conflevel', default '95/100', confidence level for the
confidence interval; it must be an expression which takes a
value in (0,1).
The output of function 'test_variance' is an 'inference_result'
Maxima object showing the following results:
1. ''var_estimate': the sample variance.
2. ''conf_level': confidence level selected by the user.
3. ''conf_interval': confidence interval for the population
variance.
4. ''method': inference procedure.
5. ''hypotheses': null and alternative hypotheses to be tested.
6. ''statistic': value of the sample statistic used for testing
the null hypothesis.
7. ''distribution': distribution of the sample statistic,
together with its parameter.
8. ''p_value': p-value of the test.
Examples:
It is tested whether the variance of a population with unknown mean
is equal to or greater than 200.
(%i1) load("stats")$
(%i2) x: [203,229,215,220,223,233,208,228,209]$
(%i3) test_variance(x,'alternative='greater,'variance=200);
| VARIANCE TEST
|
| var_estimate = 110.75
|
| conf_level = 0.95
|
| conf_interval = [57.13433376937479, inf]
|
(%o3) | method = Variance Chi-square test. Unknown mean.
|
| hypotheses = H0: var = 200 , H1: var > 200
|
| statistic = 4.43
|
| distribution = [chi2, 8]
|
| p_value = .8163948512777689
-- Function: test_variance_ratio
test_variance_ratio (<x1>, <x2>)
test_variance_ratio (<x1>, <x2>, <options> ...)
This is the variance ratio <F>-test for two normal populations.
Arguments <x1> and <x2> are lists or column matrices containing two
independent samples.
Options:
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
* ''mean1', default ''unknown', when it is known, this is the
mean of the population from which <x1> was taken.
* ''mean2', default ''unknown', when it is known, this is the
mean of the population from which <x2> was taken.
* ''conflevel', default '95/100', confidence level for the
confidence interval of the ratio; it must be an expression
which takes a value in (0,1).
The output of function 'test_variance_ratio' is an
'inference_result' Maxima object showing the following results:
1. ''ratio_estimate': the sample variance ratio.
2. ''conf_level': confidence level selected by the user.
3. ''conf_interval': confidence interval for the variance ratio.
4. ''method': inference procedure.
5. ''hypotheses': null and alternative hypotheses to be tested.
6. ''statistic': value of the sample statistic used for testing
the null hypothesis.
7. ''distribution': distribution of the sample statistic,
together with its parameters.
8. ''p_value': p-value of the test.
Examples:
The equality of the variances of two normal populations is checked
against the alternative that the first is greater than the second.
(%i1) load("stats")$
(%i2) x: [20.4,62.5,61.3,44.2,11.1,23.7]$
(%i3) y: [1.2,6.9,38.7,20.4,17.2]$
(%i4) test_variance_ratio(x,y,'alternative='greater);
| VARIANCE RATIO TEST
|
| ratio_estimate = 2.316933391522034
|
| conf_level = 0.95
|
| conf_interval = [.3703504689507268, inf]
|
(%o4) | method = Variance ratio F-test. Unknown means.
|
| hypotheses = H0: var1 = var2 , H1: var1 > var2
|
| statistic = 2.316933391522034
|
| distribution = [f, 5, 4]
|
| p_value = .2179269692254457
-- Function: test_proportion
test_proportion (<x>, <n>)
test_proportion (<x>, <n>, <options> ...)
Inferences on a proportion. Argument <x> is the number of
successes in <n> trials in a Bernoulli experiment with unknown
probability.
Options:
* ''proportion', default '1/2', is the value of the proportion
to be checked.
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
* ''conflevel', default '95/100', confidence level for the
confidence interval; it must be an expression which takes a
value in (0,1).
* ''asymptotic', default 'false', indicates whether it performs
an exact test based on the binomial distribution, or an
asymptotic one based on the Central Limit Theorem; valid
values are 'true' and 'false'.
* ''correct', default 'true', indicates whether Yates correction
is applied or not.
The output of function 'test_proportion' is an 'inference_result'
Maxima object showing the following results:
1. ''sample_proportion': the sample proportion.
2. ''conf_level': confidence level selected by the user.
3. ''conf_interval': Wilson confidence interval for the
proportion.
4. ''method': inference procedure.
5. ''hypotheses': null and alternative hypotheses to be tested.
6. ''statistic': value of the sample statistic used for testing
the null hypothesis.
7. ''distribution': distribution of the sample statistic,
together with its parameters.
8. ''p_value': p-value of the test.
Examples:
Performs an exact test. The null hypothesis is H_0: p=1/2 against
the one sided alternative H_1: p<1/2.
(%i1) load("stats")$
(%i2) test_proportion(45, 103, alternative = less);
| PROPORTION TEST
|
| sample_proportion = .4368932038834951
|
| conf_level = 0.95
|
| conf_interval = [0, 0.522714149150231]
|
(%o2) | method = Exact binomial test.
|
| hypotheses = H0: p = 0.5 , H1: p < 0.5
|
| statistic = 45
|
| distribution = [binomial, 103, 0.5]
|
| p_value = .1184509388901454
A two sided asymptotic test. Confidence level is 99/100.
(%i1) load("stats")$
(%i2) fpprintprec:7$
(%i3) test_proportion(45, 103,
conflevel = 99/100, asymptotic=true);
| PROPORTION TEST
|
| sample_proportion = .43689
|
| conf_level = 0.99
|
| conf_interval = [.31422, .56749]
|
(%o3) | method = Asympthotic test with Yates correction.
|
| hypotheses = H0: p = 0.5 , H1: p # 0.5
|
| statistic = .43689
|
| distribution = [normal, 0.5, .048872]
|
| p_value = .19662
-- Function: test_proportions_difference
test_proportions_difference (<x1>, <n1>, <x2>, <n2>)
test_proportions_difference (<x1>, <n1>, <x2>, <n2>, <options>
...)
Inferences on the difference of two proportions. Argument <x1> is
the number of successes in <n1> trials in a Bernoulli experiment in
the first population, and <x2> and <n2> are the corresponding
values in the second population. Samples are independent and the
test is asymptotic.
Options:
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided' ('p1 # p2'),
''greater' ('p1 > p2') and ''less' ('p1 < p2').
* ''conflevel', default '95/100', confidence level for the
confidence interval; it must be an expression which takes a
value in (0,1).
* ''correct', default 'true', indicates whether Yates correction
is applied or not.
The output of function 'test_proportions_difference' is an
'inference_result' Maxima object showing the following results:
1. ''proportions': list with the two sample proportions.
2. ''conf_level': confidence level selected by the user.
3. ''conf_interval': Confidence interval for the difference of
proportions 'p1 - p2'.
4. ''method': inference procedure and warning message in case of
any of the samples sizes is less than 10.
5. ''hypotheses': null and alternative hypotheses to be tested.
6. ''statistic': value of the sample statistic used for testing
the null hypothesis.
7. ''distribution': distribution of the sample statistic,
together with its parameters.
8. ''p_value': p-value of the test.
Examples:
A machine produced 10 defective articles in a batch of 250. After
some maintenance work, it produces 4 defective in a batch of 150.
In order to know if the machine has improved, we test the null
hypothesis 'H0:p1=p2', against the alternative 'H0:p1>p2', where
'p1' and 'p2' are the probabilities for one produced article to be
defective before and after maintenance. According to the p value,
there is not enough evidence to accept the alternative.
(%i1) load("stats")$
(%i2) fpprintprec:7$
(%i3) test_proportions_difference(10, 250, 4, 150,
alternative = greater);
| DIFFERENCE OF PROPORTIONS TEST
|
| proportions = [0.04, .02666667]
|
| conf_level = 0.95
|
| conf_interval = [- .02172761, 1]
|
(%o3) | method = Asymptotic test. Yates correction.
|
| hypotheses = H0: p1 = p2 , H1: p1 > p2
|
| statistic = .01333333
|
| distribution = [normal, 0, .01898069]
|
| p_value = .2411936
Exact standard deviation of the asymptotic normal distribution when
the data are unknown.
(%i1) load("stats")$
(%i2) stats_numer: false$
(%i3) sol: test_proportions_difference(x1,n1,x2,n2)$
(%i4) last(take_inference('distribution,sol));
1 1 x2 + x1
(-- + --) (x2 + x1) (1 - -------)
n2 n1 n2 + n1
(%o4) sqrt(---------------------------------)
n2 + n1
-- Function: test_sign
test_sign (<x>)
test_sign (<x>, <options> ...)
This is the non parametric sign test for the median of a continuous
population. Argument <x> is a list or a column matrix containing a
one dimensional sample.
Options:
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
* ''median', default '0', is the median value to be checked.
The output of function 'test_sign' is an 'inference_result' Maxima
object showing the following results:
1. ''med_estimate': the sample median.
2. ''method': inference procedure.
3. ''hypotheses': null and alternative hypotheses to be tested.
4. ''statistic': value of the sample statistic used for testing
the null hypothesis.
5. ''distribution': distribution of the sample statistic,
together with its parameter(s).
6. ''p_value': p-value of the test.
Examples:
Checks whether the population from which the sample was taken has
median 6, against the alternative H_1: median > 6.
(%i1) load("stats")$
(%i2) x: [2,0.1,7,1.8,4,2.3,5.6,7.4,5.1,6.1,6]$
(%i3) test_sign(x,'median=6,'alternative='greater);
| SIGN TEST
|
| med_estimate = 5.1
|
| method = Non parametric sign test.
|
(%o3) | hypotheses = H0: median = 6 , H1: median > 6
|
| statistic = 7
|
| distribution = [binomial, 10, 0.5]
|
| p_value = .05468749999999989
-- Function: test_signed_rank
test_signed_rank (<x>)
test_signed_rank (<x>, <options> ...)
This is the Wilcoxon signed rank test to make inferences about the
median of a continuous population. Argument <x> is a list or a
column matrix containing a one dimensional sample. Performs normal
approximation if the sample size is greater than 20, or if there
are zeroes or ties.
See also 'pdf_rank_test' and 'cdf_rank_test'
Options:
* ''median', default '0', is the median value to be checked.
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
The output of function 'test_signed_rank' is an 'inference_result'
Maxima object with the following results:
1. ''med_estimate': the sample median.
2. ''method': inference procedure.
3. ''hypotheses': null and alternative hypotheses to be tested.
4. ''statistic': value of the sample statistic used for testing
the null hypothesis.
5. ''distribution': distribution of the sample statistic,
together with its parameter(s).
6. ''p_value': p-value of the test.
Examples:
Checks the null hypothesis H_0: median = 15 against the alternative
H_1: median > 15. This is an exact test, since there are no ties.
(%i1) load("stats")$
(%i2) x: [17.1,15.9,13.7,13.4,15.5,17.6]$
(%i3) test_signed_rank(x,median=15,alternative=greater);
| SIGNED RANK TEST
|
| med_estimate = 15.7
|
| method = Exact test
|
(%o3) | hypotheses = H0: med = 15 , H1: med > 15
|
| statistic = 14
|
| distribution = [signed_rank, 6]
|
| p_value = 0.28125
Checks the null hypothesis H_0: equal(median, 2.5) against the
alternative H_1: not equal(median, 2.5). This is an approximated
test, since there are ties.
(%i1) load("stats")$
(%i2) y:[1.9,2.3,2.6,1.9,1.6,3.3,4.2,4,2.4,2.9,1.5,3,2.9,4.2,3.1]$
(%i3) test_signed_rank(y,median=2.5);
| SIGNED RANK TEST
|
| med_estimate = 2.9
|
| method = Asymptotic test. Ties
|
(%o3) | hypotheses = H0: med = 2.5 , H1: med # 2.5
|
| statistic = 76.5
|
| distribution = [normal, 60.5, 17.58195097251724]
|
| p_value = .3628097734643669
-- Function: test_rank_sum
test_rank_sum (<x1>, <x2>)
test_rank_sum (<x1>, <x2>, <option>)
This is the Wilcoxon-Mann-Whitney test for comparing the medians of
two continuous populations. The first two arguments <x1> and <x2>
are lists or column matrices with the data of two independent
samples. Performs normal approximation if any of the sample sizes
is greater than 10, or if there are ties.
Option:
* ''alternative', default ''twosided', is the alternative
hypothesis; valid values are: ''twosided', ''greater' and
''less'.
The output of function 'test_rank_sum' is an 'inference_result'
Maxima object with the following results:
1. ''method': inference procedure.
2. ''hypotheses': null and alternative hypotheses to be tested.
3. ''statistic': value of the sample statistic used for testing
the null hypothesis.
4. ''distribution': distribution of the sample statistic,
together with its parameters.
5. ''p_value': p-value of the test.
Examples:
Checks whether populations have similar medians. Samples sizes are
small and an exact test is made.
(%i1) load("stats")$
(%i2) x:[12,15,17,38,42,10,23,35,28]$
(%i3) y:[21,18,25,14,52,65,40,43]$
(%i4) test_rank_sum(x,y);
| RANK SUM TEST
|
| method = Exact test
|
| hypotheses = H0: med1 = med2 , H1: med1 # med2
(%o4) |
| statistic = 22
|
| distribution = [rank_sum, 9, 8]
|
| p_value = .1995886466474702
Now, with greater samples and ties, the procedure makes normal
approximation. The alternative hypothesis is H_1: median1 <
median2.
(%i1) load("stats")$
(%i2) x: [39,42,35,13,10,23,15,20,17,27]$
(%i3) y: [20,52,66,19,41,32,44,25,14,39,43,35,19,56,27,15]$
(%i4) test_rank_sum(x,y,'alternative='less);
| RANK SUM TEST
|
| method = Asymptotic test. Ties
|
| hypotheses = H0: med1 = med2 , H1: med1 < med2
(%o4) |
| statistic = 48.5
|
| distribution = [normal, 79.5, 18.95419580097078]
|
| p_value = .05096985666598441
-- Function: test_normality (<x>)
Shapiro-Wilk test for normality. Argument <x> is a list of
numbers, and sample size must be greater than 2 and less or equal
than 5000, otherwise, function 'test_normality' signals an error
message.
Reference:
[1] Algorithm AS R94, Applied Statistics (1995), vol.44, no.4,
547-551
The output of function 'test_normality' is an 'inference_result'
Maxima object with the following results:
1. ''statistic': value of the <W> statistic.
2. ''p_value': p-value under normal assumption.
Examples:
Checks for the normality of a population, based on a sample of size
9.
(%i1) load("stats")$
(%i2) x:[12,15,17,38,42,10,23,35,28]$
(%i3) test_normality(x);
| SHAPIRO - WILK TEST
|
(%o3) | statistic = .9251055695162436
|
| p_value = .4361763918860381
-- Function: linear_regression
linear_regression (<x>)
linear_regression (<x> <option>)
Multivariate linear regression, y_i = b0 + b1*x_1i + b2*x_2i + ...
+ bk*x_ki + u_i, where u_i are N(0,sigma) independent random
variables. Argument <x> must be a matrix with more than one
column. The last column is considered as the responses (y_i).
Option:
* ''conflevel', default '95/100', confidence level for the
confidence intervals; it must be an expression which takes a
value in (0,1).
The output of function 'linear_regression' is an 'inference_result'
Maxima object with the following results:
1. ''b_estimation': regression coefficients estimates.
2. ''b_covariances': covariance matrix of the regression
coefficients estimates.
3. 'b_conf_int': confidence intervals of the regression
coefficients.
4. 'b_statistics': statistics for testing coefficient.
5. 'b_p_values': p-values for coefficient tests.
6. 'b_distribution': probability distribution for coefficient
tests.
7. 'v_estimation': unbiased variance estimator.
8. 'v_conf_int': variance confidence interval.
9. 'v_distribution': probability distribution for variance test.
10. 'residuals': residuals.
11. 'adc': adjusted determination coefficient.
12. 'aic': Akaike's information criterion.
13. 'bic': Bayes's information criterion.
Only items 1, 4, 5, 6, 7, 8, 9 and 11 above, in this order, are
shown by default. The rest remain hidden until the user makes use
of functions 'items_inference' and 'take_inference'.
Example:
Fitting a linear model to a trivariate sample. The last column is
considered as the responses (y_i).
(%i2) load("stats")$
(%i3) X:matrix(
[58,111,64],[84,131,78],[78,158,83],
[81,147,88],[82,121,89],[102,165,99],
[85,174,101],[102,169,102])$
(%i4) fpprintprec: 4$
(%i5) res: linear_regression(X);
| LINEAR REGRESSION MODEL
|
| b_estimation = [9.054, .5203, .2397]
|
| b_statistics = [.6051, 2.246, 1.74]
|
| b_p_values = [.5715, .07466, .1423]
|
(%o5) | b_distribution = [student_t, 5]
|
| v_estimation = 35.27
|
| v_conf_int = [13.74, 212.2]
|
| v_distribution = [chi2, 5]
|
| adc = .7922
(%i6) items_inference(res);
(%o6) [b_estimation, b_covariances, b_conf_int, b_statistics,
b_p_values, b_distribution, v_estimation, v_conf_int,
v_distribution, residuals, adc, aic, bic]
(%i7) take_inference('b_covariances, res);
[ 223.9 - 1.12 - .8532 ]
[ ]
(%o7) [ - 1.12 .05367 - .02305 ]
[ ]
[ - .8532 - .02305 .01898 ]
(%i8) take_inference('bic, res);
(%o8) 30.98
(%i9) load("draw")$
(%i10) draw2d(
points_joined = true,
grid = true,
points(take_inference('residuals, res)) )$
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