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NAG[g02ecc] NAG[nag_cp_stat] - Calculates and values from residual sums of squares

Calling Sequence

g02ecc(mean, n, sigsq, tss, nterms, rss, rsq, cp, 'nmod'=nmod, 'fail'=fail)

nag_cp_stat(. . .)

Parameters

mean - String;

On entry: indicates if a mean term is to be included.

A mean term, intercept, will be included in the model.

The model will pass through the origin, zero-point.

Constraint: "Nag_MeanInclude" or "Nag_MeanZero". .

n - integer;

On entry: , the number of observations used in the regression model.

Constraint: must be greater than , where is the largest number of independent variables fitted (including the mean if fitted). .

sigsq - float;

On entry: the best estimate of true variance of the errors, .

Constraint: . .

tss - float;

On entry: the total sum of squares for the regression model.

Constraint: . .

nterms - Vector(1..nmod, datatype=integer[kernelopts('wordsize')/8]);

On entry: must contain the number of independent variables (not counting the mean) fitted to the th model, for .

rss - Vector(1..nmod, datatype=float[8]);

On entry: must contain the residual sum of squares for the th model.

Constraint: , for . .

rsq - Vector(1..nmod, datatype=float[8]);

On exit: contains the -value for the th model, for .

cp - Vector(1..nmod, datatype=float[8]);

On exit: contains the -value for the th model, for .

'nmod'=nmod - integer; (optional)

On entry: the number of regression models.

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_cp_stat (g02ecc) calculates and -values from the residual sums of squares for a series of linear regression models.

Description

When selecting a linear regression model for a set of observations a balance has to be found between the number of independent variables in the model and fit as measured by the residual sum of squares. The more variables included the smaller will be the residual sum of squares. Two statistics can help in selecting the best model.

a. represents the proportion of variation in the dependent variable that is explained by the independent variables.

where (if mean is fitted, otherwise ) and

, where .

The -values can be examined to find a model with a high -value but with small number of independent variables.

b. statistic.

where is the number of arguments (including the mean) in the model and is an estimate of the true variance of the errors. This can often be obtained from fitting the full model.

A well fitting model will have . is often plotted against to see which models are closest to the line.

nag_cp_stat (g02ecc) may be called after g02eac (nag_all_regsn) which calculates the residual sums of squares for all possible linear regression models.

Error Indicators and Warnings

"NE_BAD_PARAM"

On entry, argument had an illegal value.

"NE_INT"

On entry, . Constraint: .

"NE_INTERNAL_ERROR"

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.

"NE_MODEL_PARAMETERS"

On entry, number of arguments for model is too large for n. number of arguments .

"NE_REAL"

On entry, . Constraint: .

"NE_REAL_ARRAY_ELEM_CONS"

On entry, value of : , .

Value of : .

	Accuracy
	Accuracy is sufficient for all practical purposes.

	Further Comments
	None.

Examples

mean := "Nag_MeanInclude":
n := 20:
sigsq := 0.06894097715299176:
tss := 5.063404019999999:
nmod := 32:
nterms := Vector([0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5], datatype=integer[kernelopts('wordsize')/8]):
rss := Vector([5.063404019999999, 5.021872981610836, 2.504400256872566, 2.033792558702955, 1.556302662527149, 1.536980701902808, 2.43809316825141, 1.746202334318434, 1.592101895299378, 1.496267665868361, 1.470697443158826, 1.458986090473173, 1.439684706601502, 1.438803545844649, 1.328730482955034, 1.085046933797314, 1.425685328311828, 1.390030525118499, 1.389409281541255, 1.320363732523133, 1.276355711100745, 1.25824207806747, 1.217854935490384, 1.064355044934491, 1.063352079567482, 0.9871461021926979, 1.219929564008994, 1.156529834681246, 1.038833684537899, 0.987127249579224, 0.9652626827261775, 0.9651736801418845], datatype=float[8]):
rsq := Vector(32, datatype=float[8]):
cp := Vector(32, datatype=float[8]):
NAG:-g02ecc(mean, n, sigsq, tss, nterms, rss, rsq, cp, 'nmod' = nmod):

rsq;

cp;

	See Also
	Draper N R and Smith H (1985) Applied Regression Analysis (2nd Edition) Wiley Weisberg S (1985) Applied Linear Regression Wiley g02 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.