All linear regression commands have been updated in Maple 2016 with a new option, summarize, that allows for the display of a summary for the given regression model.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X ≔ \mathrm{Vector}\left(\left[1\, 2\, 3\, 4\, 5\, 6\right]\, \mathrm{datatype}\=\mathrm{float}\right)\:$

$Y ≔ \mathrm{Vector}\left(\left[2\, 3\, 4\, 3.5\, 5.8\, 7\right]\, \mathrm{datatype}\=\mathrm{float}\right)\:$

By default, the Fit command returns the resulting regression model for the given model function:

$\mathrm{Fit}\left(a\+b\*t\+c\*t\^2\, X\, Y\, t\right)\;$

The summarize option includes a full summary for each of the regression coefficients, as well as values for the r-squared and adjusted r-squared for the model. Also, the solution module for regression commands has been extended with the ability to return values for r-squared, adjusted r-squared, and the value of the t-statistic for testing whether the corresponding regression coefficient is different than 0 and its corresponding probability.

The summarize option can also be used to return an embedded table, which contains more details on the residuals:

$\mathrm{Fit}\left(a\+b\*t\+c\*t\^2\, X\, Y\, t\, \mathit{summarize}\=\mathrm{embed}\right)\:$

Summary

Model: $1.9600000\+0.16500000t\+0.11071429t^2$ Coefficients Estimate Standard Error t-value P(>|t|) a $1.96000$ $1.17199$ $1.67237$ $0.193045$ b $0.165000$ $0.766748$ $0.215194$ $0.843415$ c $0.110714$ $0.107226$ $1.03253$ $0.377769$ R-squared: $0.925169$ Adjusted R-squared: $0.875282$ Residuals Residual Sum of Squares Residual Mean Square Residual Standard Error Degrees of Freedom $1.28771$ $0.429238$ $0.655163$ $3$ Five Point Summary Minimum First Quartile Median Third Quartile Maximum $-0.891429$ $-0.290357$ $0.155714$ $0.290595$ $0.548571$

The summarize option has also been added to all hypothesis testing commands. Previously, the infolevel command would have been required to print the results of a hypothesis test as a report.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X ≔ \mathrm{Array}\left(\left[9\, 10\, 8\, 4\, 8\, 3\, 0\, 10\, 15\, 9\right]\right)\:$

$\mathrm{OneSampleChiSquareTest}\left(X\, 7\, \mathrm{confidence}\=.95\, \mathrm{summarize}\=\mathrm{embed}\right)\:$

The DataSummary, FivePointSummary, and FrequencyTable commands can also accept a summarize option as well as be used to return summary statistics for DataFrames:

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X ≔ \mathrm{DataFrame}\left(⟨\mathrm{Sample}\left(\mathrm{Uniform}\left(0\,1\right)\,\left[50\,2\right]\right)\|\mathrm{LinearAlgebra}:-\mathrm{RandomVector}\left(50\,\mathrm{generator}\=\mathrm{rand}\left(0..3\right)\right)⟩\right)$

$\mathrm{DataSummary}\left(X\,\mathrm{summarize}\=\mathrm{embed}\right)\:$

There are many new visualizations in Maple 2016 for statistics and data analysis, including new options for creating colorschemes using point values:

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$\mathrm{data}≔\mathrm{Matrix}\left(⟨\mathrm{Sample}\left(\mathrm{Uniform}\left(0\,1\right)\,\left[50\,2\right]\right) \| \mathrm{LinearAlgebra}:-\mathrm{RandomVector}\left(50\,\mathrm{generator}\=\mathrm{rand}\left(0..3\right)\right)⟩\right)$

Maple 2016 also introduces a new visualization in Statistics for generating heat maps. A heat map is a visualization method that represents the magnitude of the included data as a discrete density plot.

$$\begin{gathered} U ≔ ⟨\mathrm{seq}\left(0..10\right)⟩\: \\ V ≔ ⟨\mathrm{seq}\left(\sin \left(i\right)\, i\=0..10\right)⟩\: \\ W ≔ ⟨\mathrm{seq}\left(\cos \left(i\right)\, i\=0..10\right)⟩\: \end{gathered}$$

$\mathrm{CM}≔\mathrm{CorrelationMatrix}\left(\mathrm{Matrix}\left(\left[U\, V\, W\right]\right)\, \mathrm{ignore}\right)\;$

There are also two new visualizations related to Principal Component Analysis: Biplot, and ScreePlot.

$\mathrm{IrisDF}≔\mathrm{Import}\left(''datasets/iris.csv''\,\mathrm{base}\=\mathrm{datadir}\right)$

The new GridPlot command is useful for visualizing multidimensional datasets. GridPlot generates a matrix of plots corresponding to the columns of a dataset.

$\mathrm{GridPlot}\left(\mathrm{IrisDF}\left[\left[\mathrm{`Sepal\; Length`}\,\mathrm{`Sepal\; Width`}\,\mathrm{`Petal\; Length`}\,\mathrm{`Petal\; Width`}\right]\right]\,\mathrm{upper} \= \mathrm{ScatterPlot}\, \mathrm{lower}\=\mathrm{SunflowerPlot}\, \mathrm{width}\=600\, \mathrm{widthmode}\=\mathrm{pixels}\right)\;$