Statistics - Maple Help

 Statistics

Linear Regression

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.

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

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

 ${1.96000000000000}{+}{0.164999999999999}{}{t}{+}{0.110714285714286}{}{{t}}^{{2}}$ (1.1)

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.

 Summary: ---------------- Model: 1.9600000+.16500000*t+.11071429*t^2 ---------------- Coefficients:     Estimate  Std. Error  t-value  P(>|t|) a    1.9600    1.1720      1.6724   0.1930 b    0.1650    0.7667      0.2152   0.8434 c    0.1107    0.1072      1.0325   0.3778 ---------------- R-squared: 0.9252, Adjusted R-squared: 0.8753

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

Summary

Model:

${1.9600000}{+}{0.16500000}{}{t}{+}{0.11071429}{}{{t}}^{{2}}$

 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:

${0.925169}$

${0.875282}$

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 ${-}{0.891429}$ ${-}{0.290357}$ ${0.155714}$ ${0.290595}$ ${0.548571}$

Hypothesis Testing

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.

$\mathrm{with}\left(\mathrm{Statistics}\right):\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$

Chi-Square Test on One Sample

Null Hypothesis:

Sample drawn from population with standard deviation equal to 7

Alternative Hypothesis:

Sample drawn from population with standard deviation not equal to 7

 Sample Size Sample Standard Deviation Distribution Computed Statistic Computed p-value Confidence Interval ${10.}$ ${4.24788}$ ${\mathrm{ChiSquare}}{}\left({9}\right)$ ${3.31429}$ ${0.0989571}$ ${2.92184}{..}{7.75496}$

Result:

Accepted: This statistical test does not provide enough evidence to conclude that the null hypothesis is false.

Summary and Tabulation

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

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

 $\left[\begin{array}{cccc}{}& {1}& {2}& {3}\\ {1}& {0.814723686393179}& {0.276025076998578}& {3}\\ {2}& {0.905791937075619}& {0.679702676853675}& {2}\\ {3}& {0.126986816293506}& {0.655098003973841}& {1}\\ {4}& {0.913375856139019}& {0.162611735194631}& {2}\\ {5}& {0.632359246225410}& {0.118997681558377}& {1}\\ {6}& {0.0975404049994095}& {0.498364051982143}& {0}\\ {7}& {0.278498218867048}& {0.959743958516081}& {1}\\ {8}& {0.546881519204984}& {0.340385726666133}& {0}\\ {\mathrm{...}}& {\mathrm{...}}& {\mathrm{...}}& {\mathrm{...}}\end{array}\right]$ (3.1)

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

 1 2 3 mean ${0.5661101110386353}$ ${0.48987882283825}$ ${1.22}$ standarddeviation ${0.3125414653315035}$ ${0.27855206779473884}$ ${1.1830434635864795}$ skewness ${-}{0.3716519256798299}$ ${0.11582452515575123}$ ${0.3106598115832435}$ kurtosis ${1.729650721370971}$ ${1.7837876411157099}$ ${1.5501229720154914}$ minimum ${0.031832846377420676}$ ${0.011902069501241397}$ ${0.0}$ maximum ${0.9705927817606157}$ ${0.9597439585160811}$ ${3.0}$ cumulativeweight ${50.0}$ ${50.0}$ ${50.0}$



Visualizations

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

 $\left[\begin{array}{c}{\mathrm{50 x 3}}{\mathrm{Matrix}}\\ {\mathrm{Data Type:}}{\mathrm{anything}}\\ {\mathrm{Storage:}}{\mathrm{rectangular}}\\ {\mathrm{Order:}}{\mathrm{Fortran_order}}\end{array}\right]$ (4.1)

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.

 $\left[\begin{array}{ccc}{1.}& {-}{0.116741765101327}& {-}{0.354242435116850}\\ {-}{0.116741765101327}& {1.}& {0.0701662833954325}\\ {-}{0.354242435116850}& {0.0701662833954325}& {1.}\end{array}\right]$ (4.2)

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

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

 ${\mathrm{IrisDF}}{≔}\left[\begin{array}{cccccc}{}& {\mathrm{Sepal Length}}& {\mathrm{Sepal Width}}& {\mathrm{Petal Length}}& {\mathrm{Petal Width}}& {\mathrm{Species}}\\ {1}& {5.1}& {3.5}& {1.4}& {0.2}& {"setosa"}\\ {2}& {4.9}& {3}& {1.4}& {0.2}& {"setosa"}\\ {3}& {4.7}& {3.2}& {1.3}& {0.2}& {"setosa"}\\ {4}& {4.6}& {3.1}& {1.5}& {0.2}& {"setosa"}\\ {5}& {5}& {3.6}& {1.4}& {0.2}& {"setosa"}\\ {6}& {5.4}& {3.9}& {1.7}& {0.4}& {"setosa"}\\ {7}& {4.6}& {3.4}& {1.4}& {0.3}& {"setosa"}\\ {8}& {5}& {3.4}& {1.5}& {0.2}& {"setosa"}\\ {\mathrm{...}}& {\mathrm{...}}& {\mathrm{...}}& {\mathrm{...}}& {\mathrm{...}}& {\mathrm{...}}\end{array}\right]$ (4.3)

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

 $\mathrm{Sepal Length}$ $\mathrm{Sepal Width}$ $\mathrm{Petal Length}$ $\mathrm{Petal Width}$