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What you will learn in Statistics Every Programmer Needs

Practical Python implementations and quantitative methods

by Gary Sutton

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Chapter by chapter

Concepts explained in this book

• Monte Carlo simulationA Monte Carlo simulation estimates quantities or evaluates outcomes by repeatedly sampling from specified probability distributions or stochastic processes.
• linear regressionLinear regression is a statistical modeling technique that represents the relationship between a response variable and one or more predictors with a linear function.
• decision treeA decision tree is a graphical decision-analysis model that represents choices, uncertain events, possible outcomes, probabilities, and payoffs as branching paths.
• critical path methodA critical path is the sequence of project activities with zero scheduling slack that determines the shortest possible project completion time.
• normal distributionA normal distribution is a continuous probability distribution with a symmetric bell-shaped density determined by its mean and standard deviation.
• arimaAn ARIMA model is an autoregressive integrated moving-average time-series model that represents temporal dependence using autoregression, differencing, and moving averages.
• labelA class label is a categorical output identifying the class assigned to an observation by a classification model.
• Markov chainMarkov analysis is a technique for modeling transitions among a finite set of states using transition probabilities to predict future states.
• control limitA lower control limit is the lower boundary on a control chart that indicates the expected minimum process variation under control conditions.
• residual errorResidual error is the difference between an observed response and its value predicted by a fitted model.
• p-valueA p-value is the probability, under a specified null hypothesis, of obtaining a result at least as extreme as the observed result.
• probability theoryProbability is a mathematical framework for assigning and analyzing the likelihood of uncertain events.
• read_csvread_csv is a pandas function that reads comma-separated or otherwise delimited text data into a data frame.
• inputA feature is an input attribute of an observation used by a predictive model to make decisions or generate predictions.
• Benford's lawA Benford distribution is a probability distribution in which the first significant digits of numerical values occur with logarithmically decreasing frequencies.
• thresholdA decision threshold is a feature-value boundary used by a decision tree to divide observations into branches.
• null hypothesisA null hypothesis is a specified default claim about a population or data-generating process that a hypothesis test evaluates evidence against.
• goodness-of-fit measureGoodness of fit is the degree to which a statistical model's predictions agree with observed data.
• transition matrixA transition matrix is a matrix whose entries specify the probabilities of moving between states in a stochastic process.
• permutationA permutation without replacement is an ordered arrangement in which each item may be selected at most once.
• differencingA differencing component transforms a time series by subtracting observations from earlier observations to reduce nonstationarity.
• leading digitA leading digit is the first significant digit of a numerical value when written in positional notation.
• decision nodeA decision node is a decision-tree node that evaluates a condition to split observations into branches.
• random variableA random variable is a function that assigns numerical values to outcomes of a random experiment.
• cumulative distribution functionA cumulative distribution function is a function that gives the probability that a random variable is less than or equal to a specified value.
• multiplication ruleThe multiplication rule of counting determines the number of outcomes formed by successive choices by multiplying the numbers of options at each stage.
• probability mass functionA probability mass function assigns an actual probability to each possible value of a discrete random variable, with all probabilities nonnegative and summing to one.
• binary outcomeA binary outcome is a response variable with exactly two possible categories, conventionally represented by 0 and 1.
• conditional probabilityConditional probability is the probability of an event given that another event or piece of information is known to hold.
• stationarityStationarity is the property of a stochastic process whose statistical characteristics, such as mean, variance, and autocovariance, remain invariant over time.
• Gini impurityGini impurity is a node-impurity measure equal to the probability of misclassifying an observation when labels are assigned according to the node's class distribution.
• chance nodeA chance node is a decision-tree node representing an uncertain event with multiple possible outcomes and associated probabilities.
• probability distributionA probability distribution specifies how probability is assigned across the possible values of a random variable.
• random forestA random forest is an ensemble model that combines predictions from multiple randomized decision trees.
• combination without replacementA combination without replacement is a selection in which order does not matter and selected items cannot be selected again.
• control chartA control chart is a statistical process-monitoring graph that displays measurements over time against reference limits to identify unusual variation.
• regression coefficientA regression coefficient is a parameter quantifying the modeled relationship between a predictor and a response, conditional on the other model terms.
• exponential moving averageAn exponentially weighted moving average is a time-series average that assigns geometrically decreasing weights to older observations.
• linear programmingA linear program is an optimization problem with a linear objective function and linear equality or inequality constraints.
• meanThe mean, or expected value in a probability model, is the average level of a random variable or observed values.
• Poisson distributionThe Poisson distribution gives the probabilities of observing specified counts of events in a fixed interval when events occur independently at a constant average rate.
• varianceVariance is a measure of the average squared deviation of values from their mean.
• leaf nodeA leaf node is a terminal node in a decision tree that provides a predicted class label or continuous value.
• stateA state is a distinct condition or status that a process or system can occupy at a particular point in time.
• z-scoreA z-score is a standardized measure indicating how many standard deviations an observation lies above or below a distribution's mean.
• coefficient of determinationThe coefficient of determination, commonly denoted R-squared, is a regression metric measuring the proportion of dependent-variable variance explained by a fitted model.
• accuracyModel accuracy is the proportion of predictions that a model assigns correctly to the target outcomes.
• pruningPruning is the removal of branches or subtrees from a decision tree to simplify the model and limit unnecessary complexity.
• resultAn outcome is a single possible result of a random experiment or probabilistic process.
• addition ruleThe addition rule of counting determines the number of outcomes from mutually exclusive alternatives by adding their numbers of possibilities.
• temporal autocorrelationAutocorrelation is the correlation between observations of the same time series separated by a specified time lag.
• constraintA constraint is a condition that restricts the allowable values or solutions in an optimization problem.
• uniform distributionA continuous uniform distribution assigns equal probability density across a continuous interval of possible values.
• driftNonstationary behavior is temporal behavior whose statistical properties, such as level or variability, change over time.
• combination with replacementA combination with replacement is a selection in which order does not matter and selected items may be selected again.
• sigmoidA sigmoid function is a function with an S-shaped curve that transitions smoothly between lower and upper limiting values.
• equilibriumEquilibrium is a condition in which a system's relevant quantities remain effectively unchanged because opposing changes balance out.
• partial autocorrelation functionThe partial autocorrelation function measures the correlation between a time-series observation and a lagged observation after accounting for intervening lags.
• interceptAn intercept is the predicted value of a response variable when all predictors in a linear equation equal zero.
• data transformationmap is a pandas Series method that applies a mapping or function to each element and returns the transformed values.
• binary random variableA binary decision variable is a decision variable restricted to the values zero and one to represent a yes-or-no choice.
• ACFThe autocorrelation function measures the correlation between a time series and versions of itself shifted by different time lags.
• p-chartA p-chart is an attribute control chart that monitors the proportion of defective items in successive samples, including samples whose sizes vary.
• lagA lagged observation is a time-series observation from an earlier time point used in relation to a later observation.
• backward passA backward pass is a project-scheduling procedure that calculates the latest allowable start and finish times of activities by traversing dependencies in reverse.
• combinationA combination is a selection of items in which order does not matter.
• stock share priceA stock price is the market price of one share of a traded stock, including its value at a market close.
• quality controlQuality control is the discipline of monitoring and improving production processes to ensure that outputs meet specified quality requirements.
• dependencyA project dependency is a relationship between activities in which one activity cannot begin until one or more preceding activities are completed.
• complement ruleThe complement rule calculates the probability of an event by subtracting the probability of that event's complement from one.
• internal nodeAn internal node is a nonterminal node in a decision tree that applies a decision rule and leads to subsequent branches.
• slopeA slope is a regression coefficient representing the change in a dependent variable for a one-unit change in a predictor.
• splitA split is a decision rule that partitions observations at a decision-tree node according to a feature and condition.
• root nodeA root node is the topmost node in a decision tree and the initial point from which all branches originate.
• regression tableA regression table is a structured summary of a fitted regression model's estimates, uncertainty measures, and related statistics.
• NumPyNumPy is a Python library for efficient numerical computation using multidimensional arrays and mathematical operations.
• classification metricA classification metric is a quantitative measure of the performance of a classifier's predicted categories relative to observed outcomes.
• transition probabilityA transition probability is the conditional probability of moving from one state to another in a stochastic process during a specified transition period.
• seasonality effectA seasonal component represents a systematic pattern that repeats at regular temporal intervals in a time series.
• PythonPython is a general-purpose programming language known for readable syntax and broad use in software development, data analysis, and scientific computing.
• objective functionAn objective function is a mathematical expression that assigns a value to each feasible decision and is maximized or minimized in an optimization problem.
• autoregressive modelAn autoregressive component models the current value of a time series as a linear function of specified previous values.
• optimizationAn optimization method is an algorithmic procedure for finding a minimum or maximum of an objective function subject to specified constraints.
• squared lossThe sum of squared residuals is the sum of the squared differences between observed response values and their fitted values.
• confusion matrixA confusion matrix is a table that summarizes classification results by cross-tabulating actual classes against predicted classes.
• regression sum of squaresThe sum of squares regression is the sum of squared differences between predicted response values and their mean.
• total sum of squaresThe sum of squares total is the sum of squared differences between observed response values and their overall mean.
• math.combmath.comb is a Python math-module function that returns the number of combinations of a specified size from a given number of items.
• weighted average Gini impurityWeighted average Gini impurity is the observation-count-weighted impurity of the child groups produced by a decision-tree split.
• pandaspandas is a Python software library for data manipulation and analysis, especially with tabular and labeled data.
• binomial distributionA binomial distribution gives the probabilities of the number of successes in a fixed number of independent binary trials with a common success probability.
• false negativeA false negative is a positive-class observation incorrectly classified as negative, or the corresponding count in a classification summary.
• false positiveA false positive is a negative-class observation incorrectly classified as positive, or the corresponding count in a classification summary.
• complementA complement event is the set of outcomes in a probability space that are not contained in the specified event.
• probability densityA probability density function describes the relative likelihood of values of a continuous random variable, with probabilities obtained over intervals rather than at individual points.
• forward passA forward pass is a project-scheduling calculation that determines each activity's earliest start and earliest finish times by progressing through its dependencies.
• residual plotA residual plot is a graph displaying model residuals against fitted values or another explanatory quantity to reveal systematic error patterns.
• inner productA dot product is an algebraic operation that multiplies corresponding elements of two equal-length sequences and sums the products.
• slack timeSlack time is the amount of time an activity can be delayed without delaying subsequent activities or overall project completion.
• f-statisticAn F-statistic measures the overall significance of a regression by comparing explained variance with unexplained variance relative to a model containing only an intercept.
• generationPrediction is the process of estimating an outcome from patterns or information in input data without necessarily modeling its temporal ordering.
• regression assumptionA regression assumption is a condition about the data, errors, or model structure required for valid regression inference.
• derived variableA derived variable is a variable created from existing variables through a calculation, rule, or other transformation.
• decision tree schemaA decision tree schema is a structured blueprint specifying a decision tree's decision points, chance events, probabilities, and payoffs.
• permutation with replacementA permutation with replacement is an ordered selection in which each selected item is returned and may be selected again.
• Shapiro–Wilk testThe Shapiro–Wilk test is a statistical hypothesis test for whether a sample is consistent with a normal distribution.
• feature selectionFeature selection is the process of choosing a subset of input variables for use in a predictive model.
• augmented dickey–fuller testThe Augmented Dickey–Fuller test is a statistical test for a unit root and the associated nonstationarity of a time series, with lagged difference terms included to accommodate autocorrelation.
• stochastic trendA stochastic trend is a non-deterministic time-dependent component that causes a series' statistical properties to change over time.
• adjusted r-squaredAdjusted R-squared is a version of R-squared that penalizes a regression model for including additional predictors.
• replacementReplacement is a sampling condition in which a selected item is returned before another selection is made.
• morphological featureA morphological feature is a measurable physical characteristic describing the shape, size, or geometry of a raisin grain.
• independenceIndependence is the condition that one random quantity or error does not depend on another.
• ensembleAn ensemble model combines predictions from multiple constituent models to produce a collective prediction.
• error rateA defect rate is the number of defects divided by the number of inspected units or other relevant inspection opportunities.
• maximax methodThe Maximax method is a decision rule that selects the alternative with the highest possible payoff across all states of nature.
• true negativeA true negative is a negative-class observation correctly predicted as negative, or the corresponding count in a classification summary.
• true positiveA true positive is a positive-class observation correctly predicted as positive, or the corresponding count in a classification summary.
• matrix-matrix multiplicationMatrix multiplication is an algebraic operation that forms each result entry from the dot product of a row of one matrix and a column of another.
• data wranglingData wrangling is the process of transforming and preparing raw data into a clean, consistent, and analysis-ready format.
• market shareMarket share is the proportion of a market's total customers, sales, or usage attributable to a particular product or provider.
• activityA project activity is a distinct component of project work that must be completed for the project to be complete.
• hypothesis testingA hypothesis test is a statistical procedure for evaluating evidence against a specified null hypothesis.
• 68–95–99 ruleThe 68–95–99 rule states that approximately 68%, 95%, and 99.7% of normally distributed observations lie within one, two, and three standard deviations of the mean, respectively.
• log probabilityLog-likelihood is the logarithm of the likelihood of observed data under a statistical model and its parameter values.
• work breakdown structureA work breakdown structure is a tabular or visual decomposition of a project into component activities and their dependencies.
• evaluation datasetA testing set is a subset of observations reserved for evaluating a model on data not used for fitting.
• AICAIC is an information criterion that balances a model's log-likelihood against a penalty for the number of estimated parameters.
• BICBIC, or Bayesian information criterion, is a model-selection metric balancing goodness of fit against model complexity with a sample-size-dependent penalty.
• priority scoreA priority score is a numerical value representing the relative importance or expected value assigned to an item for selection or ranking.
• np-chartAn np-chart is an attribute control chart that tracks the number of defective items in successive samples of fixed size.
• trendA trend component is the part of a time-series representation that captures systematic directional change over time.
• factorialA factorial is the product of all positive integers from a given natural number down to one.
• Pascal's trianglePascal's triangle is a triangular array of numbers in which each interior entry is the sum of the two entries directly above it.
• paired histogramA paired histogram is a visualization that plots two histograms on the same axes to compare one variable across two groups.
• training datasetA training set is the subset of observations used to estimate or fit a predictive model.
• absorbing stateAn absorbing state is a state in a stochastic process that, once entered, cannot be left because its self-transition probability is one.
• data frameA data frame is a tabular data structure organized into labeled rows and columns that may hold different types of values.
• false-negative rateThe false negative rate is the proportion of actual positive instances that a classifier incorrectly identifies as negative.
• false-positive rateThe false positive rate is the proportion of actual negative instances that a classifier incorrectly identifies as positive.
• recallSensitivity is the proportion of actual positive instances that a classifier correctly identifies as positive.
• receiver operating characteristicA receiver operating characteristic curve plots a binary classifier's true positive rate against its false positive rate across decision thresholds.
• specificitySpecificity is the proportion of actual negative instances that a classifier correctly identifies as negative.
• oddsOdds express the ratio of the probability of an event to the probability of its complement.
• quartileA quartile is a quantile that divides ordered observations into four equal parts.
• winsorizationWinsorization is a data-treatment technique that replaces extreme observations with less extreme boundary values.
• scipy.stats.norm.cdfscipy.stats.norm.cdf is a SciPy function that evaluates the cumulative distribution function of a normal distribution at specified values.
• z-score tableA z-score table is a tabular reference that gives cumulative probabilities associated with standardized values in the standard normal distribution.
• attribute control chartAn attribute control chart is a statistical process-control chart that monitors counted or classified quality characteristics rather than continuous measurements.
• binomial experimentA binomial experiment consists of a fixed number of independent trials, each having two possible outcomes with a constant probability of success.
• anytreeanytree is a Python library for creating, modifying, traversing, and rendering tree data structures.
• expected payoffAn expected payoff is a probability-weighted average of the payoffs associated with possible outcomes.
• cumulative probabilityCumulative probability is the total probability of all outcomes up to and including a specified value.
• project planProject planning is the process of defining project activities, schedules, resources, and objectives before execution.
• logarithmic scaleA logarithmic transformation replaces each value with its logarithm to compress scale differences and reduce positive skewness.
• independent trialAn independent trial is a random trial whose outcome does not alter the probabilities of outcomes in other trials.
• local averagingA moving average represents a time-series value or forecast using averages of observations in a moving time window.
• logarithmA logarithm is the exponent to which a specified base must be raised to obtain a given number.
• mantissaA mantissa is the fractional part of a common logarithm after its integer part has been separated.
• center lineThe EWMA mean is the central reference level represented by the overall exponentially weighted moving average in an EWMA control chart.
• standard deviationStandard deviation is a measure of the typical distance of observations from their mean.
• uncertaintyUncertainty is the condition in which information, outcomes, or underlying quantities are not completely known.
• program evaluation and review techniqueThe program evaluation and review technique is a project-scheduling method that estimates activity durations using optimistic, pessimistic, and most likely durations.
• project crashingProject crashing is a scheduling technique that shortens project duration by reducing the time allocated to one or more critical-path activities, usually at additional cost.
• theoretical probabilityTheoretical probability is the ratio of the number of favorable outcomes to the total number of possible outcomes in a specified probability model.
• area under the curveThe area under the ROC curve is a measure of a binary classifier's ability to discriminate between positive and negative classes across classification thresholds.
• bugA defect is an imperfection or nonconformity that causes a product or unit to fail a specified quality criterion.
• state probabilityA state probability is the probability that a process or system occupies a particular state during a specified period.
• binom.pmfbinom.pmf is a SciPy statistics API method that evaluates the probability mass function of a binomial distribution.
• binomial coefficientA binomial coefficient is the number of ways to choose a specified number of items from a larger set without regard to order.
• linproglinprog is a SciPy function that solves linear programming problems by minimizing a linear objective subject to specified constraints.
• expected activity timeActivity duration is the expected amount of time required to complete a project activity.
• homoscedasticityHomoscedasticity is the regression condition that errors have constant variance across levels of the predictors or fitted values.
• data groupinggroupby is a pandas method that partitions data into groups defined by one or more key columns for separate operations.
• fundamental matrixA fundamental matrix is the matrix obtained by inverting the difference between the identity matrix and the transient-state transition matrix in an absorbing Markov chain.
• random numberA random number is a generated numerical value treated as a sample from a specified probability distribution or numerical interval.
• first_digitsfirst_digits is an API function that analyzes the distribution of leading digits and compares it with an expected Benford distribution.
• statisticsA statistical method is a formal procedure for analyzing data, quantifying uncertainty, or drawing conclusions from observations.
• rate parameterA rate parameter is the average rate at which events occur in a Poisson distribution over a specified interval.
• grouped bar chartA grouped bar chart is a bar chart that places multiple bars together for each category to compare subcategories.
• resource allocationResource allocation is the assignment of limited resources among competing activities or uses subject to constraints.
• multicollinearityMulticollinearity is a condition in regression modeling where predictor variables are strongly linearly related to one another.
• Holt-Winters exponential smoothingA Holt–Winters exponential smoothing model is an exponential-smoothing model that accounts for level, trend, and seasonal components in time-series data.
• c-chartA c-chart is an attribute control chart for monitoring the count of defects per inspection unit when the inspection opportunity is constant.
• critical path activityA critical path activity is a project activity with no scheduling slack whose delay extends the project timeline.
• importance scoreFeature importance is a measure of how strongly each input feature contributes to a model's predictions, often based on its effect on split quality.
• minimax regret methodThe minimax regret method selects the alternative that minimizes the largest possible difference between its payoff and the best payoff in each scenario.
• decision variableA decision variable is an unknown quantity whose value represents a selectable decision in an optimization problem.
• samplingRandom sampling is a sampling procedure in which selections are made according to a probability mechanism rather than a deterministic choice.
• trainingfit is an estimator method that learns model parameters or structure from supplied training data.
• trialA trial is one execution of a simulated experiment that produces a possible system outcome.
• intervalAn interval is a set of real numbers lying between specified lower and upper bounds, possibly including those bounds.
• Breusch–Pagan testhet_breuschpagan is a statsmodels function that computes Breusch–Pagan heteroscedasticity test results.
• Durbin–Watson testdurbin_watson is a statsmodels function that computes the Durbin–Watson statistic from regression residuals.
• heteroscedasticityHeteroscedasticity is the condition that the variance of regression residuals changes systematically across levels of the predictors.
• independence of residualsIndependence of residuals is the condition that regression errors are not correlated with one another.
• Jarque–Bera testThe Jarque–Bera test is a statistical test of normality based on sample skewness and kurtosis.
• quantile-quantile plotA Q–Q plot is a graph comparing sample quantiles with theoretical quantiles to assess whether data follow a specified distribution.
• bootstrap samplingA bootstrap sample is a sample formed by repeatedly selecting observations with replacement from an original sample.
• scatter plotA scatterplot is a two-dimensional graph that represents paired observations as points to show relationships between variables.
• variable control chartA variable control chart monitors process quality using quantitative measurements on a continuous or numerical scale.
• chi-square testA chi-square test is a statistical hypothesis test that compares observed categorical counts with expected counts to assess whether their discrepancy is statistically significant.
• project durationProject duration is the total time required to complete a project, calculated here from expected times on the critical path.
• statistical significanceStatistical significance is an assessment of whether observed evidence is sufficiently inconsistent with a specified null hypothesis under a statistical model.
• decision alternativeA decision alternative is one of the mutually exclusive courses of action available to a decision-maker.
• payoff tableA payoff table is a tabular structure listing decision alternatives, scenarios, and the payoffs associated with their combinations.
• state of natureA state of nature is a possible external condition that affects the outcome of a decision but is not controlled by the decision-maker.
• robustnessModel robustness is the ability of a predictive model to maintain reliable performance across variation in data or conditions.
• missing valueA null value is a missing or undefined data value represented as having no usable value.
• maximin methodThe maximin method selects the alternative whose worst possible payoff is better than the worst possible payoff of every other alternative.
• logarithmic returnA log return is the natural logarithm of the ratio of an asset's current price to its previous price, representing a compounded proportional price change.
• latest finish timeA latest finish time is the latest point at which a project activity can be completed without delaying the project's completion.
• latest start timeA latest start time is the latest point at which a project activity can begin without delaying the project's completion.
• empirical probabilityEmpirical probability is probability estimated from the relative frequency of an event in observed trials or real-world data.
• integrationIntegration in ARIMA is the differencing operation used to remove nonstationary temporal structure from a time series.
• attribute dataAttribute data are quality-control observations recorded as counts or proportions rather than continuous measurements.
• r-chartAn r-chart is a statistical process-control chart that monitors within-sample variability by plotting sample ranges over time.
• HQICHQIC is an information criterion that balances model fit and parameter complexity using a sample-size-dependent penalty between those of AIC and BIC in growth rate.
• white noiseWhite noise is a random process with uncorrelated values across time and typically constant variance.
• McFadden's pseudo R-squaredMcFadden's pseudo R-squared is a likelihood-based measure of how much a fitted discrete-choice model improves over an intercept-only null model.
• ExponentialSmoothingExponentialSmoothing is a statsmodels model class for constructing exponential smoothing models with configurable components such as trend.
• feature setA feature subset is a selected collection of predictor variables considered for a model operation such as a tree split.
• statsmodelsA Python library for statistical modeling, estimation, hypothesis testing, and statistical data exploration.
• mutually exclusive eventA mutually exclusive event is an event that cannot occur simultaneously with another event in the same set of alternatives.
• data conversionData type conversion is the process of changing values from one representation or data type to another.
• nanNaN is a special floating-point value representing a numerical result that is undefined or cannot be represented as a valid number.
• x-bar chartAn x-bar chart is a statistical process-control chart that plots subgroup means over time against a center line and control limits.
• anomalyAn outlier is an observation that is unusually distant from the pattern represented by the rest of a dataset.
• poisson.pmfpoisson.pmf is a SciPy statistical function that returns probability mass function values for the Poisson distribution.
• volatilityVolatility is the degree and frequency of variation in a quantity such as a financial price over time.
• logitLog odds are the natural logarithm of the odds of an event, calculated as the logarithm of its probability divided by the complement probability.
• classifierClassification is a modeling technique that assigns observations to predefined categories.
• sample spaceA sample space is the set of all possible outcomes of a random experiment or situation.
• trend lineA regression line is a straight-line representation of the relationship between a dependent variable and an independent variable in a linear regression model.
• earliest finish timeAn earliest finish time is the earliest point at which a project activity can be completed based on its earliest start and expected duration.
• earliest start timeAn earliest start time is the earliest point at which a project activity can begin while respecting its predecessor dependencies.
• visualizationData visualization is the graphical representation of data or information to communicate patterns, comparisons, trends, and other insights.
• numpy.arangeNumPy.arange is a function that returns evenly spaced values within a specified half-open interval.
• correlationCorrelation is a measure of the degree to which two quantities vary together in a linear association.
• overfittingOverfitting is a modeling condition in which a model captures idiosyncrasies of the fitting data at the expense of performance on new data.
• plot_treeplot_tree is a scikit-learn function that renders a fitted decision tree as a visual tree diagram.
• moving average modelA moving-average component represents a time-series observation as a function of current and past residual errors.
• simple exponential smoothingSimpleExpSmoothing is a statsmodels model class for constructing simple exponential smoothing models.
• descriptive statisticsDescriptive statistics are methods for summarizing and presenting the main characteristics of observed data.
• uniform distribution of mantissasThe uniform distribution of mantissas is the property that logarithmic fractional parts are uniformly distributed between zero and one.
• class imbalanceClass imbalance is a condition in which classes in a labeled dataset have substantially unequal representation.
• history()history() is a yfinance Ticker method that retrieves historical market data for a security over specified dates and intervals.
• ISO 8601ISO 8601 is an international standard for unambiguous representation of dates, times, durations, and intervals.
• yfinanceyfinance is a Python library that retrieves market data from Yahoo Finance.
• noiseRandom noise is stochastic variation in observations that is not explained by the systematic structure of a model.
• determinismA deterministic model produces the same result whenever its inputs and conditions are the same, without representing random variation.
• countingA counting method is a mathematical procedure or rule for determining the number of possible outcomes or arrangements.
• pseudo r-squaredPseudo R-squared is a family of fit measures for logistic regression that quantify model fit using likelihood-based comparisons rather than explained variance.
• double exponential smoothingDouble exponential smoothing is an exponential smoothing technique that models both the level and a linear trend in a time series.
• time series analysisTime series analysis is the analysis of observations ordered over time to identify temporal patterns, dependence, or trends.
• activity varianceActivity variance is a measure of uncertainty or variability in a project's estimated activity duration.
• project varianceProject variance is the sum of the duration variances of the activities on a project's critical path under an independence assumption.
• schedule compressionSchedule compression is a project-management technique for shortening a project schedule without reducing its scope.
• benford libraryThe benford library is a Python library for analyzing whether numerical data follows Benford's law.
• branchA branch is an edge in a decision tree representing one possible outcome of a node's test.
• time-series modelA time series model describes observations indexed over time and their temporal dependencies or patterns.
• chi-square statisticA chi-square statistic is the sum of squared observed-minus-expected count differences divided by their expected counts.
• degree of freedomDegrees of freedom are the number of independently varying values contributing to a statistical calculation after constraints are accounted for.
• stats.chisquarestats.chisquare is a SciPy function that performs a chi-square test by comparing observed and expected frequencies.
• comprehensionA list comprehension is a Python syntax construct that creates a list by evaluating an expression for items from an iterable, optionally subject to a condition.
• supervised learningSupervised learning is a machine-learning approach that learns a mapping from inputs to known target outcomes using labeled examples.
• information gainInformation gain is the reduction in uncertainty about a target produced by a partition or feature.
• categorical dataA categorical variable is a variable whose values represent membership in distinct qualitative classes or categories.
• moving rangeA moving range is the absolute difference between consecutive observations in an ordered sequence, used to measure short-term process variability.
• discrete variableDiscrete data are observations whose possible values are separate, countable outcomes rather than values throughout a continuous interval.
• data explorationExploratory analysis is the investigation of data to discover patterns, relationships, anomalies, and plausible hypotheses.
• excess kurtosisExcess kurtosis is kurtosis measured relative to the normal distribution, with zero indicating normal-distribution tail behavior.
• order of magnitudeAn order of magnitude is a scale corresponding to a tenfold change in numerical size, commonly represented by an integer power of ten.
• optimal solutionAn optimal solution is a feasible assignment of decision variables that gives the best objective value under the problem's optimization direction.
• smoothing parameterA smoothing constant is a parameter that determines the relative weight assigned to a new observation versus accumulated historical information in a smoothed average.
• nonlinear mappingA nonlinear relationship is a relationship in which changes in one quantity are not represented by a linear function of another.
• statistical sampleA sample is a subset of a population observed for the purpose of statistical analysis.
• language modelA mathematical model represents relationships in a system using mathematical structures to analyze or predict its behavior.
• sample sizeSample size is the number of observations or trials included in a statistical sample or simulation.
• machine learningMachine learning is the development of computational models that learn patterns or decisions from data rather than relying only on explicitly programmed rules.
• logitlogit is a statsmodels formula API function that constructs a logistic regression model from a formula and data.
• variance inflation factorA variance inflation factor measures how much the variance of an estimated regression coefficient is inflated by collinearity among predictors.

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