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| − | This is a General Advanced-Placement (AP) Statistics Curriculum E-Book
| + | #REDIRECT [[Probability and statistics EBook]] |
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| − | ==[[AP_Statistics_Curriculum_2007_Preface| Preface]]==
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| − | This is an Internet-based E-Book for advance-placement (AP) statistics educational curriculum. The E-Book is initially developed by the UCLA [[SOCR | Statistics Online Computational Resource (SOCR)]], however, any statistics instructor, researcher or educator is encouraged to contribute to this effort and improve the content of these learning materials.
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| − | ===[[AP_Statistics_Curriculum_2007_Format| Format]]===
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| − | Follow the instructions in [[AP_Statistics_Curriculum_2007_Format| this page]] to expand, revise or improve the materials in this E-Book.
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| − | ==Chapter I: Introduction to Statistics==
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| − | ===[[AP_Statistics_Curriculum_2007_IntroVar | The Nature of Data & Variation]]===
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| − | No mater how controlled the environment, the protocol or the design, virtually any repeated measurement, observation, experiment, trial, study or survey is bound to generate data that varies because of intrinsic (internal to the system) or extrinsic (due to the ambient environment) effects. How many natural processes or phenomena in real life can we describe that have an exact mathematical closed-form description and are completely deterministic? How do we model the rest of the processes that are unpredictable and have random characteristics?
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| − | ===[[AP_Statistics_Curriculum_2007_IntroUses |Uses and Abuses of Statistics]]===
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| − | Statistics is the science of variation, randomness and chance. As such, statistics is different from other sciences, where the processes being studied obey exact deterministic mathematical laws. Statistics provides quantitative inference represented as long-time probability values, confidence or prediction intervals, odds, chances, etc., which may ultimately be subjected to varying interpretations. The phrase ''Uses and Abuses of Statistics'' refers to the notion that in some cases statistical results may be used as evidence to seemingly opposite theses. However, most of the time, common [http://en.wikipedia.org/wiki/Logic principles of logic] allow us to disambiguate the obtained statistical inference.
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| − | ===[[AP_Statistics_Curriculum_2007_IntroDesign | Design of Experiments]]===
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| − | Design of experiments is the blueprint for planning a study or experiment, performing the data collection protocol and controlling the study parameters for accuracy and consistency. Data, or information, is typically collected in regard to a specific process or phenomenon being studied to investigate the effects of some controlled variables (independent variables or predictors) on other observed measurements (responses or dependent variables). Both types of variables are associated with specific observational units (living beings, components, objects, materials, etc.)
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| − | ===[[AP_Statistics_Curriculum_2007_IntroTools |Statistics with Tools (Calculators and Computers)]]===
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| − | All methods for data analysis, understanding or visualization are based on models that often have compact analytical representations (e.g., formulas, symbolic equations, etc.) Model are used to study processes theoretically. Empirical validations of the utility of models is achieved by plugging in data and actually testing the models. This validation step may be done manually, by computing the model prediction or model inference from recorded measurements. This however is possible by hand only for small number of observations (<10). In practice, we write (or use existent) algorithms and computer programs that automate these calculations for better efficiency, accuracy and consistency in applying models to larger datasets.
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| − | ==Chapter II: Describing, Exploring, and Comparing Data==
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| − | ===[[AP_Statistics_Curriculum_2007_EDA_Freq |Summarizing data with Frequency Tables ]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_EDA_Pics |Pictures of Data]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_EDA_Center |Measures of Central Tendency]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_EDA_Var |Measures of Variation]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_EDA_Shape |Measures of Shape]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_EDA_Plots | Graphs & Exploratory Data Analysis]] ===
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| − | ==Chapter III: Probability==
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| − | ===[[AP_Statistics_Curriculum_2007_Prob_Basics |Fundamentals]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Prob_Rules |Addition & Multiplication Rules]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Prob_Simul |Probabilities Through Simulations]] ===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Prob_Count |Counting]]===
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| − | Overview TBD
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| − | ==Probability Distributions==
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| − | ===[[AP_Statistics_Curriculum_2007_Distrib_RV | Random Variables]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Distrib_Binomial |Bernoulli & Binomial Experiments]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Distrib_Dists |Geometric, HyperGeometric & Negative Binomial]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Distrib_Poisson |Poisson Distribution]]===
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| − | Overview TBD
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| − | ==Chapter IV: Normal Probability Distributions==
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| − | ===[[AP_Statistics_Curriculum_2007_Normal_Std |The Standard Normal Distribution]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Normal_Prob |Nonstandard Normal Distribution: Finding Probabilities]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Normal_Critical |Nonstandard Normal Distributions: Finding Scores (critical values)]]===
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| − | Overview TBD
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| − | ==Chapter V: Relations Between Distributions==
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| − | ===[[AP_Statistics_Curriculum_2007_Limits_CLT |The Central Limit Theorem]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Limits_LLN |Law of Large Numbers]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Limits_Norm2Bin |Normal Distribution as Approximation to Binomial Distribution]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Limits_Poisson2Bin |Poisson Approximation to Binomial Distribution]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Limits_Bin2HyperG |Binomial Approximation to HyperGeometric]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Limits_Norm2Poisson |Normal Approximation to Poisson]]===
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| − | Overview TBD
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| − | ==Chapter VI: Estimates and Sample Sizes==
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| − | ===[[AP_Statistics_Curriculum_2007_Estim_L_Mean |Estimating a Population Mean: Large Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Estim_S_Mean |Estimating a Population Mean: Small Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Estim_Proportion |Estimating a Population Proportion]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Estim_Var |Estimating a Population Variance]]===
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| − | Overview TBD
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| − | ==Chapter VII: Hypothesis Testing==
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| − | ===[[AP_Statistics_Curriculum_2007_Hypothesis_Basics |Fundamentals of Hypothesis Testing]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Hypothesis_L_Mean |Testing a Claim about a Mean: Large Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Hypothesis_S_Mean |Testing a Claim about a Mean: Small Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Hypothesis_Proportion |Testing a Claim about a Proportion]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Hypothesis_Var |Testing a Claim about a Standard Deviation or Variance]]===
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| − | Overview TBD
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| − | ==Chapter VIII: Inferences from Two Samples==
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| − | ===[[AP_Statistics_Curriculum_2007_Infer_2Means_Dep |Inferences about Two Means: Dependent Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Infer_2Means_Indep |Inferences about Two Means: Independent and Large Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Infer_BiVar |Comparing Two Variances]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Infer_2Means_S_Indep |Inferences about Two Means: Independent and Small Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Infer_2Proportions |Inferences about Two Proportions]]===
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| − | Overview TBD
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| − | ==Chapter IX: Correlation and Regression==
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| − | ===[[AP_Statistics_Curriculum_2007_GLM_Corr |Correlation]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_GLM_Regress |Regression]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_GLM_Predict |Variation and Prediction Intervals]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_GLM_MultLin |Multiple Regression]]===
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| − | Overview TBD
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| − | ==Chapter X: Non-Parametric Inference==
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| − | ===[[AP_Statistics_Curriculum_2007_NonParam_2MeansPair | Differences of Means of Two Paired Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_NonParam_2MeansIndep | Differences of Means of Two Independent Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_NonParam_2MedianPair | Differences of Medians of Two Paired Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_NonParam_2MedianIndep | Differences of Medians of Two Independent Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_NonParam_2PropIndep | Differences of Proportions of Two Independent Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_NonParam_ANOVA | Differences of Means of Several Independent Samples]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_NonParam_VarIndep | Differences of Variances of Two Independent Samples]]===
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| − | Overview TBD
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| − | ==Chapter XI: Multinomial Experiments and Contingency Tables==
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| − | ===[[AP_Statistics_Curriculum_2007_Contingency_Fit |Multinomial Experiments: Goodness-of-Fit]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Contingency_Indep |Contingency Tables: Independence and Homogeneity]]===
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| − | Overview TBD
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| − | ==Chapter XII: Statistical Process Control==
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| − | ===[[AP_Statistics_Curriculum_2007_Control_MeanVar |Control Charts for Variation and Mean]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_Control_Attrib |Control Charts for Attributes]]===
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| − | Overview TBD
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| − | ==Chapter XIII: Survival/Failure Analysis==
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| − | Overview TBD
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| − | ==Chapter XIV: Multivariate Statistical Analyses==
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| − | ===[[AP_Statistics_Curriculum_2007_MultiVar_ANOVA | Multivariate Analysis of Variance]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_MultiVar_LinRegression | Multiple Linear Regression]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_MultiVar_Logistic | Logistic Regression]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_MultiVar_LogLinear | Log-Linear Regression]]===
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| − | Overview TBD
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| − | ===[[AP_Statistics_Curriculum_2007_MultiVar_ANCOVA | Multivariate Analysis of Covariance]]===
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| − | Overview TBD
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| − | ==Chapter XV: Time Series Analysis==
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| − | Overview TBD
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| − | <hr>
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| − | * SOCR Home page: http://www.socr.ucla.edu
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| − | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007}}
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