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- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/14%3A_Multiple_and_Logistic_Regression/14.01%3A_Introduction_to_Multiple_RegressionMultiple regression extends simple two-variable regression to the case that still has one response but many predictors. The method is motivated by scenarios where many variables may be simultaneously ...Multiple regression extends simple two-variable regression to the case that still has one response but many predictors. The method is motivated by scenarios where many variables may be simultaneously connected to an output.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/13%3A_Introduction_to_Linear_Regression/13.06%3A_ExercisesExercises for Chapter 7 of the "OpenIntro Statistics" textmap by Diez, Barr and Çetinkaya-Rundel.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/01%3A_Basics/1.02%3A_Working_with_Data/1.2.06%3A_Observational_Studies_and_Sampling_StrategiesGenerally, data in observational studies are collected only by monitoring what occurs, what occurs, while experiments require the primary explanatory variable in a study be assigned for each subject b...Generally, data in observational studies are collected only by monitoring what occurs, what occurs, while experiments require the primary explanatory variable in a study be assigned for each subject by the researchers. Making causal conclusions based on experiments is often reasonable. However, making the same causal conclusions based on observational data can be treacherous and is not recommended. Thus, observational studies are generally only sufficient to show associations.
- https://stats.libretexts.org/Bookshelves/Probability_Theory/Applied_Probability_(Pfeiffer)/01%3A_Probability_Systems/1.03%3A_Interpretations(IF5): \(I_{A \cup B} = I_A + I_B - I_A I_B = \text{min }{I_A, I_B}\) (the maximum rule extends to any class) The maximum rule follows from the fact that \(\omega\) is in the union iff it is in any on...(IF5): \(I_{A \cup B} = I_A + I_B - I_A I_B = \text{min }{I_A, I_B}\) (the maximum rule extends to any class) The maximum rule follows from the fact that \(\omega\) is in the union iff it is in any one or more of the events in the union iff any one or more of the individual indicator function has value one iff the maximum is one.
- https://stats.libretexts.org/Courses/American_River_College/STAT_300%3A_My_Introductory_Statistics_Textbook_(Mirzaagha)/08%3A_Finding_Confidence_Interval_for_Population_Mean_and_Proportion/8.01%3A_Inference_for_Numerical_Data/8.1.03%3A_Difference_of_Two_MeansIn this section we consider a difference in two population means, μ1−μ2, under the condition that the data are not paired. The methods are similar in theory but different in the details. Just as with...In this section we consider a difference in two population means, μ1−μ2, under the condition that the data are not paired. The methods are similar in theory but different in the details. Just as with a single sample, we identify conditions to ensure a point estimate of the difference is nearly normal. Next we introduce a formula for the standard error, which allows us to apply our general tools discussed previously.
- https://stats.libretexts.org/Bookshelves/Probability_Theory/Applied_Probability_(Pfeiffer)/12%3A_Variance_Covariance_and_Linear_Regression/12.01%3A_Variancejdemo1 % Call for data jcalc % Set up Enter JOINT PROBABILITIES (as on the plane) P Enter row matrix of VALUES of X X Enter row matrix of VALUES of Y Y Use array operations on matrices X, Y, PX, PY, t...jdemo1 % Call for data jcalc % Set up Enter JOINT PROBABILITIES (as on the plane) P Enter row matrix of VALUES of X X Enter row matrix of VALUES of Y Y Use array operations on matrices X, Y, PX, PY, t, u, and P G = t.^2 + 2*t.*u - 3*u; % calcculation of matrix of [g(t_i, u_j)] EG = total(G.*P) % Direct calculation of E[g(X,Y)] EG = 3.2529 VG = total(G.^.*P) - EG^2 % Direct calculation of Var[g(X,Y)] VG = 80.2133 [Z,PZ] = csort(G,P); % Determination of distribution for Z EZ = Z*PZ' % E[Z] from d…
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/02%3A_Descriptive_StatisticsStatistics naturally divides into two branches, descriptive statistics and inferential statistics. Our main interest is in inferential statistics to try to infer from the data what the population migh...Statistics naturally divides into two branches, descriptive statistics and inferential statistics. Our main interest is in inferential statistics to try to infer from the data what the population might thin or to evaluate the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Nevertheless, the starting point for dealing with a collection of data is to organize, display, and summarize it effectively.
- https://stats.libretexts.org/Bookshelves/Probability_Theory/Applied_Probability_(Pfeiffer)/17%3A_Appendices/17.05%3A_Appendix_E_to_Applied_Probability_-_Properties_of_Mathematical_Expectation(E19): Special case of the Radon-Nikodym theorem If \(g(Y)\) is integrable and \(X\) is a random vector, then there exists a real-valued Borel function \(e(\cdot)\), defined on the range of \(X\), uni...(E19): Special case of the Radon-Nikodym theorem If \(g(Y)\) is integrable and \(X\) is a random vector, then there exists a real-valued Borel function \(e(\cdot)\), defined on the range of \(X\), unique a.s. \([P_X]\), such that \(E[I_M(X) g(X)] = E[I_M (X) e(X)]\) for all Borel sets \(M\) on the codomain of \(X\). \(\sum_{n = 0}^{\infty} P(X \ge n + 1) \le E[X] \le \sum_{n = 0}^{\infty} P(X \ge n) \le N \sum_{k = 0}^{\infty} P(X \ge kN)\), for all \(N \ge 1\)
- https://stats.libretexts.org/Courses/American_River_College/STAT_300%3A_My_Introductory_Statistics_Textbook_(Mirzaagha)/08%3A_Finding_Confidence_Interval_for_Population_Mean_and_Proportion/8.01%3A_Inference_for_Numerical_DataChapter 4 introduced a framework for statistical inference based on con dence intervals and hypotheses. In each case, the inference ideas remain the same: Identify an appropriate distribution for the ...Chapter 4 introduced a framework for statistical inference based on con dence intervals and hypotheses. In each case, the inference ideas remain the same: Identify an appropriate distribution for the point estimate or test statistic. Each section in Chapter 5 explores a new situation: the difference of two means (5.1, 5.2); a single mean or difference of means where we relax the minimum sample size condition (5.3, 5.4); and the comparison of means across multiple groups (5.5).
- https://stats.libretexts.org/Courses/American_River_College/STAT_300%3A_My_Introductory_Statistics_Textbook_(Mirzaagha)/10%3A_Hypothesis_Testing_about_Two_Population_Means_and_Proportions/10.01%3A_Inference_for_Categorical_Data/10.1.04%3A_Testing_for_Independence_in_Two-Way_Tables_(Special_Topic)If there really is no difference among the algorithms and 70.78% of people are satisfied with the search results, how many of the 5000 people in the "current algorithm" group would be expected to not ...If there really is no difference among the algorithms and 70.78% of people are satisfied with the search results, how many of the 5000 people in the "current algorithm" group would be expected to not perform a new search? 26 The test statistic is larger than the right-most column of the df = 2 row of the chi-square table, meaning the p-value is less than 0.001.
- https://stats.libretexts.org/Courses/American_River_College/STAT_300%3A_My_Introductory_Statistics_Textbook_(Mirzaagha)/10%3A_Hypothesis_Testing_about_Two_Population_Means_and_Proportions/10.01%3A_Inference_for_Categorical_Data/10.1.02%3A_Difference_of_Two_ProportionsWe would like to make conclusions about the difference in two population proportions: p1−p2. We consider three examples. In the first, we compare the approval of the 2010 healthcare law under two dif...We would like to make conclusions about the difference in two population proportions: p1−p2. We consider three examples. In the first, we compare the approval of the 2010 healthcare law under two different question phrasings. In the second application, a company weighs whether they should switch to a higher quality parts manufacturer.
