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- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/08%3A_Estimating_Unknown_Quantities_from_a_Sample/8.04%3A_Estimating_Population_Parametersknitr::kable(data.frame(stringsAsFactors=FALSE, Symbol = c("$s$", "$\\sigma$", "$\\hat{\\sigma}$", "$s^2$", "$\\sigma^2$", "$\\hat{\\sigma}^2$"), What.is.it = c("Sample standard deviation", "Populatio...knitr::kable(data.frame(stringsAsFactors=FALSE, Symbol = c("$s$", "$\\sigma$", "$\\hat{\\sigma}$", "$s^2$", "$\\sigma^2$", "$\\hat{\\sigma}^2$"), What.is.it = c("Sample standard deviation", "Population standard deviation", "Estimate of the population standard deviation", "Sample variance", "Population variance", "Estimate of the population variance"), Do.we.know.what.it.is = c("Yes - calculated from the raw data", "Almost never known for sure", "Yes - but not the same as the sample standard dev…
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/02%3A_Introduction_to_R/2.13%3A_Using_CommentsBefore discussing any of the more complicated stuff, I want to introduce the comment character, #. It has a simple meaning: it tells R to ignore everything else you’ve written on this line. seeker <- ...Before discussing any of the more complicated stuff, I want to introduce the comment character, #. It has a simple meaning: it tells R to ignore everything else you’ve written on this line. seeker <- 3.1415 # create the first variable lover <- 2.7183 # create the second variable keeper <- seeker * lover # now multiply them to create a third one print( keeper ) # print out the value of 'keeper'
- 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/15%3A_Regression_in_R/15.12%3A_Model_SelectionIf we ignore the low level details, it’s fairly obvious what the AIC does: on the left we have a term that increases as the model predictions get worse; on the right we have a term that increases as t...If we ignore the low level details, it’s fairly obvious what the AIC does: on the left we have a term that increases as the model predictions get worse; on the right we have a term that increases as the model complexity increases. where N is the number of observations, p is the number of predictors in the full model (not including the intercept), and k is the difference in the number of parameters between the two models.
- 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/Bookshelves/Introductory_Statistics/Inferential_Statistics_and_Probability_-_A_Holistic_Approach_(Geraghty)/14%3A_Correlation_and_Linear_Regression/14.09%3A_Residual_AnalysisWe will make three graphs to test the residual; a scatterplot with the regression line, a plot of the residuals, and a histogram of the residuals Model B looks like a strong fit, but the residuals are...We will make three graphs to test the residual; a scatterplot with the regression line, a plot of the residuals, and a histogram of the residuals Model B looks like a strong fit, but the residuals are showing a pattern of being positive for low and high values of \(X\) and negative for middle values of \(X\). Model C has a linear fit, but the residuals are showing a pattern of being smaller for low values of \(X\) and higher for large values of \(X\).
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Inferential_Statistics_and_Probability_-_A_Holistic_Approach_(Geraghty)/10%3A_One_Population_Hypothesis_Testing/10.02%3A_Formulate_General_Research_Questions(Labor) What is the effect of undocumented immigration and outsourcing of jobs on the current unemployment rate? On the basis of available or potentially available data, we can decide later what speci...(Labor) What is the effect of undocumented immigration and outsourcing of jobs on the current unemployment rate? On the basis of available or potentially available data, we can decide later what specific research hypotheses will be formulated and tested to address the general question. During the data collection and testing process other ideas may come up and we may choose to redefine the general question.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Inferential_Statistics_and_Probability_-_A_Holistic_Approach_(Geraghty)/12%3A_Chisquare_Tests_for_Categorical_Data/12.02%3A_Chisquare_Test_of_IndependenceYou can pick any two events in the table above to verify that Gender and Opinion of Legalization of Marijuana are independent events. In that case, we would expect the 450 people who supported legaliz...You can pick any two events in the table above to verify that Gender and Opinion of Legalization of Marijuana are independent events. In that case, we would expect the 450 people who supported legalization of marijuana to have a higher number of women (and a smaller number of men) compared to the first table. If only one variable is randomized, then the test is called a Chi‐square Test of Homogeneity, but the execution of the test is exactly the same.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/15%3A_Regression_in_RThe goal in this chapter is to introduce linear regression, the standard tool that statisticians rely on when analysing the relationship between interval scale predictors and interval scale outcomes. ...The goal in this chapter is to introduce linear regression, the standard tool that statisticians rely on when analysing the relationship between interval scale predictors and interval scale outcomes. Stripped to its bare essentials, linear regression models are basically a slightly fancier version of the Pearson correlation (Section 5.7) though as we’ll see, regression models are much more powerful tools.
- 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/Courses/Cerritos_College/Introduction_to_Statistics_with_R/04%3A_Summarizing_Data_Visually_Using_R/4.07%3A_Saving_Image_Files_Using_R_and_RstudioIf you’re running R through Rstudio, then the easiest way to save your image is to click on the “Export” button in the Plot panel (i.e., the area in Rstudio where all the plots have been appearing). T...If you’re running R through Rstudio, then the easiest way to save your image is to click on the “Export” button in the Plot panel (i.e., the area in Rstudio where all the plots have been appearing). The reason for this is that my experience with the graphical device provided by Rstudio has led me to suspect that it still has a bunch on non-standard (or possibly just undocumented) features, and so I don’t quite trust that it always does what I expect.
