Publications by STAT 115 Basic Statistical Methods

Variable Selection

27.11.2023

Variable Selection - Stepwise Regression Variable selection selects a subset of variables based on model fit and model complexity. A common criterion for model fit and complexity is the Akaike Information Criterion (AIC): \[\text{AIC} = n \text{log}(\text{RSS}/n) + k,\] where RSS is the residual sum of squares, \(n\) is the number of data points...

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Testing Overdispersion

06.10.2023

BASICS OF COUNT MODEL FIT STATISTICS Most statisticians consider overdispersion the key problem when considering count model fit. That is, an analyst typically attempts to evaluate whether a count model is extradispersed – which usually means overdispersed. If there is evidence of overdispersion in a Poisson model, the problem then is to dete...

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More Examples

03.10.2023

Example of Number of Accidents Let X is a binary variable of 0 for sunny day and 1 for rainy day. We have a sample of 20 days with 10 rainy and 10 sunny days from Poisson with rates 5 and 2 respectively. In fact we can artificially generate this sample using R: y <- c(rpois(10, lambda = 2), rpois(10, lambda = 5)) x <- rep(c(0,1), each = 10) pri...

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Poisson Regression

21.09.2023

EXAMPLE 1 The number of awards earned by students at one senior high school. Predictors of the number of awards earned include the type of program in which the student was enrolled (e.g., HUMSS, ABM or STEM) and the score on their final exam in statistics. In this example, num_awards is the outcome variable and indicates the number of awards ea...

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R Examples and Illustrations

06.10.2022

Example 1 Suppose we would like to estimate the mean height (in inches) of a certain type of plant in a certain field. We gather a simple random sample of 13 plants and measure the height of each plant. Solution: The following code shows how to calculate the sample mean: #define data data <- c(8, 8, 9, 12, 13, 13, 14, 15, 19, 22, 23, 23, 24) ...

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Multiple Linear Regression in R

07.10.2022

MULTIPLE LINEAR REGRESSION Linear Regression: It is the basic and commonly used type for predictive analysis. It is a statistical approach for modeling the relationship between a dependent variable and a given set of independent variables. These are of two types: Simple linear Regression Multiple Linear Regression Multiple Linear Regression ...

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Hypothesis Testing in R

13.10.2022

Testing of Hypothesis In many situations, we are called upon to make decision about a population characteristics. We may decide whether a new medicine is effective in curing disease or we made to compare a new brand of vaccine with more popular brand. To reach a decision, it is useful to make speculations or guesses regarding the population p...

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