Publications by Laboratory Exercise No. 5
Stat 136- First Long Exam (Part 3)
Stat 136 (Bayesian Statistics) Long Exam No. 1 (Part 3) Author Norberto E. Milla, Jr. Published March 22, 2023 Problem No. 1: Suppose two persons are interested in estimating the proportion \(p\) of students at a college who owns an Iphone 14. Suppose Joe uses a discrete prior given in the following table: \(p\) 0.1 0.2 0.3 0.4 0.5 \(f(p)...
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Econ 115s- First Long Exam (Part 3)
Econ 115s (Introduction to Econometrics) First Long Exam (Part 3) Published March 20, 2023 One of the very popular and useful economic models is the Cobb-Douglas production model given by \[ Y_i = \beta_0 X_{1i}^{\beta_1}X_{2i}^{\beta_2} e^{u_i} \tag{1} \] where \(Y\) is the output; \(X_1\) is the labor input; \(X_2\) is the capital input; and...
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Econ 115s- Lesson 2.1 (Multiple Linear Regression: Estimation)
Table of contents 1 Regression model with two explanatory variables 2 Regression model with k explanatory variables 3 OLS Estimation 4 Examples 5 Fitted values and residuals 6 Sums of squares and goodness-of-fit 7 Assumptions for unbiasedness of OLS estimators 8 Variances of OLS estimators Stat 115s (Introduction to Econometrics) Lesson 2...
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Stat 136 Lab Exercise No. 2
Problem 1 Another way to choose the “best” Beta prior for a proportion is using the mean and standard deviation of the Beta distribution. Recall that if \(Y \sim Beta(a, b)\), then \[\begin{align} E(Y) &= \frac{a}{a+b}, \; \text{and} \notag \\ V(Y) &= \frac{ab}{(a+b)^2(a+b+1)} \end{align}\] If the prior mean and prior variance (or stand...
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Stat 142 Lesson 2.1 (Time Series Decomposition)
Table of contents 1 Review of time series components 2 More on moving averages 3 Classical decomposition 3.1 Additive decomposition 3.2 Multiplicative decomposition 3.3 Comments on classical decomposition 4 X11 decomposition 5 SEATS decomposition 6 STL decomposition Stat 142 (Time Series Analysis) Time Series Decomposition Author Nor...
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Stat 142 Lesson 1.3 (Overview of Forecasting Strategies)
1 Introduction The ultimate end goal of time series is forecasting. Forecasting refers to predicting what will happen in the future by taking into consideration the past and present events. Forecasting methods can be generally classified into two: Quantitative and Qualitative. Quantitative forecasting methods include, among others, naive method...
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Stat 136 Lesson 2.2 (Bayesian inference for a proportion using continuous prior)
1 Motivation A limitation of specifying a discrete prior for \(p\) is when a plausible value is not specified in the prior distribution (e.g. \(p = 0.2\)), it will be assigned a \(0\) probability in the posterior distribution Ideally, we want a distribution that allows p to be any value in [0, 1] Two possible distributions come into mind: Co...
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Stat 136 Lesson 2.2 (Bayesian inference for a proportion using continuous prior)
class: center, middle, inverse, title-slide .title[ # Lesson 2.2: Bayesian Inference for p ] .subtitle[ ## (Continuous Prior) ] .author[ ### Norberto E. Milla, Jr. ] .institute[ ### Department of Statistics, VSU ] .date[ ### 2023-03-08 ] --- ## Motivation - A limitation of specifying a discrete prior for `\(p\)` is when a plau...
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Stat 122- Problem Set No. 2
INSTRUCTION: Present neat and detailed solutions. Problem No. 1 The proportion of impurities in certain water samples is a random variable \(Y\) with a density function given by \[ f_Y(y) = \begin{cases} \frac{3}{2} y^2 + y, \; \text{if} \; 0\leq y \leq 1 \\ 0, \; \text{elsewhere} \end{cases} \] Find the probability density function of \(U...
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Econ 115s Lesson 1.4 (Properties of OLS Estimators)
1 Statistical Properties of OLS Estimators What are the properties of the distributions of \(\beta_0\) and \(\beta_1\) over different random samples from the population? What are the expected values and variances of OLS estimators? We will first examine finite sample properties: unbiasedness and efficiency. These are valid for any sample size ...
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