Publications by Laboratory Exercise No. 5
Stat 136 Lab Exercise No. 3
INSTRUCTION: Provide details of all calculations. Problem 1 The number of claims received by an insurance company during a week follows a Poisson(\(\lambda\)) distribution. The weekly number of claims observed over a ten week period are: 5, 8, 4, 6, 11, 6, 6, 5, 6, 4. Suppose a prior uniform distribution is used for \(\lambda\). Find the post...
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Data Visualization
Plotting One Variable Introduction To visualize one variable, the type of graphs to be used depends on the type of the variable: For categorical variable or grouping variables. You can visualize the count of categories using a bar plot or using a pie chart to show the proportion of each category. Dot charts can be another alternative. For con...
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Stat 142- Lesson 2.2 (Exponential Smoothing)
Table of contents 1 Introduction 2 Simple exponential smoothing 2.1 Example of SES implementation with fixed smoothing parameter 2.2 Example of SES implementation with optimal smoothing parameter 3 Holt’s linear trend method 3.1 An example 4 Damped trend methods 4.1 An example 4.2 One more example 5 Holt-Winters’ seasonal metho...
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Econ 115s Lesson 2.2- Multiple Linear Regression Model (Statistical Inference)
Table of contents 1 Sampling distribution of OLS estimators 2 Testing Hypotheses about a single population parameter: the t test 2.1 Some examples 3 Large standard errors, small t statistics, and confidence intervals 3.1 An example: Model of R&D expenditures 4 Testing Hypotheses about a single linear combination of the parameters 4.1 A...
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Sta 142 Long Exam No. 1 (Part 3)
Stat 142 (Time Series Analyis) Long Exam No. 1 (Part 3) Author Norberto E. Milla, Jr. Published March 23, 2023 Show algebraically that a \(3 \times 5\) moving average is the same as a 7-term moving weighted average with weights of 0.067, 0.133, 0.200, 0.200, 0.133, and 0.067. [5 points] The plastics data set in the fma package consists of th...
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Stat 136 Lesson 2.3 (Bayesian Inference for the Poisson Mean)
Table of contents Review: The Poisson Distribution Bayesian Inference for the Poisson Mean Using Discrete Prior Bayesian Inference for the Poisson Mean Using Continuous Prior An Example Stat 136 (Bayesian Statistics) Lesson 2.3: Bayesian Inference for the Poisson Mean Author Norberto E. Milla, Jr. Published March 23, 2023 Review: The Poiss...
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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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