Publications by Laboratory Exercise No. 5
Econ 115s Lesson 1.3 (Incorporating Nonlinearities in the SLR Model)
1 Incorporating Nonlinearities in Simple Regression Linear relationships may not be appropriate in some cases. By appropriately redefining variables we can easily incorporate nonlinearities into the simple regression. Our model will still be linear in parameters. We do not use nonlinear transformations of parameters. In practice natural logari...
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Econ 115s Lesson 1.2 (The Simple Linear Regression Model)
1 Definition of the Simple Regression Model \[ y = \beta_0 +\beta_1x + u \] \(y\): the dependent variable (explained variable, response variable, predicted variable, regressand, outcome variable) \(x\): the explanatory variable (independent variable, cotrol variable, predictor variable, regressor, input variable) Also called “bivariate li...
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Stat 142 Lab Exercise 1
INSTRUCTIONS: Document your work by creating and compiling an R Markdown document in HTML format. Place heading for each section of your analysis. Upload your document to Rpubs and send the link in the GC. Open the livestock.xlsx file and study it. Save it in CSV format and read the file into R/RStudio. Convert the data for Cattle, Hog, and Goa...
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Stat 136 Lab Exercise No. 1
Problem 1 Let \(Y_1\) be the number of successes in \(n = 10\) independent trials where each trial results in a success or failure, and p, the probability of success, remains constant over all trials. Suppose the 4 possible values of \(p\) are 0.20, 0.40, 0.60, and 0.80. We do not wish to favor any value over the others so we make them equall...
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Stat 142 Lab Exercise 1 Guide
1 Required packages First, let us load the necessary packages for this lab session. library(tidyverse) library(forecast) library(timetk) 2 Data sets Monthly inflation rate Annual inflation rate Quarterly HH consumption expenditure Global CO2 concentration 3 Examples of time series data 3.1 Monthly Inflation Rate for Eastern Visayas: 201...
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Stat 136 Lesson 2.1 (Bayesian inference for a proportion using discrete prior)
1 Three general steps of Bayesian inference: Express an opinion about the location of the proportion \(p\) before sampling (prior). Take the sample and record the observed proportion (data/likelihood). Use Bayes’ rule to sharpen or update the previous opinion about \(p\) given the information in the sample (posterior). 2 An example Suppose...
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Stat 136 Lesson 1.4 (Elements of Bayesian Models)
Elements of a Bayesian model Bayes’ formula extends naturally to statistical models. A Bayesian model is a parametric model in the classical (or frequentist) sense, but with the addition of a prior probability distribution for the model parameter, which is treated as a random variable rather than an unknown constant. The basic elements of a B...
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Stat 136- Lesson 1.3 (Odds and Bayes Factor)
1 Odds Another way of dealing with uncertain events that we are modeling as random is to form the odds of the event. The odds for an event C equals the probability of the event occurring divided by the probability of the event not occurring: \[ odds(C) = \frac{P(C)}{P(\overline{C})} \] Since the probability of the event not occurring equals on...
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Stat 122- Problem Set No. 1
Problem No. 1 Suppose a random variable \(Y\) has the following density function \[ f_Y(y) = \begin{cases} \frac{3}{2} y^2 + y, \; \text{if} \; 0\leq y \leq 1 \\ 0, \; \text{elsewhere} \end{cases} \] Find the probability density function of \(U = 5 - \frac{Y}{2}\). [10 pts.] Problem No. 2 The amount of flour used per day by a bakery is a r...
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Econ 115s Lesson 1.1 (Introduction to econometrics)
1 What is econometrics? Econometrics is based upon the development of statistical methods for estimating economic relationships, testing economic theories, and evaluating and implementing government and business policy. A common application of econometrics is the forecasting of such important macroeconomic variables as interest rates, inflatio...
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