FinQuiz - Battle-ready Summaries, Study Session 1, Reading 2

University:
Davenport University
Course:
FINC 382 | International Finance
Academic year:

2024
Views:

231

Pages:

2
Author:

Mohamed Waheed

2024 | QM | Learning Module 2 Evaluating Regression Model Fit & Interpreting Model Results 1. GOODNESS OF FIT Measures of Goodness of Fit Goodness of fit can be measured using coefficient of determination 𝑅 " . 𝑅" = $%&'()*+, -(.)(/)0*(223) 50/(' -(.)(/)0* (225) Adjusted R2 R2 in Multiple Linear Regression ANOVA AIC & BIC Two measures to determine model parsimony by comparison of models. • Akaike’s information criterion (AIC): Lower AIC means a better fit. It is used for prediction purpose. • Schwarz’s Bayesian information criterion (BIC or SBC): is used when goodness of fit is required. • The lower the AIC or BIC the better. Adjusted R2 resolves artificial increase in accuracy issue. 𝑛−1 𝑅6 " = 1 − : = (1 − 𝑅 ") 𝑛−𝑘−1 Problems in Multiple Linear Regression • 𝑅 " does not indicate coefficient significance. • 𝑅 " does not indicate biases in coefficients & forecasts. • 𝑅 " cannot assess model fit. • Overfitting issue The higher the value the better is the model fit. Analysis of Variance Table for Simple Linear Regression ANOVA df SS 𝑆𝑆𝑅 * Regression 1 = ?(𝑦A) )BC " − 𝑦6) 𝑆𝑆𝐸 * Error n-2 = ?(𝑦) )BC − 𝑦A)" MS F 𝐹= 𝑀𝑆𝑅 = 𝑆𝑆𝑅 𝑘 F23 F2$ = 𝑆𝑆𝑅G 1 𝑆𝑆𝐸G (𝑛 − 2) 𝑀𝑆𝐸 = 𝑆𝑆𝐸 𝑛−2 𝑆𝑆𝑇 * Total n–1 = ?(𝑦) )BC − 𝑦6)" Copyright © FinQuiz.com. All rights reserved. 1 2024 | QM | Learning Module 2 2. TESTING JOINT HYPOTHESES FOR COEFFICIENTS Significance of two or more coefficients in Multiple Regression In multiple regression, o intercept predicts the dependent variable when all independent variables are zero. o slope coefficient predicts the change in the dependent variable with a one-unit change in an independent variable, keeping other variables constant. Unrestricted Models & Restricted (Nested) Models • unrestricted model -a model with all independent variables. • restricted model – a model that limits the slope coefficients. It is also called nested model. F-Distributed Joint Test of Hypotheses General Linear F-Test F-distributed test statistic examines the role of jointly omitted variables. F= 𝑆𝑆𝐸 𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 𝑚𝑜𝑑𝑒𝑙 − U a c 𝑆𝑆𝐸 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 𝑞 𝑆𝑆𝐸 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 𝑚𝑜𝑑𝑒𝑙 d (𝑛 − 𝑘 − 1) • The F-statistic in multiple regression tests if at least one independent variable explains a significant portion of variation in the dependent variable. F23 • 𝐹 𝑠𝑡𝑎𝑡𝑖𝑠𝑖𝑡𝑐 = = Steps for Hypothesis Testing 1. State the hypothesis 2. Identify the appropriate test statistic 3. Specify the level of significance 4. State the decision rule 5. Calculate the test statistic 6. Make a decision fgg F2$ U h a ggi Ujkhkla 3. FORECASTING USING MULTIPLE REGRESSION Predicting the Dependent Variable in a Multiple Regression Model Errors • Prediction equation: 𝑌L) = 𝑏LN + 𝑏LC 𝑋C) + 𝑏L" 𝑋") +. . . +𝑏LR 𝑋R) • • Model Error 𝜺𝒊 : observations not falling on the predicted line. It is stochastic component of the model. Sampling Error: when a sample inaccurately represents the population due to inaccurate forecasting. Model and sampling errors widen the prediction interval. Copyright © FinQuiz.com. All rights reserved. 2