# Philosophic Method, SAIL Fall 2022

• Nature of Philosophy
• Subject Matter: Any Fundamental Issue
• Method: Analysis of Arguments
• Mindset: Skepticism
• Examples of Arguments
• President John Oliver
• Black Swans
• Editorial on Capital Punishment
• Declaration of Independence
• Philosophic Arguments
• Abortion
• Is it rational to believe the report of a miracle?
• Consciousness
• Persons
• Free Will and Determinism
• Political Philosophy
• Skepticism
• What is knowledge?
• Applied Philosophy
• Application of philosophic analysis to matters of practical concern, e.g. issues in politics, law, medicine, religion, environment, economics, education, science, and technology.
• Philosophical analysis is applied to:
• Arguments
• Claims
• Decisions
• Investigations
• Analysis of:
• Arguments
• Decisions
• Investigations
• Investigation
• Mueller Report
• Durham Report, when it’s released.
• Report of Select Committee to Investigate the January 6 Attack on the Capitol, when it’s released.
• Warren Commission Report on the Assassination of President Kennedy
• Claims

#### Tools for Evaluating Regressions

Statisticians have developed various kinds of tools for evaluating regressions.

##### Graphics
• Graphics are essential to evaluating regressions. Indeed, different datasets can have nearly the same statistics but look totally different graphically.
• One of the most useful charts for simple linear regression is a scatter plot of the data with regression line.
• But graphs have limitations.  For example, graphing the data and equation for a regression with two IV’s requires three dimensions.
• View Regression Graphics
##### Correlation
• Variables are correlated to the extent that they vary together, in the same or opposite directions.
• Correlation coefficients are useful
• between an independent variable and the dependent variable
• among independent variables
• The Correlation Matrix for multiple regression displays all the correlation coefficients between variables, independent and dependent.
• View Correlation
##### Prediction
• An hypothesis is supported or disproved by its predictions. A regression equation is an hypothesis. So a natural way of evaluating a regression is to assess its predictions for “out-of-sample” data.
• An interesting metric, the Prediction Sum of Squares (PRESS), evaluates a regression by seeing how well regressions on the sample data, minus one datapoint, predict the missing data item.
##### Residual Metrics
• A residual is the difference, at a given datapoint, between the values of the observed and predicted dependent variable. There are different ways of combing the residuals into a single statistic.
##### Likelihood Metrics
• A hypothesis is more likely if it better predicts the data than competing hypotheses, other things being equal.
• Regression likelihood metrics are based on the idea that the more likely the data given the regression equation, the better the regression.
• View Likelihood Metrics
###### Linear Regression on IMF

The regression stats are:

• Regression Equation; y = 74.6433 –71.4322 m
• DataPoints = 167
• NbrofIVs = 1
• Sum of Squares Equation: 2369.03 + 7307.92 = 9676.95
• SSR + SSE = SST, where SSR, SSE, and SST are the sums of squares for
• predicted y’s
• residuals
• observed y’s
• Standard Error of the Regression = 6.6551
• = √(SSE / (Datapoints – (NbrofIVs + 1)))
• R-Squared = 0.244811
• = SSR / SST
• AICc = 1111.13
• The regression on IMF is not as good the regression on GDP
• SER is higher, 6.6551 versus 5.18411.
• R-Squared is lower, 0.244811 versus 0.541759
• AICc is higher, 1111.13 versus 1027.7
###### NonLinear Regression on GDP

The regression stats:

• Regression Equation; y = 12.8393 + 5.86683 Log[\$]
• DataPoints = 167
• NbrofIVs = 1
• Sum of Squares Equation: 6599.56 + 3077.39 = 9676.95
• SSR + SSE = SST, where SSR, SSE, and SST are the sums of squares for
• predicted y’s
• residuals
• observed y’s
• Standard Error of the Regression = 4.31866
• = √(SSE / (Datapoints – (NbrofIVs + 1)))
• R-Squared = 0.681988
• = SSR / SST