- How I became a philosopher
- I had an irreligious experience

- 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
- Fact Checkers
- View Fact-Checking Sites

- Beyond Fact Checkers

- Fact Checkers

- Other Stuff

**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.
- View Anscombe’s Quartet

- 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 Matrix

- 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.
- View Residual Metrics

##### Sum-of-Squares Metrics

- The Least Squares Algorithm is a method finding the equation that, given the observed values of the dependent and independent variables, yields the lowest possible residual sum of squares.
- The residual sum of squares, along with other sums of squares, is thus a natural basis for statistics that evaluate regressions.
- View Principle of Sums of Squares
- View R-Squared
- View Adjusted R-Squared
- View ANOVA for Simple Regression
- View ANOVA for Multiple Regression

##### Standard Error Metrics

- The standard error of an estimate is how statisticians quantify the idea of average error, i.e. as the standard distribution of the estimate’s sampling distribution.
- Of interest in regression are the standard errors of the regression, the mean of the residuals, the coefficients of the independent variables, and the intercept.
- View Standard Errors of the Regression, the Mean, the Independent Variables, and the Intercept

##### 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

- SSR + SSE = SST, where SSR, SSE, and SST are the sums of squares for
- Standard Error of the Regression = 6.6551
- = √(SSE / (Datapoints – (NbrofIVs + 1)))

- R-Squared = 0.244811
- = SSR / SST

- Adjusted R-Squared = 0.240234
- 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

- SSR + SSE = SST, where SSR, SSE, and SST are the sums of squares for
- Standard Error of the Regression = 4.31866
- = √(SSE / (Datapoints – (NbrofIVs + 1)))

- R-Squared = 0.681988
- = SSR / SST

- Adjusted R-Squared = 0.68006
- AICc = 966.696

- As you can tell from the scatter plot, this nonlinear regression on GDP is better than its linear counterpart
- SER is lower, 4.31866 versus 5.18411.
- R-Squared is higher, 0.681988 versus 0.541759
- AICc is lower, 966.696 versus 1027.7

- Incidentally, although the regression is nonlinear, R-Squared is valid since SSR and SSE add up to SST. I did my own calculation, since Mathematica calculates nonlinear R-Squareds differently, getting a much higher number, in this case 0.996545.