class: center, middle, inverse, title-slide # Final Review ## EC 320: Introduction to Econometrics ### Winter 2022 --- class: inverse, middle # Prologue --- # Housekeeping ## Final Exam Friday, March 18 at 10:15am in Tykeson 140. ## Lab Additional review session. ## Office hours Next week: Tuesday and Thursday over Zoom --- class: inverse, middle # Final Exam --- # Final Exam Topics .green[Anything from the lectures, labs, or problem sets] .hi-green[is fair game!] 1. Midterm Topics 2. Multiple Linear Regression: Inference 3. Categorical Variables 4. Interactive Relationships 5. Nonlinear Relationships --- # Final Exam Topics ## 1. Midterm Topics Making predictions using fitted regression model - *e.g.,* using a Hedonic model Goodness of fit Hypothesis testing -- .pink[Omitted-variable bias] - Know when omitting a variable causes bias - Sign the bias - Back out correlations between explanatory variables - Provide examples of problematic omitted variables --- # Final Exam Topics ## 2. Multiple Linear Regression: Inference *F* tests (multiple parameters) - State null hypothesis - Identify restricted and unrestricted models - Calculate *F* statistic - Use table to find *F*.sub[*crit*] - *F* .mono[>] *F*.sub[*crit*]? - State conclusion of the test *t* tests (single parameter) -- **Q:** Which test should you choose? -- **A:** Depends on the null hypothesis! --- # Final Exam Topics ## 2. Multiple Linear Regression: Inference Confidence intervals - Formula, interpretation, and comparison of different intervals for the same coefficient -- .pink[Proof:] Show that the *F* statistic formula containing *RSS* implies the *F* statistic formula containing *R*.super[*2*] - For practice, you can also prove that the second formula implies the first --- # Final Exam Topics ## 3. Categorical Variables How do you interpret coefficients on binary variables? - **Note:** Depends on the presence of interaction terms and whether the outcome variable is transformed Dummy variable trap What is the reference category? - How do you back out group-specific averages from a dummy variable regression? - How do coefficient estimates change when you change the reference category? --- # Final Exam Topics ## 4. Interactive Relationships How do you interpret interaction coefficients? - Binary `\(\times\)` binary - Binary `\(\times\)` continuous - Continuous `\(\times\)` continuous How does an interaction term change how you interpret the effect of the variable of interest on the outcome variable? - Marginal effects (partial derivative) --- # Final Exam Topics ## 5. Nonlinear Relationships Identify nonlinear models - OLS can handle nonlinear variables, but not nonlinear parameters Transform nonlinear models - Give OLS a chance --- # Final Exam Topics ## 5. Nonlinear Relationships How do you interpret coefficients in the presence of logarithmic transformations? - Level `\(Y\)`, level `\(X\)` - Level `\(Y\)`, log `\(X\)` - Log `\(Y\)`, level `\(X\)` - Log `\(Y\)`, log `\(X\)` -- **Quadratic models:** interacting `\(X\)` with itself - Calculate marginal effects to understand how `\(X\)` affects `\(Y\)` --- # Final Exam Structure ### Mix of fill-in-the blanks, multiple choice questions, T/F questions (60 points) - Total of 20 questions (3 points each) ### Long answer questions (40 points) - Four questions --- # Final Exam Protocol ## Materials - Writing utensil - 3-inch-by-5-inch note card - Basic or scientific calculator (no graphing or programming capabilities) - .hi[Nothing else] ## Procedure - 120 minutes from *"you may begin"* to *"pencils down"* - First 30 minutes: .hi[quiet period] (no questions, no getting up) - Last 90 minutes: ask lots of questions --- class: inverse, middle # Practice --- # .mono[gapminder] Package Data on population, GDP per capita, and life expectancy Unit of observation: country-year - All countries, every 5.super[th] year between 1957 and 2007 ```r p_load(gapminder) data <- get('gapminder') head(data) ``` ``` #> # A tibble: 6 × 6 #> country continent year lifeExp pop gdpPercap #> <fct> <fct> <int> <dbl> <int> <dbl> #> 1 Afghanistan Asia 1952 28.8 8425333 779. #> 2 Afghanistan Asia 1957 30.3 9240934 821. #> 3 Afghanistan Asia 1962 32.0 10267083 853. #> 4 Afghanistan Asia 1967 34.0 11537966 836. #> 5 Afghanistan Asia 1972 36.1 13079460 740. #> 6 Afghanistan Asia 1977 38.4 14880372 786. ``` --- class: white-slide .center[**Association of GDP per Capita with Life Expectancy**] <table class="table" style="font-size: 18.2px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> log(Life Expectancy) </th> <th style="text-align:center;"> log(Life Expectancy) </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 6.42 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 5.69 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.112 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.111 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.183) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.325) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.004) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.006) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Americas </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 4.03 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.047 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.674) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.013) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Asia </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.561 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -0.002 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.421) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.008) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Europe </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.614 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -0.019 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.597) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.012) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Oceania </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 5.2 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.035 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (4.36) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.084) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Continent Dummies? </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Observations </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> R-Squared </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.71 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.665 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.669 </td> </tr> </tbody> </table> --- class: white-slide .center[**Association of GDP per Capita with Life Expectancy**] <table class="table" style="font-size: 18.2px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> log(Life Expectancy) </th> <th style="text-align:center;"> log(Life Expectancy) </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 6.42 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 5.69 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.112 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.111 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.183) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.325) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.004) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.006) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Americas </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 4.03 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.047 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.674) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.013) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Asia </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.561 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -0.002 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.421) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.008) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Europe </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.614 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -0.019 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.597) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.012) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Oceania </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 5.2 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.035 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (4.36) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.084) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Continent Dummies? </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Observations </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> R-Squared </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.71 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.665 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.669 </td> </tr> </tbody> </table> --- class: white-slide .center[**Association of GDP per Capita with Life Expectancy**] <table class="table" style="font-size: 18.2px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> log(Life Expectancy) </th> <th style="text-align:center;"> log(Life Expectancy) </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 6.42 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 5.69 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.112 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.111 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.183) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.325) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.004) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.006) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Americas </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 4.03 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.047 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.674) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.013) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Asia </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.561 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -0.002 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.421) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.008) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Europe </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.614 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -0.019 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.597) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.012) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Oceania </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 5.2 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.035 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (4.36) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.084) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Continent Dummies? </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Observations </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> R-Squared </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.71 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.665 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.669 </td> </tr> </tbody> </table> --- class: white-slide .center[**Association of GDP per Capita with Life Expectancy**] <table class="table" style="font-size: 18.2px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> Life Expectancy </th> <th style="text-align:center;"> log(Life Expectancy) </th> <th style="text-align:center;"> log(Life Expectancy) </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 6.42 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 5.69 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.112 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.111 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.183) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.325) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.004) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.006) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Americas </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 4.03 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.047 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.674) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.013) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Asia </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.561 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> -0.002 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.421) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.008) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Europe </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.614 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> -0.019 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.597) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.012) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> log(GDP/Capita) ? Oceania </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 5.2 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.035 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (4.36) </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> </td> <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.084) </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Continent Dummies? </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> Yes </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> Yes </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Observations </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 1704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 1704 </td> </tr> <tr> <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> R-Squared </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.704 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.71 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.665 </td> <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.669 </td> </tr> </tbody> </table>