Models are simplified representations of complex things
Goal of regression
Use a model to explain (or predict) variation in an outcome using one or more explanatory variables
Drawing lines with stats
\(y = mx + b\)
\(\widehat{y} = b_0 + b_1 x\)
\(y\)
Outcome variable (Y)
\(\widehat{y}\)
\(x\)
Explanatory variable (X)
\(x\)
\(m\)
Slope
\(b_1\)
\(b\)
y-intercept
\(b_0\)
Building models in R
name_of_model <-lm(<Y>~<X>, data =<DATA>)
lm() = linear model
<Y> ~ <X> is a model formula (same as in get_correlation()!)
library(moderndive)# Make the modelname_of_model <-lm(..., data = BLAH)# Coefficients in a nice tableget_regression_table(name_of_model)# Fitted values and residuals for # every observationget_regression_points(name_of_model)
In an African country with a GDP per capita of $0, average life expectancy would be 53.74 years
GDP
Controlling for continent, a $1,000 increase in GDP per capita is associated with a 0.35 year increase in life expectancy, on average
Europe
Controlling for GDP per capita, life expectancy in Europe is 15.23 years higher than in Africa, on average
“Controlling for…”
Controlling for…
Taking all other variables in the model into account…
Holding … constant
Accounting for…
Adjusting for…
These all mean the same thing—we’re comparing countries that have the same values for every other variable in the model, or filtering out the variation that comes from the other variables and isolating just one slider or switch
# A tibble: 8 × 2
term estimate
<chr> <dbl>
1 intercept 79.3
2 fert_rate -3.48
3 gdp_1000 0.092
4 continent-Asia 1.88
5 continent-Europe 2.10
6 continent-North America 1.78
7 continent-Oceania 4.57
8 continent-South America 1.87
Move one slider/switch at a time
Imagine an African country with a fertility rate of 3 and a GDP per capita of $10,000
Scenario
Fertility rate
GDP per capita
Continent
Predicted life exp.
Change
Start
3
$10,000
Africa
69.78
0.000
Fertility + 1
4
$10,000
Africa
66.29
-3.482
GDP + $1,000
3
$11,000
Africa
69.87
0.092
Europe
3
$10,000
Europe
71.87
2.097
You can only interpret one slider or switch at a time; keep the others constant
Interpreting everything
Parameter
Interpretation
Intercept
In an African country with a fertility rate of 0 and a GDP per capita of $0, average life expectancy would be 79.3 years (not a real country!)
Fertility
Taking GDP per capita and continent into account, a one-child increase in the fertility rate is associated with a 3.48 year decrease in life expectancy, on average
GDP
Holding fertility and continent constant, a $1,000 increase in GDP per capita is associated with a 0.092 year increase in life expectancy, on average
Europe
Controlling for fertility and GDP per capita, life expectancy in Europe is 2.1 years higher than in Africa, on average
Our turn #3
Is national happiness explained by wealth, internet access, and continent?
Use multiple-regression.qmd in the “Regression playground” project
Fit a model with lm() that explains happiness with gdp_per_cap_1000, internet_use_prop, and continent
Look at the coefficients with get_regression_table()
Write out the model as an equation
Interpret the intercept and the coefficients for GDP per capita, internet use, and Europe
Your turn #3
Is national happiness explained by health, jobs, and income?
Fit a model that explains happiness with life_expectancy, unemployment_rate, and income_group
Look at the coefficients with get_regression_table()
What’s the base case for income_group?
Interpret the coefficients for life expectancy, unemployment, and high income
Intercept: A small school with 0% economically disadvantaged students would have an average math SAT score of 588.19
% disadvantaged: Controlling for school size, a one percentage point increase in economically disadvantaged students is associated with a 2.78 point decrease in average math SAT scores, on average
Medium: Taking the % of disadvantaged students into account, medium schools score 11.91 points lower than small schools, on average
Large: Taking the % of disadvantaged students into account, large schools score 6.36 points lower than small schools, on average
Intercept: A 0-year-old female professor with a beauty rating of 0 would have an average evaluation score of 4.06 (not a real professor!)
Age: Controlling for beauty and gender, a one-year increase in a professor’s age is associated with a 0.006 point decrease in evaluation scores, on average
Beauty: Holding age and gender constant, a one-point increase in beauty rating is associated with a 0.064 point increase in evaluation scores, on average
Male: Taking age and beauty into account, male professors have evaluation scores that are 0.201 points higher than female professors, on average
Intercept: An Adelie penguin with 0 mm flippers and a 0 mm bill would weigh -3904.4 grams (not a real penguin!)
Flipper length: Controlling for bill length and species, a one-mm increase in flipper length is associated with a 27.4 gram increase in body mass, on average
Bill length: Holding flipper length and species constant, a one-mm increase in bill length is associated with a 61.7 gram increase in body mass, on average
Chinstrap: Taking flipper and bill length into account, Chinstrap penguins weigh 748.6 grams less than Adelie penguins, on average
Gentoo: Taking flipper and bill length into account, Gentoo penguins weigh 90.4 grams more than Adelie penguins, on average
