Multiple least squares quadratic fit in ggplot

Question

Notice that your graphic constructed from Problem 4 shows a quadratic or curved relationship between log_wages against exp. The next task is to plot three quadratic functions for each race level "black", "white" and "other". To estimate the quadratic fit, you can use the following function quad_fit:

```{r}
quad_fit <- function(data_sub) {
  return(lm(log_wage~exp+I(exp^2),data=data_sub)$coefficients)
}
quad_fit(salary_data)
```

The above function computes the least squares quadratic fit and returns coefficients a1, a2, a3, where

Y(hat) = a1 + a2x + a3x^2

where Y(hat) = log(wage) and x = exp

Use ggplot to accomplish this task or use base R graphics for partial credit. Make sure to include a legend and appropriate labels.

My attempt

blackfit <- quad_fit(salary_data[salary_data$race == "black",])
whitefit <- quad_fit(salary_data[salary_data$race == "white",])
otherfit <- quad_fit(salary_data[salary_data$race == "other",])

yblack <- blackfit[1] + blackfit[2]*salary_data$exp + blackfit[3]*(salary_data$exp)^2
ywhite <- whitefit[1] + whitefit[2]*salary_data$exp + whitefit[3]*(salary_data$exp)^2
yother <- otherfit[1] + otherfit[2]*salary_data$exp + otherfit[3]*(salary_data$exp)^2

soloblack <- salary_data[salary_data$race == "black",]
solowhite <- salary_data[salary_data$race == "white",]
soloother <- salary_data[salary_data$race == "other",]

ggplot(data = soloblack) +
  geom_point(aes(x = exp, y = log_wage)) +
  stat_smooth(aes(y = log_wage, x = exp), formula = y ~ yblack)

This is only the first attempt for the data filtered with for race == "black". I am not clear how the formula should look like because through the quad_fit function it seems it already does the calculations for you.

Where is *your graphic constructed from Problem 4*? Simply pass in subsets to that process. — Parfait, Mar 09 '19 at 01:18
library(ggplot2) ggplot(data = salary_data) + geom_point(aes(x = exp, y = log_wage, alpha = exp)) + labs(x = "Job Experience", y = "Log of Wage", title = "Salary Dataset") This is the code for the graph, but I feel my arguments in geom_smooth are wrong. — Dario Gentiletti, Mar 09 '19 at 05:07

score 1 · Answer 1 · answered Mar 09 '19 at 18:27

Consider plotting fitted values using output of quad_fit (as shown by @StefanK here) and use by to plot across all distinct values of race:

reg_plot <- function(sub) {
   # PREDICTED DATA FOR LINE PLOT
   q_fit <- quad_fit(sub)
   predicted_df <- data.frame(wage_pred = predict(q_fit, sub), exp = sub$exp)

   # ORIGINAL SCATTER PLOT WITH PREDICTED LINE
   ggplot(data = sub) + 
     geom_point(aes(x = exp, y = log_wage, alpha = exp)) +
     labs(x = "Job Experience", y = "Log of Wage", 
          title = paste("Wage and Job Experience Plot for",    
                        sub$race[[1]], "in Salary Dataset") 
     geom_line(color='red', data = predicted_df, aes(x = exp, y = wage_pred))
}

# RUN GRAPHS FOR EACH RACE
by(salary_data, salary_data$race, reg_plot)

Multiple least squares quadratic fit in ggplot

1 Answers1