Different types of intervals

Inference for Linear Regression in R

Jo Hardin

Professor, Pomona College

Predicting average calories at specific fat

library(broom)
alpha <- .05
crit_val <- qt((1-alpha/2), df = nrow(starbucks) - 2) 
newfood <- data.frame(Fat = c(0,10,20,30))
augment(lm(Calories ~ Fat, data=starbucks), newdata = newfood) %>%
   mutate(lowMean = .fitted - crit_val*.se.fit,
          upMean = .fitted + crit_val*.se.fit)

  Fat  .fitted   .se.fit  lowMean   upMean
1   0 147.9833 14.971985 118.3153 177.6513

2  10 275.5693  8.516206 258.6938 292.4447

3  20 403.1552  7.378555 388.5341 417.7763
4  30 530.7412 13.035040 504.9114 556.5710

Creating CI for average response

predMeans <- augment(lm(Calories ~ Fat, data = starbucks)) %>%
   select(Calories, Fat, .fitted, .se.fit) %>%
   mutate(lowMean = .fitted - crit_val*.se.fit,
          upMean =  .fitted + crit_val*.se.fit) 
head(predMeans)

  Calories Fat  .fitted   .se.fit  lowMean   upMean
1      300   5 211.7763 11.473843 189.0401 234.5125
2      380   6 224.5349 10.823741 203.0869 245.9828
3      410  22 428.6724  8.176354 412.4704 444.8744
4      460  23 441.4310  8.663769 424.2632 458.5989
5      420  22 428.6724  8.176354 412.4704 444.8744
6      380  16 352.1209  6.756473 338.7324 365.5093

Plotting CI for average response

ggplot(predMeans, aes(x = Fat, y = Calories)) + 
   geom_point() +
   stat_smooth(method = "lm", se = FALSE) + 
   geom_ribbon(aes(ymin = lowMean, ymax = upMean), alpha=.2)

alpha <- .05
crit_val <- qt((1-alpha/2), df = nrow(twins) - 2)
FatCal_lm <- lm(Calories ~ Fat, data = starbucks)
FatCal_gl <- glance(FatCal_lm)
FatCal_sig <- pull(FatCal_gl, sigma)
FatCal_pred <- augment(FatCal_lm) %>% 
    mutate(.se.pred = sqrt(FatCal_sig^2 + .se.fit^2))
predResp <- FatCal_pred %>% 
    mutate(lowResp = .fitted - crit_val*.se.pred, upResp = .fitted + crit_val*.se.pred)
predResp

A tibble: 113 x 12
   Calories   Fat  .fitted   .se.fit     .resid        .hat   .sigma
      <int> <dbl>    <dbl>     <dbl>      <dbl>       <dbl>    <dbl>
 1      300     5 211.7763 11.473843  88.223722 0.025567957 71.57640
 2      380     6 224.5349 10.823741 155.465125 0.022752704 70.50502
 3      410    22 428.6724  8.176354 -18.672436 0.012983674 72.05959
... with 103 more rows, and 5 more variables: .cooksd <dbl>, .std.resid <dbl>, .se.pred <dbl>,
    lowResp <dbl>, upResp bl>

Plotting prediction intervals

ggplot(predResp, aes(x = Fat, y = Calories)) + 
  geom_point() +
  stat_smooth(method = "lm", se = FALSE) + 
  geom_ribbon(aes(ymin = lowResp, ymax = upResp), alpha = .2)

Let's practice!

Inference for Linear Regression in R