Question 5

```{r}
#| message: false
#| warning: false

modelq5 <- lm(nazivote/nvoter ~ other, nazisdata)

modelq5_pred <- expand.grid(
other = seq(from = 0, to = 1, by = .01),
nazivote = nazisdata$nazivote)

modelq5_pred$nazivote = predict(modelq5, newdata = modelq5_pred)

conf_interval2 <- predict(modelq5, newdata = modelq5_pred,  
                         interval = "confidence",
                         level = 0.95)

merged_predict2 <- cbind(conf_interval2, modelq5_pred)

merged_predict2$bad_case <- 1 - merged_predict2$lwr 
merged_predict2$good_case <- 1 - merged_predict2$upr

ggplot(merged_predict2, aes(x = other, y = bad_case)) +
  geom_line() +
  labs(
    title = "Min. nº of blue-collars vote for nazis",
    x = "Other workers",
    y = "Blue collar"
  ) +
  theme_bw() +
   theme(plot.title = element_text(hjust = 0.5))

ggplot(merged_predict2, aes(x = other, y = good_case)) +
  geom_line()  +
  labs(
    title = "Max. nº of blue-collars vote for nazis",
    x = "Other workers",
    y = "Blue collar"
  ) +
  theme_bw() +
   theme(plot.title = element_text(hjust = 0.5))

```
```{r}
#| message: false
#| warning: false

denominator <- sum(nazisdata$nazivote * nazisdata$shareblue)
average_mean <- (nazisdata$nazivote* nazisdata$shareblue) / denominator
nazisdata$average_mean <- average_mean

modelq52 <- lm(nazivote/nvoter ~ average_mean, nazisdata)

modelq52_pred <- expand.grid(
other = seq(from = 0, to = 1, by = .01),
nazivote = nazisdata$nazivote)

modelq52_pred$nazivote = predict(modelq52, newdata = modelq52_pred)

conf_interval3 <- predict(modelq52, newdata = modelq52_pred,  
                         interval = "confidence",
                         level = 0.95)  

lower_bound <- conf_interval3[, "lwr"]
upper_bound <- conf_interval3[, "upr"]

min_lower_bound <- min(lower_bound)
max_upper_bound <- max(upper_bound)

min_lower_bound
max_upper_bound
```