```{r data generation, echo = FALSE, results = "hide"}
## DATA GENERATION
data("USairpollution", package = "HSAUR2")
nsize <- sample(50:150, 1)
sampled_dat <- sample(1:nrow(USairpollution), nsize, replace = TRUE)
final_data <- USairpollution[sampled_dat, ]
full_model <- lm(SO2 ~ ., data = final_data)
sum_fullmod <- summary(full_model)
# % of explained variance
sol_adjr2 <- round(sum_fullmod$adj.r.squared * 100, digits = 1)
# no of statistically sign. variables
pvals <- summary(full_model)$coefficients[-1, 4]
no_sig <- sum(pvals < 0.05)
# Increase in CO2 with more factories
SO2_fact <- round(full_model$coefficients["manu"] * 100, digits = 1)
attributes(SO2_fact) <- NULL
## QUESTION/ANSWER GENERATION
quest <- c(
"What is the % of explained variance (adjusted for number of variables)? (Round to 1 digit, e.g. 1.5% or 22.4%)",
"How many explanatory variables in the model are statistically significant?",
"What is the approximate increase in the SO2 content if 100 new factories would open in a city? (Round to 1 digit)"
)
sol <- c(sol_adjr2, no_sig, SO2_fact)
sel_q <- sample(1:length(quest), 1)
finquest <- quest[sel_q]
finsol <- sol[sel_q]
```
Question
========
The annual mean concentration of sulphur dioxide, in micrograms per cubic metre,
is a measure of the air pollution of a city. Related measurements have been taken
in `r nsize` US cities along with the following variables that may determine the SO2 levels:
* `temp`: average annual temperature in Fahrenheit.
* `manu`: number of manufacturing enterprises employing 20 or more workers.
* `popul`: population size (1970 census); in thousands.
* `wind`: average annual wind speed in miles per hour.
* `precip`: average annual precipitation in inches.
* `predays`: average number of days with precipitation per year.
A multiple linear regression model has been fitted that returned the following summary information:
```{r lm output, echo = FALSE}
print(sum_fullmod)
```
`r finquest`
Meta-information
================
exname: Multiple_regression
extype: num
exsolution: `r finsol`
extol: 0.01