code_along_answers.txt

Code along answers

## CODE ALONG 1

1. Model `y` as a function of `z` using `lm(y ~ z, data = d)` and save to an object called `mod2`. View the summary. What formula does the model return? What is the estimated standard deviation of the Normally distributed noise?

mod2 <- lm(y ~ z, data = d)
summary(mod2)

2. Use the model to simulate density histograms and compare to the original density histogram of `d$y`.

hist(d$y, freq = FALSE)
lines(density(d$y))
lines(density(73.0003 + d$z*0.2312 + rnorm(25, 0, sd = 36.36)), col = "red")



## CODE ALONG 2

1. Insert a code chunk below and model `log(totalvalue)` as function of `fullbath` and `finsqft.` Call your model `m3`

m3 <- lm(log(totalvalue) ~ fullbath + finsqft, data = homes)

2. Insert a code chunk below and check the diagnostic plots

plot(m3)

3. How do we interpret the fullbath coefficient?

round(exp(coef(m3)), 3)

Adding a full bath increases value of house by about 17% 

4. Insert a code chunk below and simulate data from the model and compare to the observed `totalvalue`. Does this look like a good model?

sim_m3 <- simulate(m3, nsim = 50)
plot(density(log(homes$totalvalue)))
for(i in 1:50)lines(density(sim_m3[[i]]), lty = 2, col = "grey80")


## CODE ALONG 3

1. Insert a code chunk below and model `log(totalvalue)` as function of `fullbath`, `finsqft` and `cooling.` Call your model `m5`. 

m5 <- lm(log(totalvalue) ~ fullbath + finsqft + cooling, data = homes)

2. What is the interpretation of cooling? 

round(exp(coef(m5)), 3)

Expected value of a home with No Central Air is about 19-20% lower than an equivalent home with Central Air.


## CODE ALONG 4

1. Insert a code chunk below and model `log(totalvalue)` as function of `fullbath`, `finsqft`, `cooling`, and the interaction of `finsqft` and `cooling`. Call your model `m7`. Is the interaction warranted?

m7 <- lm(log(totalvalue) ~ fullbath + finsqft + cooling + finsqft:cooling, 
        data = homes)
anova(m7)

2. Visualize the interaction using the `ggpredict` function. Perhaps use `[1000:4000 by=500]` to set the range of `finsqft` on the x-axis.

plot(ggpredict(m7, terms = c("finsqft[1000:4000 by=500]", "cooling")))

## CODE ALONG 5

1. Insert a code chunk below and model `log(totalvalue)` as function of `finsqft` with a natural spline of 5 `df`, `cooling`, and the interaction of `cooling` and `finsqft` (natural spline of 5 `df`). Call your model `nlm4`.

nlm4 <- lm(log(totalvalue) ~ ns(finsqft, df = 5) + cooling + 
             ns(finsqft, df = 5):cooling, data = homes)


2. Use the `anova` function to check whether the interaction appears necessary. What do you think?

anova(nlm4)

3. Create an effect plot of `finsqft` by `cooling`. Maybe try `[1000:5000 by=250]` for the range of values for `finsqft`.

plot(ggpredict(nlm4, terms = c("finsqft[1000:5000 by=250]", "cooling")))