```{r data generation, echo = FALSE, results = "hide"}
d <- data.frame(x = runif(100, -1, 1))
a <- 0
b <- sample(c(-1, 1), 1) * sample(c(0, 0.6, 0.9), 1)
d$y <- a + b * d$x + rnorm(100, sd = 0.25)
write.csv(d, "regression.csv", row.names = FALSE, quote = FALSE)
m <- lm(y ~ x, data = d)
bhat <- coef(m)[2]
bpvl <- summary(m)$coefficients[2, 4]
bsol <- c(bpvl >= 0.05, (bpvl < 0.05) & (bhat > 0), (bpvl < 0.05) & (bhat < 0))
```
Question
========
Using the data provided in [regression.csv](regression.csv) estimate a linear regression of
`y` on `x` and answer the following questions.
Answerlist
----------
* `x` and `y` are not significantly correlated
* `y` increases significantly with `x`
* `y` decreases significantly with `x`
* Estimated slope with respect to `x`:
Solution
========
\
```{r scatterplot, echo = FALSE, results = "hide", fig.height = 4.5, fig.width = 4.5, fig.path = "", fig.cap = ""}
plot(y ~ x, data = d)
abline(m)
legend(if(bhat > 0) "topleft" else "topright", bty = "n",
paste0("b = ", fmt(bhat, 3), "\np = ", fmt(bpvl, 3)))
```
To replicate the analysis in R:
```
## data
d <- read.csv("regression.csv")
## regression
m <- lm(y ~ x, data = d)
summary(m)
## visualization
plot(y ~ x, data = d)
abline(m)
```
Meta-information
================
exname: Linear regression
extype: cloze
exsolution: `r mchoice2string(bsol)`|`r fmt(bhat, 3)`
exclozetype: schoice|num
extol: 0.01