```{r data generation, echo = FALSE, results = "hide"} ## regression parameters n <- sample(40:90, 1) b <- sample(c(-1, 1), 1) * runif(1, 1, 2) * sample(c(0.1, 0.5, 1), 1) s <- sample(c(0.5, 1, 2), 1) ## data and regression d <- data.frame( x = rnorm(n), err = rnorm(n, sd = s) ) d$y <- 0 + b * d$x + d$err ## different types type <- sample(c("linear", "semi-logarithmic", "log-log"), 1) if(type == "linear") { m <- lm(y ~ x, data = d) xunit <- "unit" yunit <- "units" eff <- round(coef(m)[2], digits = 2) } else if(type == "semi-logarithmic") { d$y <- exp(d$y) m <- lm(log(y) ~ x, data = d) xunit <- "unit" yunit <- "percent" eff <- round(100 * exp(coef(m)[2]) - 100, digits = 2) } else if(type == "log-log") { d$y <- exp(d$y) d$x <- exp(d$x) m <- lm(log(y) ~ log(x), data = d) xunit <- "percent" yunit <- "percent" eff <- round(100 * exp(0.01 * coef(m)[2]) - 100, digits = 2) } ## summaries direct <- if(coef(m)[2] > 0) "increases" else "decreases" if(summary(m)$coefficients[2, 4] < 0.05) { sign1 <- "Also" sign2 <- "" } else { sign1 <- "However" sign2 <- "_not_" } ``` Question ======== Consider the following regression results: ```{r lm output, echo = FALSE, comment = NA} summary(m) ``` Describe how the response `y` depends on the regressor `x`. Solution ======== The presented results describe a `r type` regression. The mean of the response `y` `r direct` with increasing `x`. If `x` increases by 1 `r xunit` then a change of `y` by about `r eff` `r yunit` can be expected. `r sign1`, the effect of `x` is `r sign2` significant at the 5 percent level. Meta-information ================ extype: string exsolution: nil exname: regression essay exstringtype: essay|file exextra[essay,logical]: TRUE exextra[essay_format,character]: editor exextra[essay_required,logical]: FALSE exextra[essay_fieldlines,numeric]: 0 exextra[essay_attachments,numeric]: 1 exextra[essay_attachmentsrequired,logical]: TRUE exmaxchars: 1000, 10, 50