RRegression.Rmd

---
title: "Linear Regression Analysis in R"
output:
  html_document:
    df_print: paged
---
# Linear Regression Analysis in R

This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 

Executing a chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Cmd+Shift+Enter*. 

## Code

The chunk below loads the `ggplot2` library into R. We will need this to make a pretty plot of the result.

```{r}
library(ggplot2)
```

The chunk below loads the *x* and *y* points into a dataframe named `mydata`. Replace the numbers in parenthesees with your data points before running it.

```{r}
xpts <- c(1, 2, 3, 4, 5, 6)
ypts <- c(1, 4.02, 5.9, 8.11, 10.02, 11.99)
mydata <- data.frame(xpts, ypts)
```

Run the chunk below to display the dataframe `mydata` so you can be sure it is correct.

```{r}
mydata
```

The chunk below produces a linear regression and displays a summary with the essential information.

```{r}
linefit <- lm(ypts ~ xpts, data=mydata)
summary(linefit)
```

The chunk below gives the fit values for the intercept and slope estimates. These are in the Estimate column in the summary above.

```{r}
coefficients(linefit)
```

Since we often express a linear equation in the form $y = Ax + B$, the two cells below store the intercept as `B` and the slope as `A`. The chunks below define them for later.

```{r}
B <- coefficients(linefit)[[1]]
A <- coefficients(linefit)[[2]]
```

We will use the standard error of the fit residuals (residual standard error in the summary above) as our error bars. Run the chunk below to define the varaible `stderror` with this value.

```{r}
stderror = sigma(linefit)
stderror
```

The chunk below gives the T-test confifence intervals of the fit parameters (intercept and slope). These are 95% confidence intervals since there is a 5% total chance that the actual values are outside the intervals.

```{r}
confint(linefit)
```

The chunk below produces a basic plot of the data points, error bars, and fit line.
```{r}
plt <- ggplot(mydata, aes(x=xpts, y=ypts)) + 
    geom_point() +
    geom_errorbar(aes(ymin=ypts-stderror, ymax=ypts+stderror), width=.2,
                 position=position_dodge(0.05)) +
    geom_abline(slope=A, intercept=B) 
print(plt)
```

The chunk below produces a configurable plot of the data points, error bars, and fit line. Adjust the following parameters to customize the plot.

* Change the values of `xmin`, `xmax`, `ymin`, and `ymax` to adjust the domain and range of the plot.
* Change the values of `xlabel` and `ylabel` (inside the quotes) to set the axis labels.
* Change the parameter `ratio.display` to adjust the aspect ratio of the plot. The value 1.618 is a common value used in publications.
* Change the theme in the second to last line to change the look of the plot. Some themes to try are `theme_gray()`, `theme_bw()`, `theme_linedraw()`, `theme_light()`, `theme_dark()`, `theme_minimal()`, and `theme_classic()`.

```{r}
xmin <- 0
xmax <- 7
ymin <- 0
ymax <- 15

xlabel <- "x"
ylabel <- "y"


ratio.display <- 1.618
ratio.values <- (xmax-xmin)/(ymax-ymin)
plt <- ggplot(mydata, aes(x=xpts, y=ypts)) + 
    geom_point() +
    geom_errorbar(aes(ymin=ypts-stderror, ymax=ypts+stderror), width=.2,
                 position=position_dodge(0.05)) +
    geom_abline(slope=A, intercept=B) + 
    coord_fixed(ratio.values / ratio.display) +
  xlim(xmin, xmax) +
  ylim(ymin, ymax) +
  xlab(xlabel) +
  ylab(ylabel) +
  theme_bw()
print(plt)
```

The chunk below saves the latest `ggplot`. Change the filename to whatever you want. Change the extension to change the file type. Possible file types include "eps", "ps", "tex" (pictex), "pdf", "jpeg", "tiff", "png", "bmp", or "svg".

```{r}
ggsave("myplot.pdf")
```