How to solve

This lab uses data from the Prevention of REnal and Vascular END$-$stage Disease $($PREVEND$)$ study, which took place between $2003$ and $2006$ in the

Netherlands. Clinical and demographic data for $4,095$ individuals are stored in the $\backslash$texttt$\{$prevend$\}$ dataset in the $\backslash$texttt$\{0$ibiostat$\}$ package.

As adults age, cognitive function declines over time; this is largely due to various cerebrovascular and neurodegenerative changes.

The Ruff Figural Fluency Test $($RFFT$)$ is one measure of cognitive function that provides information about cognitive abilities such as planning and

the ability to switch between different tasks. Scores on the RFFT range from $0$ to $175$ points, where higher scores are indicative of better

cognitive function.

The goal of this lab is to begin exploring the relationship between age and RFFT score in the $\backslash$texttt$\{$prevend$\}$ dataset.

Ivspace $\{0\mathrm{.}5cm\}$

Fitting and interpreting a line

The questions in this lab will be based around data from a random sample of $$n=500$$ individuals from the $\backslash$texttt$\{$prevend$\}$ dataset; the sample is

stored as $\backslash$texttt$\{$prevend$.$ samp$\}$ in the $\backslash$texttt$\{$oibiostat$\}$ package.

Run the following code chunk to load the $\backslash$texttt$\{$prevend$.$samp$\}$ dataset.

#load the dataset, copy the following code, without hastag, and run in the console

#install. packages$("$devtools$")$

#library$($devtools$)$

#devtools::install$\_$github$("$OI$-$Biostat$/$oi$\_$biostat$\_$data"$)$

library$($oibiostat$)$

data$("$prevend$.$samp"$)$

$($reate a scatterplot of RFFT score $(\backslash$texttt$\{$RFFT$\})$ and age in years $($ texttt$\{$Age$\})$ in $\backslash$texttt$\{$prevend$.$samp$\}.$

plot $=$ ggplot $($prevend$.$samp, aes Age,$y=$ RFFT

Examine the plot and consider possible lines that are a reasonable approximation for the relationship in the plot.

a$)$ Consider the line $\frac{\text{\$}}{\frac{?}{?}}$hat$\{y\}=-20+2$$$.$

i$.$ Add the line to the plot. Does the line appear to be a good fit to the data?

This line is not a good fit for the data. The data has a somewhat negative slope, and this line has a positive

slope. Also, the

$y-$intercept should be a score more around $100$ I believe, not $20.$

ii$.$ Calculate the SSE, the sum of the squared residuals, for this line. Do you expect this SSE to be relatively low or relatively high?

Explain your answer.

I would expect to see a higher SSE, due to the line not being a proper fit to the model.

$\{C)$ fitted $(plot)$

$[1]0$

b$)$ From a visual inspection, determine a line that you think is a good fit to the data and add the line to the plot. Calculate the SSE and

compare it to the SSE from the line in part $a).$

c$)$ Consider the line $ $\backslash$hat $\{y\}=137\mathrm{.}55-1\mathrm{.}261$$$.$ Add this line to the plot. Calculate the SSE and compare it to the SSE from the line in

part b$).$