1. Speed and test taking (60 pts)
Last year I graded the midterms in the order in which I received them. The data is available as midtermscores06.txt on cTools. You are interested in whether people who turn in the exam early tend to receive better scores.

A. (20pts) Run a simple linear regression (using summary(lm())). From the resulting output, report on and interpret the slope of the regression line and the coefficient of determination. Are you able to reject the null hypothesis that there is no correlation between the time the test was turned in and the score it received?

B. (20pts) Overlay the fitted regression line and the prediction and confidence intervals on a scatter plot of the data. How useful would the prediction interval be in predicting the score a person would receive if e.g. they are the 15th to turn in the exam?

C. (10pts) Compute the Pearson's correlation coefficient for the two variables. Does it correspond to the coefficient of determination in the way that you would expect?

D. (10pts) Assuming that A. is true, that you can reject the null hypothesis, would you be able to draw a causal conclusion from the data? Explain.

2. inter-rater agreement (40 pts)

Two raters were asked to specify on a scale of 0 to 4 the amount of space each of 49 web pages on the "risk and prevention" of melanoma devoted to each particular risk and prevention fact. Here we will just consider their ratings of web pages with regard to their discussion of the fact that avoiding UV radiation can help minimize the risk of melanoma (i.e. UV is bad for you). 0 means that a page did not mention this fact at all, and 4 means that the whole page was devoted to this one fact. Download the file uvinterrater.txt from cTools (thanks to Prof. Bhavnani who provided the data).

A. (20pts) Obtain a correlation coefficient for inter-rater agreement using a nonparametric correlation test of your choice. Comment on the extent of the agreement between the two raters.

B. (20pts) Now keep only the web pages where at least one rater thought that the page mentioned the fact. Measure the inter-rater agreement again. Is it higher or lower? Give your interpretation of the change.