Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Suppose these are the last few national mean scores, on a scale of 0 to 500. Year 1990 1992 1996 2000 2003 2005 2008 Score 262 267 273 274 278 279 281 (a) Make a time plot of the mean scores, by hand. This is just a scatterplot of score against year. There is a slow linear increasing trend. (Do this on your own.) (b) Find the regression line of mean score on time step-by-step. First calculate the mean and standard deviation of each variable and their correlation (use a calculator with these functions). Then find the equation of the least-squares line from these. (Round your answers to two decimal places.) y = + x Draw the line on your scatterplot. What percent of the year-to-year variation in scores is explained by the linear trend? (Round your answer to one decimal place.) %