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 263 268 271 272 276 277 279
(a) 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
(b) What percent of the year-to-year variation in scores is explained by the linear trend?