Every few years, the National Assessment of Educational Progressasks a national sample of eighth-graders to perform the same mathtasks. The goal is to get an honest picture of progress in math.Suppose these are the last few national mean scores, on a scale of0 to 500
. Year 1990 1992 1996 2000 2003 2005 2008 2011 2013
Score 263 266 272 273 277 278 280 286 288
(a) Make a time plot of the mean scores, by hand. This is just ascatterplot of score against year. There is a slow linearincreasing trend.
(b) Find the regression line of mean score on time step-by-step.First calculate the mean and standard deviation of each variableand their correlation (use a calculator with these functions). Thenfind the equation of the least-squares line from these. (Round youranswers to two decimal places.)
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Draw the line on your scatterplot. What percent of theyear-to-year variation in scores is explained by the linear trend?(Round your answer to one decimal place.)
  %
