Every few years, the National Assessment of Educational Progress asks a national
ID: 3261091 • Letter: E
Question
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. (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 cap = ________ + _______ x Draw the line on your scatterplot. What percent of the year-to-year variation in scores is explained by the linear trend? __________ % (c) Now use software or the regression function on your calculator to verify your regression line. (Do this on your own.)Explanation / Answer
Regression Analysis: year versus score
The regression equation is
year = 1699 + 1.099 score
S = 2.86276 R-Sq = 85.0% R-Sq(adj) = 82.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 231.880 231.880 28.29 0.003
Error 5 40.977 8.195
Total 6 272.857
Regression Analysis: score versus year
The regression equation is
score = - 1273 + 0.7733 year
S = 2.40142 R-Sq = 85.0% R-Sq(adj) = 82.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 163.166 163.166 28.29 0.003
Error 5 28.834 5.767
Total 6 192.000
Fitted Line: score versus year
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.