Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote