AP StatsName______

Coefficient of Determination

  1. Nine students were tested to determine the effect of test anxiety on test scores. The data is shown below.
  1. Find the correlation coefficient.
  1. Find the least squares line.
  1. Compute the residuals & describe the residual plot.
  1. Compute the coefficient of determination. How does it compare to part a?
  1. Find and describe the standard deviation about the least squares line.
  1. A sample of automobiles traveling a certain stretch of highway is selected. Each one travels at roughly a constant rate of speed, although speed does vary from car to car. Let x = speed and y = time needed to travel this segment of highway. Would the sample correlation coefficient be closest to .9, .3, -.3, or -.9. Explain.
  1. A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since termination of the molding process (x, in hours). Summary quantities are shown below. Calculate and interpret the coefficient of determination and

SSE = 1235.470SST = 25,321.368

  1. Shells of mollusks function as part of the skeletal system and as protective armor. It has been argued that many features of these shells were the result of natural selection in the constant battle against predators. The data let x = shell height (in cm) and y = breaking strength (in newtons). The least-squares line was
  2. What are the slope and the intercept of this line?
  1. When shell height increases by 1 cm, by how much does breaking strength tend to change?
  1. What breaking strength would you predict when the shell height is 2 cm?
  1. Does this approximate linear relationship appear to hold for shell heights as small as 1 cm? Explain.
  1. When shell height increases by 3 cm, by how much does breaking strength tend to change?
  1. There have been numerous studies on the effects of radiation. The following data on the relationship between degree of exposure to alpha particles (x) and the percentage of exposed cells without aberrations (y) appeared in a research journal as follows.
  1. What is the least squares line?
  1. Construct a residual plot, and comment on any interesting features.
  1. Look back at the scatter plot – does the correlation coefficient tell the whole story?
  1. What’s the typical deviation about the least squares line?
  1. What percent of variation in percentage of cells without aberrations can be explained by the least squares line?