Radioactive decay. An experiment was conducted using a Geiger-Mueller tube in a physics lab. Geiger-Mueller tubes respond to gamma rays and to beta particles (electrons). A pulse that corresponds to each detection of a decay product is produced, and these pulses were counted using a computer-based nuclear counting board. Elapsed time (in seconds) and counts of pulses for a short-lived unstable isotope of silver are shown in Table 28.5 (see page 28-38).7
(a) Create a scatterplot of the counts versus time and describe the pattern.
(b) Since some curvature is apparent in the scatterplot, you might want to consider the quadratic model for predicting counts based on time. Fit the quadratic model and identify the estimated mean response. (c) Add the estimated mean response to your scatterplot. Would you recommend the use of the quadratic model for predicting radioactive decay in this situation? Explain.
(d) Transform the counts using the natural logarithm and create a scatterplot of the transformed variable versus time.
(e) Fit a simple linear regression model using the natural logarithm of the counts. Provide the estimated regression line, a scatterplot with the estimated regression line, and appropriate residual plots.
(f) Does the simple linear regression model for the transformed counts fit the data better than the quadratic regression model? Explain.