Suppose the following data record the densities of an organism in a containment vessel for 10…
Suppose the following data record the densities of an organism in a containment vessel for 10 days. Suppose we consider the simple normal linear regression to describe the relationship between the response Y (density) and the predictor X (day)
(a) Plot the data in a scatter plot.
(b) Calculate the least-squares line and plot this on the scatter plot in part (a).
(c) Plot the standardized residuals against X
(d) Produce a normal probability plot of the standardized residuals.
(e) What are your conclusions based on the plots produced in parts (c) and (d)?
(f) Can you think of a transformation of the response that might address any problems found? If so, repeat parts (a) through (e) after performing this transformation.
(g) Calculate 0.95-confidence intervals for the appropriate intercept and slope.
(h) Construct the appropriate ANOVA table to test whether or not there is a relationship between the response and the predictors. What is your conclusion?
(i) Do the results of your analysis allow you to conclude that there is a relationship between Y and X? Explain why or why not.
(j) Compute the proportion of variation explained by the predictor for the two models you have considered. Compare the results.