Question: In a study of the relationship between amphetamine metabolism and amphetamine

psychosis, sixteen chronic amphetamine users were tested and given a psychosis

intensity rating. Plasma amphetamine levels (mg/ml) were also determined for these

patients.. The data for this problem is in Table below

Table for Question 2. The Psychosis Intensity Rating and Plasma Amphetamine levels for 16 chronic amphetamine users in a psychiatric ward of a metropolitan hospital..

a) Provide a graphical summarization of the possible association between PIR and Plasma Amphetamine Level.

b) Determine the Pearson correlation coefficient. Does the data provide sufficient evidence to conclude a linear relationship between PIR and Plasma Amphetamine? (Use a = 0.05 and interpret or describe your results.

c) Determine the least-squares regression line relating Plasma Amphetamine levels (X) to Psychosis Intensity rating (Y). What are the resulting estimated values of the coefficientsa and ?? for this problem. How would you interpret these regression estimates?

d) What would be the estimated PIR with a corresponding Plasma Amphetamine level = 275? Construct a 95% confidence interval for the true mean value of PIR?

e) Referring to the data in problem 2, suppose we are concerned that cases 6 and 10 are potential outliers so as an alternative look at correlation we use Spearman’s Rank Correlation in addition to Pearson’s Correlation:

i) Compute the Spearman’s Rank Correlation Coefficient.

ii) Test the significance of this statistic. (Perform a hypothesis test on the Spearman’s statistic you just found.)

iii) Compare the Spearman vs. Pearson Correlation Coefficient for this data.