Several levels of a drug were used to assess its toxic effects on a particular animal species. Twenty-four animals were used and each was administered a particular dose of the drug. After a fixed time...

Several levels of a drug were used to assess its toxic effects on a particular animal species. Twenty-four animals were used and each was administered a particular dose of the drug. After a fixed time interval, each animal was scored as 0 if it showed no ill effects and as 1 if a toxic effect was observed. That is, the dependent variable takes the value of 0 or 1 depending on the absence or presence of a toxic reaction. (a) Which assumptions of ordinary least squares would you expect not to be satisfied with this dependent variable?

(b) The dependent variable was used in a linear regression on dose. The resulting regression equation was
 = −.214 + .159X. Plot this regression line for X = 1 to X = 8. Superimpose on the plot what you might expect the observed data to look like if 24 approximately equally spaced dose levels were used. What problems do you see now?

(c) The researcher anticipated using
 to estimate the proportion of affected individuals at the given dose. What is the estimated proportion of individuals that will be affected by a dose of X = 2 units? Use the conventional method to compute the 95% con- fidence interval estimate of the mean at X = 2 if s²
= .1284 with 22 degrees of freedom,
 = 4.5, and Σ(X_i
−
)₂
= 126. Comment on the nature of this interval estimate.

(d) Suppose each observation consisted of the proportion of mosquitoes in a cage of 50 that showed response to the drug rather than the response of a single animal. Would this have helped satisfy some of the least squares assumptions? Which?