Question: Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, 3 chickens were randomly assigned to each of 5 different doses of growth hormone (0, 0.2, 0.4, 0.8, and 1.0 milligrams). The subsequent weight gain (in ounces) was recorded for each chicken. A researcher plots the data and finds that a linear relationship appears to hold. Computer output from a least-squares regression analysis for these data is shown below. Assume that the conditions for performing inference about the slope b of the true regression line are met.
Predictor Coef SE Coef T P
Constant 4.5459 0.6166 7.37 <0.0001
Dose 4.8323 1.0164 4.75 0.0004
S = 3.135 R-Sq = 38.4% R-Sq(adj) = 37.7%
(a) What is the equation of the least-squares regression line for these data? Define any variables you use.
(b) Interpret each of the following in context:
(i) The slope
(ii) The y intercept
(iii) s
(iv) The standard error of the slope
(v) r2
(c) Do the data provide convincing evidence of a linear relationship between dose and weight gain? Carry out a significance test at the a = 0.05 level.
(d) Construct and interpret a 95% confidence interval for the slope parameter.