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.