Question: Weeds among the corn Lamb's-quarter is a common weed that interferes with the growth of corn. An agriculture researcher planted corn at the same rate in 16 small plots of ground and then weeded the plots by hand to allow a fixed number of lamb'squarter plants to grow in each meter of corn row. The decision of how many of these plants to leave in each plot was made at random. No other weeds were allowed to grow. Here are the yields of corn (bushels per acre) in each of the plots:9 Some computer output from a least-squares regression analysis on these data is shown below.
Predictor Coef SE Coef T P
Constant 166.483 2.725 61.11 0.000
Weeds per -1.0987 0.5712 -1.92 0.075
meter
S = 7.97665 R-Sq = 20.9% R-Sq(adj) = 15.3%
(a) What is the equation of the least-squares regression line for predicting corn yield from the number of lamb's quarter plants per meter? Interpret the slope and y intercept of the regression line in context.
(b) Explain what the value of s means in this settting.
(c) Do these data provide convincing evidence at the a = 0.05 level that more weeds reduce corn yield? Assume that the conditions for performing inference are met.