Laetisaric acid is a compound that holds promise for control of fungus diseases in crop plants. The accompanying data show the results of growing the fungus Pythium ultimum in various concentrations of laetisaric acid. Each growth value is the average of four radial measurements of a P. ultimum colony grown in a petri dish for 24 hours; there were two petri dishes at each concentration. Do the following problem by hand, except for the scatterplot.
(a) Is this study an observational study or an experiment?
(b) Generate a scatterplot of the data. You may overlay the least-squares regression line once you compute it. Based upon the scatter plot, does a linear relationship seem plausible?
(c) Estimate the regression parameters using least-squares. Provide the full equation of the prediction line and plot that line in part (b).
(d) Is there significant evidence for a linear relationship between fungus growth and acid concentration? Carry out the following tests using α = 0.05.
i. First test the hypotheses H0 : rho = 0 versus HA : rho 6= 0.
ii. Then test the hypothesis H0 : β1 = 0 versus HA : β1 6= 0.
(e) Compute and interpret a 95% confidence interval for rho.
(f) Compute and interpret a 95% confidence interval for β1.
Laetisaric acid X | Fungus Growth Y
0 | 33.3
0 | 31.0
3 | 29.8
3 | 27.8
6 | 28.0
6 | 29.0
10 | 25.5
10 | 23.8
20 | 18.3
20 | 15.5
30 | 11.7
30 | 10.0
Mean 11.500 | 23.642
sd 10.884 | 7.8471