Assignment #7 (2020) - Treating x as categorical or continuous in general linear models

For this analysis, you have conducted an experiment to determine the effect of forest thinning on red-cockaded woodpecker (RCW) density. In each of 20 forest stands, you have thinned those stands to 100, 90, 80, 70, and 60 basal area (sq. feet of lumber/acre) respectively (for a total of 100 forest stands). You maintained those stands at those levels of basal area and after 5 years measured RCW density (RCWs/hectare). The data from this experiment is here. Using this data, perform the following analyses and report on your findings in a MS-Word document:

1. Analyze the linear relationship between RCW density (y-variable) and basal area ('BasalArea'; x-variable), WHERE BASAL AREA IS TREATED AS A CONTINUOUS VARIABLE.

a. Describe the relationship between basal area and RCW density using the standard sentence we've been using throughout this class.

2. Analyze the relationship between RCW density (y-variable) and basal area (x-variable), WHERE BASAL AREA IS TREATED AS A CATEGORICAL VARIABLE. Use the summary output from 'results2' to extract the following information:

b. Write a sentence describing the significance (or not) of the categorical Basal Area variable as a whole.

c. Using the summary output from lm, describe the estimated difference (with confidence intervals and p-values) in RCW density between 60 and 100 basal area plots using the standard sentence we've been using throughout this class. Note that you may need to change the reference in order to get this information.

d. Using the summary output from lm, describe the estimated difference (with confidence intervals and p-values) in RCW density between 90 and 80 basal area plots using the standard sentence we've been using throughout this class. Note that you may need to change the reference in order to get this information.

e. Why are the p-values and confidence intervals provided in this analysis inappropriate?

3. Compare the model where basal area is treated as continuous to the model where basal area is treated as categorical using an f-drop test.

f. When comparing the models using an f-drop test, what would be the null hypothesis?

g. Report the resulting p-value from your f-drop test

h. Should we reject or fail to reject the null hypothesis?

i. So which model should we use the one where basal area is continuous or the one where it is categorical?

j. What does your answer for 'i' imply regarding the linearity of the relationship between RCW density and basal area?