Using Regression Models to Grow the Best Crops

Part 2D: Greenhouse Challenge: Drawing Conclusions from Data

1. Use Settings A for the following (make sure only sample1 is selected):

a) Explain why you would expect the quadratic model to have a higher R-squared value than the linear model

b) Explain why you would expect the quadratic model to have a similar R-squared value as the cubic model

c) When we used only sample1 data, the linear model was somewhat effective. When both sample1 and sample2 data are used for the corn crop, the coefficients for the linear model changed. Explain why the R-squared valued dropped so much when both sample1 and sample2 data are used.

d) Give a possible explanation as to why the p-value for X² under the cubic model is so different than with the quadratic model. How does this help to explain why these individual p-values should not be used when trying to determine whether or not a term is important in our model?

2. Use Settings B for the following (make sure only sample2 is selected):

a) Explain how the interaction term (i.e. Water*Tomatoes in this example) modifies our predictions.

b) Explain why the interaction term should be included if you are interested in accurately predicting crop yields.

c) Notice that the linear coefficient is negative ( - 0.30347*X) in the model with an interaction. However it is positive ( 0.01632*X) in the model without an interaction. When there are multiple terms in a regression model, does it appear that the direction of the coefficients are meaningful? In other words, explain why we should be hesitant to say that the model shows “adding water will increase yields” or “adding water will decrease yields”.

2E: Data Literacy Breakdown

3. Take a few minutes to read the one-page Nature article

a) What are the two explanatory variables?
b) What is the response variable for this data?
c) What was the authors’ reasoning for focusing on the simple linear regression technique and not the other techniques mentioned?
d) Do the authors’ arguments seem reasonable? Give a brief explanation as to why the model created by the authors does not appropriately address their research question.
e) In part 1 of the Greenhouse game, a linear model looked like a good fit, but the linear model was not helpful in identifying the optimum Yield or the optiumum Profit. How is this related to the errors made in the Nature article?