IEOR E4650: Business Analytics Professor Van-Anh Truong
Assignment 1: Linear Regression
Due date: Nov 11, 11:59pm
Attention: Please prepare two files for each homework assignment: a .pdf file
for your answers including relevant figurs, and a .R file for your relevant R
scripts. File names should be Last_First_hw.pdf and Last_First_hw.R, e.g.,
Nemoy_Leonard_1.pdf and Nemoy_Leonard_1.R. Your submissions must be based
on your own original work. Late submissions will not be accepted.
A farmer is trying to optimize the crop yield by varying the amount of water, fertilizer
and herbecide used. The file Crops_updt.csv contains data on various experiments the
farmer conducted, documenting the amount of each input used and the resulting crop yield.
Crop yields are also affected by other attributes that cause the yield to randomly vary.
1. Load the data from Crops_updt.csv into R. You can use setwd() to set the current
working directory. Print a summary of the variables.
2. Regress the yield on the amount of water used. Explain and interpret the results.
3. Regress the yield on the amount of fertilizer used. Explain and interpret the results.
4. Regress the yield on the amount of herbicide used. Explain and interpret the results.
5. Regress the yield on all the variables. Explain and interpret the results.
6. The farmer suspects that high levels of fertilizer may not be effective. To check this
conjecture, plot the yield against the amount of fertilizer used. Explain why the plot
is consistent with the regression results.
7. Based on the plot, create an indicator appropriateFertilizer whose value is 1 when
the amount of fertilizer is appropriate, and 0 when the amount of fertilizer is too high
or too low. Regress Yield on the indicator you created and interpret the results.
8. The farmer suggests that an appropriate amount of fertilizer should raise the effectiv-
ness of watering the crops. Run a regression with an interaction between water and
appropriateFertilizer to check this. Interpret the results.
9. Select a collection of variables and interaction terms to use as predictors for the yield.
Run the regression, and interpret the results. Explain why you chose this regression
model.
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10. For this model, what is a 90% confidence interval for the regression coefficients. Inter-
pret the results.
11. For this model, what is a 99% prediction for the yeild of a single sample that gets
water=25,fertilizer =6 and herbicide =5? Interpret the results.
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