#There are 11 questions below. Please work on these as homework for Wednesday.


#The newproduct dataset (on course website) has data about 50 new product development 
#projects at a company that makes shampoo and other hair care products. The goal of the 
#dataset is to learn about what determines how long it takes to develop a new product.
#The data consist of a response, time (days), and three covariates: cost (units of $100K),
#FTEs (full time equivalent people), and an assessment of difficulty (higher is more 
#difficult).
 
# download and read in the data from the course web page:
data <- read.csv("~/newproduct.csv") # your "path" might be different.

# Plsae use head(data) and tail(data) to make sure you have the data before continuing!

# fit models with covariates in all 6 orders.

fit.cFd <- lm(time~cost+FTEs+difficulty,data=data)
fit.Fcd <- lm(time~FTEs+cost+difficulty,data=data)
fit.dcF <- lm(time~difficulty+cost+FTEs,data=data)
fit.cdF <- lm(time~cost+difficulty+FTEs,data=data)
fit.Fdc <- lm(time~FTEs+difficulty+cost,data=data)
fit.dFc <- lm(time~difficulty+FTEs+cost,data=data)

# Below is an example of some code to visualize sequential sums of squares.
# Please run it line by line to see what it does.

anova.result <- anova(fit.dcF)
labels <- c("SSR(difficulty)","SSR(cost|difficulty)","SSR(FTE|cost,difficulty)")

barplot(as.matrix(anova.result[,2]),density=0,ylab="Sum of Squares")
text(.67,anova.result[1,2]/2,labels[1])
text(.67,anova.result[1,2]+anova.result[2,2]/2,labels[2])
text(.67,anova.result[1,2]+anova.result[2,2]+anova.result[3,2]/2,labels[3])
text(.67,anova.result[1,2]+anova.result[2,2]+anova.result[3,2]+anova.result[4,2]/2,"SSE")


# 1. What is the interpretation of the total height of the stacked bars? 
# 2. Modify the code above to show sequential sums of squares for fit.Fdc. (Please hand in your code and the figure.)
# 3. Please run the following two lines and explain why they give the same number.

var(data$time)*(49)
sum(anova(fit.dcF)[,2])

# Use anova tables (or plots) to answer the following questions.

# 4. What explains most of the variability in time by itself? How do you know?
# 5. Does cost explain the variability in time? Does the answer depend on what else is in the model? How?
# 6. Do FTEs explain the variability in time? Does the answer depend on what else is in the model? How?
# 7. Does difficulty explain the variability in time? Does the answer depend on what else is in the model? How?

# Use the results of the "summary" function to answer the following questions:

# 8. What is the estimated function for the mean of time when all covariates are used?
# 9. What is the estimated variance of the errors? 
# 10. What percentage of the variance in time is accounted for by the covariates?
# 11. The line 
#  "F-statistic: 74.34 on 3 and 46 DF,  p-value: < 2.2e-16"
#  is at the end of summary(fit.dcF). 
# Show how the numbers in the anove table can be used to compute the 74.34.
# Which two models does this F statistic compare? Which model is preferred and why?









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