Linear/Logistic HW SOLUTION

Linear/Logistic HW
Download dataset http://www.cse.sc.edu/~rose/590B/CSV/gold_target1.csv The description of
dataset is http://www.stat.ufl.edu/~winner/data/gold_target1.txt
1. Explore the first two columns which contain real numbers:
a. Plot first column (Y) against second column (X). Save the plot to a pdf file.
b. Try fitting these two columns with a linear model lm(). Hint: You might want to review
the linear regression lab.
c. As in the linear regression lab, visualize the model with the commands, where m is the
variable you used to hold the model:
par(mfrow=c(2,2))
plot(m)
Save this plot to a pdf file.
d. Explain the top left figure. What does this tell us about the fit of our model?
e. Do the residuals have the property of homoscedasticity? Explain!
f. Visualize the predicted and observed y values similar to what we did in slide 6 of the
linear regression lab. Save this graph to a pdf file.
2. Explore column 4 versus columns 1 and 2.
a. Plot column 4 (Y) against column 1 (X). Save this plot to a pdf file.
b. Plot column 4 (Y) against column 2 (X). Save this plot to a pdf file.
c. Try fitting column 4 versus column 2 with a logistic model glm(). Hint: You might want to
review the logistic regression lab.
d. Visualize the fit of your model using:
plot(gold_target1$V4~gold_target1$V2)
lines(gold_target1$V2,lrm1$fitted,type="l", col="red")
Save this plot to a pdf.
e. Now try fitting column 4 versus columns 1 and 2 with the logistic model glm(). How can
you accomplish this? When you only have Y versus X, you use Y~X as you did in step c.
When you have X1 and X2 then you use Y~X1+X2. Note: RStudio will give a warning
that glm fitted probabilities numerically 0 or 1 occurred. This is caused by the data in
column 1.
f. Compare the models from step c with that of step e using the function summary(). In
particular, compare the estimated coefficient for gold_target$V2. What are the two
values? How have the confidence values for these estimates changed? (Hint: look at the
significance codes.)
3. If the probability of rain tomorrow is 25%, what are the odds of rain tomorrow?