Download Home work 1

Home work 1: Stat 530 Due Feb Feb 3:
1. Write TRUE or FALSE with reasons for the following:
a.
b.
c.
d.
Zip code is a categorical random variable.
Normal distribution is symmetric, t, chi-square and F are skewed.
If y follows normal with mean 2 and variance 1, y^2 follows a chi-square distribution with 1 df.
If y1 is a normal with mean 0 and variance 1, and y2 follows chi-square with n-1 degrees of
freedom then y1/sqrt(y2/n-1) follows a F distribution with (n-1) degrees of freedom
e. If y3 follows a t distribution then y3^2 follows F.
2. Consider the data set on age and cholesterol given in our class website names Hw1-2017.xls. or
Hw1-2017.csv (same data set in two formats). Answer the questions based on this data set:
a. Why is Cholesterol considered the response variable? Why is age the explanatory variable?
b. Plot the relationship. What do you see from the plot?
c. Determine least squares’ equation that can be used for predicting Cholesterol.
d. Give 95% confidence intervals for the change in Cholesterol for a unit change in age. Use the
following code:
proc reg data=a outseb outest=b;
model y=x;
output out=new r=resid p=pred;
run;
proc print data=b;
run;
data set “b” will have the estimate and the standard error for the confidence interval.
e. Is this rate (in d) significantly greater than 0. Use alpha = .05.
f.
Do the results in (d) and (e) agree? Should they?
g. Use your model to predict Cholesterol when age is 45
h. Provide 95% confidence intervals for g.
i.
Provide 95% prediction intervals for (g)
j.
Comment on your findings in (h) and (i).
3. Why is the regression estimates called the LEAST SQUARE estimates. Comment.
4. Give an example from your discipline where you think linear regression would be appropriate.