STAT 512 MIDTERM I
15 pt total
1. This
exam is open-book and open-notes.
2. Write your full name – I don’t want to deal with anonymous exam takers.
3. Write your solution clearly with intermediate steps instead of just the final answer.
4. Try to answer all the questions. I will not be able to give you partial credit if you do
not write anything.
5. Please write legibly. If your handwriting is difficult to read, I will not be able to
understand and give you credit.
1. (4pt) In a simple linear regression there are two intervals associated with X = 5: (20,
29) and (15, 35). Which is the prediction interval and which is the confidence interval for
the mean response at this level of X? Explain you answer.
2. (9pt) Consider the following output for the diamond price vs. weight (in carats)
dataset
a. (1pt) Write down the 90% confidence interval for the intercept coefficient

0
.
You don't need to give an exact critical value for this level of significance - just
specify the number of degrees of freedom and the argument.
b. (1pt) Now write down the 90% confidence interval for the slope coefficient

1
.
Again, it is not necessary to give the exact critical value.
c.
(1pt) Suppose that you want to test whether the true intercept
null hypothesis being H 0 :

1

1
 0 with the
 0 . Is it ok to use F-test for this purpose? Explain.
d. (1pt) How much of the total variation in the diamond price is explained by the
variation in their weights? Give a percentage estimate. What is a correlation
between the diamond price and its weight?
e.
(3pt) Suppose that the average weight of all the diamonds in this dataset is 0.21
carats. Give the 95% confidence interval for the average price of the diamond
whose weight is 0.30 carats.
f. (2pt) Again, assuming that the average weight of all the diamonds in this dataset
is 0.21 carats, give the 95% prediction interval for the price of the diamond whose
weight is 0.30 carats.