STAT 516 HW 1 

Please write your answers neatly and clearly!

You MUST make sure your answers to these questions are
written in the same order as the questions are listed in 
the assignment.  If this instruction is not followed, 
your homework WILL NOT be graded.

HAND CALCULATIONS:

1.  We will analyze the data in Table 7.14 on pg. 327 of the textbook.  
The dependent (Y) variable is Sugar (sugar content of a fruit) and the 
independent (X) variable is Days (number of days after picking it).

Do the following by hand, SHOWING WORK.  You may use SAS to check your answers 
if you want.

(a)  Find S_yy, S_xx and S_xy.  Use these to calculate the estimated 
least-squares line and to find SSE and MSE.  Write the equation of the 
estimated least-squares line and write the SSE and MSE.

(b)  Find a 95% confidence interval for the true slope of the regression.

COMPUTER CALCULATIONS:

2.  Look at the data in Table 5.1 on page 186 of the textbook. 
We will analyze only the observations having "Big8 = YES".

This modified data set is also given in the SAS code "auditdata.txt" on the 
course web page. (Equivalent R code to read in the data is given as 
"auditdataR.txt" on the course web page.)

The dependent variable is fee (audit fees charged) and the independent 
variable is pop (population) for a sample of 13 cities using Big 8 firms. 

The fee variable is measured in THOUSANDS of dollars, and the population 
variable is measured in THOUSANDS of people. 

Complete a SAS or R program to answer the following questions about the data set:

(a) Does a scatter plot indicate a linear relationship between the two 
variables? Explain.

(b) Fit the least-squares regression line (using SAS or R), state the equation,
and interpret the estimated slope in the context of this data set.  
Does it make sense to interpret the estimated intercept?

(c) For these data, what is the unbiased estimate of the error 
variance?  (Give a number.)

(d) Using the SAS output, test the hypothesis that the true slope of the 
regression line is zero (as opposed to nonzero).  State the appropriate null 
and alternative hypotheses, give the value of the test statistic and give the 
appropriate P-value.  (Use a significance level of 0.05.)  Explain precisely 
what this means in terms of the relationship between the two variables.


TRUE-FALSE QUESTIONS:

3.  Answer True/False Concept Questions 3,4,5,6,15,16,18
on pages 326-327.  If the statement is false, either correct it or explain 
why it is false.  If you only write "FALSE", that is NOT sufficient.