STAT 516 HW 1 

HAND CALCULATIONS:

1.  We will analyze the data in Table 7.14 on pg. 366 of the textbook.  The dependent (Y) 
variable is Oxidation and the independent (X) variable is Temperature.

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.

(b)  Find a 90% confidence interval for the true slope of the regression.  Interpret the interval
in the context of the variables in the problem.

(c)  Find the residual for the first observation in the data set.

(d) Find a 95% prediction interval for the Oxidation of a new alloy having 
Temperature of 1.3.


COMPUTER CALCULATIONS:

2.  Look at the data in Table 7.19 on page 369 of the textbook.  These data are also 
given in the SAS code labeled "U.S. Cities data set" on the course web page. 

The dependent variable is latitude and the independent variable is
mean monthly temperature range for a sample of cities.  

Complete a SAS program and answer the following questions about the data set:

(a) Does a scatter plot indicate a linear relationship between the two variables? 
Is there anything disconcerting about the scatter plot? Explain.

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

(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 what this means in terms of the relationship between the two 
variables.

(e)  Using SAS, find a 95% confidence interval for the mean latitude for 
 cities having temperature range 20.  Also, find a 95% prediction interval for
 the latitude for a city having temperature range 20.


TRUE-FALSE QUESTIONS:

3.  Answer True/False Concept Questions 4,5,7,10,14,15,18 on pages 365-366.
If the statement is false, either correct it or briefly explain why it is false.