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 equation of the estimated least-squares line 
and to find SSE and MSE.

(b)  Find a 90% confidence interval for the true slope of the regression equation.  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 7.20 on page 370 of the textbook.  
These data are also given in the SAS code link labeled 
"Heating Cost data set (plain text)" on the course web page. 

The dependent variable is kwh (electricity consumption in kilowatts per hour) and the independent 
variable is tavg (temperature in degrees) for a sample of 47 autumn days.  

Complete a SAS program to answer the following questions about the data set.
Please turn in the scatter plot requested in (a) and the plots requested in (f).  
It is recommended but not required that you turn in the printout of the SAS output 
for the other parts.

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

(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.

(e)  Using SAS, find a 95% confidence interval for the mean electricity 
consumption for all days having average temperature 73.6 degrees.  Also, 
find a 95% prediction interval for the electricity consumption for a new 
day with average temperature 73.6 degrees.

(f)  Using SAS, make a residual plot and Q-Q plot of the residuals for this 
regression.  Comment about whether each of the regression assumptions seems 
to be violated, based on the plots.

(g)  Find the r^2 for this regression from the SAS printout, and interpret it 
in the context of this data set.


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.