STAT 516 HW 2

NOTE:  For all hypothesis tests, you should use alpha=0.05 unless otherwise instructed.

1.  We will analyze the data in Table 7.14 on pg. 341 of the textbook.  The dependent (Y) 
variable is Oxidation and the independent (X) variable is Temperature. These data were also 
analyzed in Homework 1.

Do the following by hand, SHOWING WORK.  You may use R to check your answers if you want (do this
to ensure that your answers are correct!)  You can read the data into R via this code:

Oxidation <- c(4, 3, 3, 2, 2)
Temperature <- c(-2, -1, 0, 1, 2)

(a)  Find the correlation coefficient r.  What does this tell you about the 
nature of the relationship between Oxidation and Temperature?  Be specific!

(b) Find the value of r^2, and interpret it in the context of the variables in the problem.

2.  Look at the data in Table 8.29 on page 435 of the textbook.  These data and code to read the data into R
are also given in the R code labeled "Basket Goals data set" on the course web page.

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

(a)  Estimate the multiple regression model with 'goalmade' as the dependent variable and 
'weight', 'height', and 'dash100' as the independent variables.  Write the estimated regression function.
Carefully interpret the partial regression coefficient for 'height'.

(b) Plot the residuals of the regression in part (a) against the fitted values (the Y-hat values)
from that regression model.  Also make a normal Q-Q plot of the residuals from that regression.
Give both plots and report what the plots indicate about whether any model assumptions are violated.

(c) Using the model in part (a), find a 90% confidence interval for the mean number of goals made 
for athletes having weight 150 pounds, height 72 inches and 100-yard dash of 11.5 seconds.
Is it a problem that this interval contains non-integer values?  Why or why not?

(d)  Using the t* values and the P-values listed in R, carefully state what the t-tests 
about the regression coefficients tell you about the individual effects of 'weight', 'height', 
and 'dash100' on 'goalmade'.

(e) Using an anova command in R, test whether at least one of 'weight' and 'dash100' is needed 
in the model, given that 'height' is in the model.

(f) Find the value of R^2, and interpret it in the context of the variables in the problem.


CONCEPT QUESTIONS:

Answer Concept Questions 1,3,4,13 on pages 423.
[Hint for #3:  Use the relationship between F* and R^2 that is given on page 358:
F* = [(n-m-1)(R^2)]/[m(1-R^2)]  
Also verify in Table A.4A that F_.05(5,24) = 2.62.]