Problem 1:
A. Verify the regression model assumptions.
B. Perform the hypotheses test for the linear relationship between x and y, using level of significance =0.05.
The accompanying table shows the teams winning percentage (x) and power rating (y) for the 2011 NCAA basketball tournament.
|
School
|
Win % (x)
|
Rating (y)
|
|
OSU
|
91.9
|
121
|
|
Kansas
|
92.1
|
119.5
|
|
SD state
|
91.4
|
118.1
|
|
Duke
|
86.5
|
117.8
|
|
Connecticut
|
77.5
|
117.5
|
|
Pitt
|
82.4
|
116.9
|
|
Kentucky
|
76.3
|
116.6
|
|
ND
|
79.4
|
116.3
|
Problem 2:
Listed in the table are the low (x) and high (y) temperatures for a particular day in 2006, measure in degrees Fahrenheit, for a random sample of cities worldwide.
|
City
|
Low(x)
|
High(y)
|
|
Kolkata
|
57
|
77
|
|
London
|
36
|
45
|
|
Montreal
|
7
|
21
|
|
Rome
|
39
|
55
|
|
San juan
|
70
|
83
|
|
shanghai
|
34
|
45
|
Refer to above data.
a. Construct a 99% prediction interval for the high temp for a randomly chosen city with a low temp of 30 degrees.
b. Which of the intervals you constructed is wider and why?