For the accompanying data
set, (a) draw a scatter diagram of the
data, (b) compute the correlation
coefficient, and
(c) determine whether there is a linear relation between x and y.
x
22
66
11
77
99
y
88
77
66
99
55
n
3
0.997
4
0.950
5
0.878
6
0.811
7
0.754
8
0.707
9
0.666
10
0.632
11
0.602
12
0.576
13
0.553
14
0.532
15
0.514
16
0.497
17
0.482
18
0.468
19
0.456
20
0.444
21
0.433
22
0.423
23
0.413
24
0.404
25
0.396
26
0.388
27
0.381
28
0.374
29
0.367
30
0.361
A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ModifyingAbove y with caret equals negative 0.0505 x plus 2.9315y=−0.0505x+2.9315.
(a) Predict the grade-point average of a student who plays video games 8 hours per week.
An author of a book discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this analysis is that a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-squares regression equation ModifyingAbove y with caretyequals=2.942.94xnegative 0.4871−0.4871. Complete parts (a) through (d).
(d) A certain team had an on-base percentage of 0.3260.326 and a winning percentage of 0.5480.548. What is the residual for that team? How would you interpret this residual?
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