Numerous studies have shown that watching too much television hurts children’s school grades. Others have argued that television is not necessarily a bad thing for children (Mail Online; July 2009). Like books and stories, television not only entertains, it also exposes a child to new information about the world. While watching too much TV is harmful, a little bit may actually help. Suppose a researcher gathers information on the grade point average (GPA) of 28 middle school children and the number of hours of TV they watch per week. GPA Hours TV 3.24 19 3.1 21 3.24 18 2.61 30 3.03 23 3.37 10 1.6 36 3.2 10 2.96 13 2.18 31 2.5 33 2.95 4 2.72 25 3.05 21 3.45 8 2.49 27 3.62 11 2.33 29 2.36 30 3.28 10 3.35 15 2.64 18 2.88 24 2.02 29 2.6 22 3.18 21 3.31 4 a. Estimate a quadratic regression model where the GPA of middle school is the response, and the two predictors are hours of TV and (hours of TV)^2 b. Is the quadratic term in this model justified? c. Based on this data, find the optimal number of weekly hours of TV for middle school children. d. Are there any high leverage values in this data set? If so, list which observations are high leverage (don’t delete them, just list them)
Numerous studies have shown that watching too much television hurts children’s school grades. Others have argued that television is not necessarily a bad thing for children (Mail Online; July 2009). Like books and stories, television not only entertains, it also exposes a child to new information about the world. While watching too much TV is harmful, a little bit may actually help. Suppose a researcher gathers information on the grade point average (GPA) of 28 middle school children and the number of hours of TV they watch per week.
|
GPA |
Hours TV |
|
3.24 |
19 |
|
3.1 |
21 |
|
3.24 |
18 |
|
2.61 |
30 |
|
3.03 |
23 |
|
3.37 |
10 |
|
1.6 |
36 |
|
3.2 |
10 |
|
2.96 |
13 |
|
2.18 |
31 |
|
2.5 |
33 |
|
2.95 |
4 |
|
2.72 |
25 |
|
3.05 |
21 |
|
3.45 |
8 |
|
2.49 |
27 |
|
3.62 |
11 |
|
2.33 |
29 |
|
2.36 |
30 |
|
3.28 |
10 |
|
3.35 |
15 |
|
2.64 |
18 |
|
2.88 |
24 |
|
2.02 |
29 |
|
2.6 |
22 |
|
3.18 |
21 |
|
3.31 |
4 |
a. Estimate a quadratic regression model where the GPA of middle school is the response, and the two predictors are hours of TV and (hours of TV)^2
b. Is the quadratic term in this model justified?
c. Based on this data, find the optimal number of weekly hours of TV for middle school children.
d. Are there any high leverage values in this data set? If so, list which observations are high leverage (don’t delete them, just list them)
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