Question

In: Statistics and Probability

Numerous studies have shown that watching too much television hurts school grades. Others have argued that...

Numerous studies have shown that watching too much television hurts school grades. Others have argued that television is not necessarily a bad thing for children (Psychology Today, October 22, 2012). Like books and stories, television not only entertains, it also exposes a child to new information about the world. While watching too much television is harmful, a little bit may actually help. Researcher Matt Castle gathers information on the grade point average (GPA) of 28 middle school children and the number of hours of television they watched per week. A portion of the data is shown in the accompanying table.

GPA Hours
3.24 19
2.86 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

1. Estimate a quadratic regression model where the GPA of middle school children is regressed on hours and hours-squared ( Round answer to 4 decimal places)

Constant?

Hours?

Hours Squared?

2. Find the optimal number of weekly hours of TV for middle school children (Round answer to 2 decimal places)

Optimal number of hours weekly?

Solutions

Expert Solution

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.888319
R Square 0.78911
Adjusted R Square 0.771536
Standard Error 0.232366
Observations 27
ANOVA
df SS MS F Significance F
Regression 2 4.84886 2.42443 44.90174 7.74E-09
Residual 24 1.295859 0.053994
Total 26 6.144719
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 3.120866 0.20233 15.4246 5.9E-14 2.703277 3.538456 2.703277 3.538456
Hours 0.036551 0.022755 1.60632 0.121282 -0.01041 0.083515 -0.01041 0.083515
hours² -0.00208 0.000573 -3.63118 0.00133 -0.00326 -0.0009 -0.00326 -0.0009

1)

constant 3.1209
Hours 0.0366
hours² -0.0021

2) optimal number

taking derivative,

d/dx (3.1209+0.0366*X-0.0021X²) = 0+0.0366-2X*0.0021 = 0

x=0.0366/(2*0.0021) = 8.79

please revert for doubts and UPVOTE the answer

orchestra answered 1 year ago
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