(Round all intermediate calculations to at least 4 decimal places.) Numerous stu

Question

(Round all intermediate calculations to at least 4 decimal places.) 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 (Mail Online, July 18, 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. Researcher Matt Castle gathers information on the grade point average (GPA) of 28 middle school children and the number of hours of TV they watched per week. A portion of the data is shown in the accompanying table GPA Hours TV 3.24 3.10 3.24 2.61 3.03 3.37 1.60 3.20 2.96 2.18 2.50 2.95 2.72 3.05 3.45 2.49 3.62 2.33 2.36 3.28 3.35 2.64 2.88 2.02 2.60 3.18 3.31 19 18 30 23 10 10 13 31 04 25 21 08 27 29 30 10 15 18 24. 29 21 04 Click here for the Excel Data File Estimate a quadratic regression model where the GPA of middle school children is regressed on hours and hours squared. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) a. CPA= 3.0945 + 0.041 Hours + -0.022 Hours2 b. Is the quadratic term in this model justified? Yes, based on the R2 Yes, based on the significance of Hours No, based on the R2 No, based on the insignificance of Hours c. Find the optimal number of weekly hours of TV for middle school children. (Round your answer to 2 decimal places.) Optimal number of weekly hours

Explanation / Answer

a)

GPA=3.0917-0.0052854*Hours-0.0002574*Hours^2

b)

No, based on the insignificance of Hours^2

c)

Optimal number of hours looking at the data would be 13

SUMMARY OUTPUT Regression Statistics Multiple R 0.286197099 R Square 0.081908779 Adjusted R Square 0.005401178 Standard Error 0.487151581 Observations 27 ANOVA df SS MS F Significance F Regression 2 0.508140831 0.254070416 1.070596614 0.35861629 Residual 24 5.695599909 0.237316663 Total 26 6.203740741 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.09167189 0.424181905 7.288552041 1.57516E-07 2.216203466 3.967140313 Hours TV -0.005285413 0.04770471 -0.110794353 0.912700757 -0.103743095 0.09317227 Hours^2 -0.000257449 0.001200235 -0.214499133 0.83196994 -0.002734614 0.002219715

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