Question

Exercise 7-25 Algo 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. Hours GPA 3.24 3.10 19 21 3.31 picture Click here for the Excel Data File a. Estimate a quadratic regression model where the GPA of middle school children is regressed on hours and hours-squared. (Negative values for regression coefficients should be indicated by a minus sign. Round your answers to 4 decimal places.) Coefficient Predictor Variable Constant Hours Hours-squared b. Is the quadratic term in this model justified? No, because the estimated coefficient for Hours is not statistically significant at the 5% level. Yes, because the estimated coefficient for Hours is statistically significant at the 5% level. No, because estimated coefficient for Hours-squared is not statistically significant at the 5% level. Yes, because estimated coefficient for Hours-squared is statistically significant at the 5% level.

GPA	Hours
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
2.86	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

Answer 1

a) coefficient are

constant = 3.1326

hours = 0.0342

hours squared = - 0.0020

b) Yes, because the estimated coefficient for hours squared is statistically significant at 5% level as the p value is 0.00661 < 0.05. Hence significant. So the correct answer is  (d option)

Also from the plot of data it is clear that there should be some quadratic relationship