Question

10. In Exercise 6, we examined the relationship between years of education and hours of television watched per day. We saw that as education increases, hours of television viewing decreases. The number of children a family has could also affect how much television is viewed per day. Having children may lead to more shared and supervised viewing and thus increases the number of viewing hours. The following SPSS output displays the relationship between television viewing (measured in hours per day) and both education (measured in years) and number of children. We hypothesize that whereas more education may lead to less viewing, the number of children has the opposite effect. Having more children will result in more hours of viewing per day.

Model Summary

Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .200^{a} |
.040 | .038 | 2.555 |

a. Predictors: (Constant), childs Number of Children, educ Highest Year of School Completed

ANOVA

Model | Sum of Squares | df | Mean Square | F | Sig. |

1 Regression | 213.426 | 2 | 106.713 | 16.344 | .000^{b} |

Residual | 5099.206 | 781 | 6.529 | ||

Total | 5312.633 | 783 |

a. Dependent Variable: tvhours Hours Per Day Watching TV

b. Predictors: (Constant), childs Number of Children, educ Highest Year of School Completed

Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | |

B | Std. Error | Beta | |||

1 (Constant) | 5.095 | .461 | 11.061 | .000 | |

educ Highest Year of School Completed | -.164 | .030 | -.194 | -5.422 | .000 |

childs Number of Children | .040 | .056 | .026 | .714 | .475 |

a. Dependent Variable: tvhours Hours Per Day Watching TV

10a. What is the b coefficient for education? For number of children? Interpret each coefficient. Is the relationship between each independent variable and hours of viewing as hypothesized?

10b. Using the multiple regression equation with both education and number of children as independent variables, calculate the number of hours of television viewing for a person with 16 years of education and two children. Using the equation from Exercise 6, how do the results compare between a person with 16 years of education (number of children not included in the equation) and a person with 16 years of education with two children?

10c. Compare the r^{2} value from Exercise 6 with the
R^{2} value from this regression. Does using education and
number of children jointly reduce the amount of error involved in
predicting hours of television viewed per day?

Answer #1

10a) The -0.164 coefficient for education. For number of children is 0.04

For every increase in year there will be -0.164 decrease in tv Hours Per Day Watching TV.

For an every increase in number of children there will be an increase of 0.04 tv Hours Per Day Watching TV.

Education is significant and number of children is not significant.

10b. y(hat)= 5.095-0.164*x1+0.04*x2

y(hat)= 5.095-0.164*16+0.04*2

y(hat)= 2.551

10c. The r2 value is 0.04.

Interpretation:0.04 indicates that the model explains 4% of the variability of the response data around its mean.

NOTE: You have not provided the data for exercise 6.

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model:
YRSEDUC(I)=7.4451+0.1104HSSCOREI+0.0906WAGESI-0.0391UNEMPI+0.3361BLACKI
(0.523) (0.006) (0.048) (0.022) (0.134)
R2 = 0.269 , SER=1.556
(values in parentheses are the standard error of coefficients,
respectively)
The definitions and units of measurement of the variables are as
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b=24.302
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1. A regression analysis was performed to determine if there is
a relationship between hours of TV watched per day (xx) and number
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a=-1.072
b=31.456
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42
6
48
7
82
1
46
3
67
1
54
5
105
6
42
0
38
4
56
6
90
2
44
7
67
5
64
7
143
12
43
0
76
7
64
4
127
6
42
0
a. Find...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
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Salary
Education
40
3
53
4
80
6
42
2
70
5
50
4
110
8
38
0
42
3
55
4
85
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40
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70
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60
4
140
8
40
0
75
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65
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125
8
38
0
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between educational attainment (in years of higher education) and
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34
3
66
1
89
4
56
3
71
7
80
2
111
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51
0
23
7
36
2
100
1
35
1
71
6
68
9
163
5
56
0
86
5
58
4
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33
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