State the estimated coefficient for time and its interpretation. Also, state what the coefficient of determination is and its interpretation.

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State the estimated coefficient for time and its interpretation. Also, state what the coefficient of determination is and its interpretation. 

### Analysis of the Fragile Families and Child Wellbeing Study

In the Fragile Families and Child Wellbeing study, the goal is to evaluate the impact of the primary caregiver's relationship to the youth and household income on the number of days the youth is absent from school. 

#### Variables Considered
- **Time:** How much time the youth lives with the primary caregiver. A value of 1 suggests less than half of the time, and 0 suggests most of the time.
- **Income:** The household income of the primary caregiver, measured in thousands of dollars.
- **Days:** The number of days the youth is absent from school.
- **Relationship:** The relationship of the primary caregiver to the youth, represented by dummy variables: 
  - **R1 (dummy 1):** Biological mother (1), others (0).
  - **R2 (dummy 2):** Biological father (0), others (0).

#### Multiple Regression Model
A multiple regression model is fitted with a significance level of 5%.

#### Regression Analysis Output

**Analysis of Variance Table**

| Source      | Sum Sq | DF  | Mean Sq | F value | Pr(>F) |
|-------------|--------|-----|---------|---------|--------|
| Model       | 70     | 4   | 17.5    | 1.40    | 0.2364 |
| Error       | 1971   | 159 | 12.40   |         |        |
| Corrected Total | 2041 | 163 |         |         |        |

**Parameter Estimates**

| Parameter | Estimate | Std. Error | t value | Pr(>|t|) |
|-----------|----------|------------|---------|----------|
| Intercept | 3.826098 | 2.151170   | 1.779   | 0.0772   |
| Time      | -2.676970| 1.056423   | -2.534  | 0.0113   |
| Income    | -0.004215| 0.005963   | -0.707  | 0.4806   |
| R1        | 1.092612 | 1.280399   | 0.853   | 0.3940   |
| R2        | 2.251431 | 1.151844   |
Transcribed Image Text:### Analysis of the Fragile Families and Child Wellbeing Study In the Fragile Families and Child Wellbeing study, the goal is to evaluate the impact of the primary caregiver's relationship to the youth and household income on the number of days the youth is absent from school. #### Variables Considered - **Time:** How much time the youth lives with the primary caregiver. A value of 1 suggests less than half of the time, and 0 suggests most of the time. - **Income:** The household income of the primary caregiver, measured in thousands of dollars. - **Days:** The number of days the youth is absent from school. - **Relationship:** The relationship of the primary caregiver to the youth, represented by dummy variables: - **R1 (dummy 1):** Biological mother (1), others (0). - **R2 (dummy 2):** Biological father (0), others (0). #### Multiple Regression Model A multiple regression model is fitted with a significance level of 5%. #### Regression Analysis Output **Analysis of Variance Table** | Source | Sum Sq | DF | Mean Sq | F value | Pr(>F) | |-------------|--------|-----|---------|---------|--------| | Model | 70 | 4 | 17.5 | 1.40 | 0.2364 | | Error | 1971 | 159 | 12.40 | | | | Corrected Total | 2041 | 163 | | | | **Parameter Estimates** | Parameter | Estimate | Std. Error | t value | Pr(>|t|) | |-----------|----------|------------|---------|----------| | Intercept | 3.826098 | 2.151170 | 1.779 | 0.0772 | | Time | -2.676970| 1.056423 | -2.534 | 0.0113 | | Income | -0.004215| 0.005963 | -0.707 | 0.4806 | | R1 | 1.092612 | 1.280399 | 0.853 | 0.3940 | | R2 | 2.251431 | 1.151844 |
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