What is the general linear test presented in the previous question Q1.1 doing with respect to the full model fitted in Q1 description? Pick only one O Testing to see if your fitted model is the best model. O Testing to see if your fitted model is better than a model with all the covariates in it. O Testing to see if your fitted model is better than a model with only a single covariate in it. O Testing to see if your fitted model is better than a model with only an intercept in it.

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**Question:**

What is the general linear test presented in the previous question Q11 doing with respect to the full model fitted in Q1 description? Pick only one.

- ○ Testing to see if your fitted model is the best model.
- ○ Testing to see if your fitted model is better than a model with all the covariates in it.
- ○ Testing to see if your fitted model is better than a model with only a single covariate in it.
- ○ Testing to see if your fitted model is better than a model with only an intercept in it.
Transcribed Image Text:**Question:** What is the general linear test presented in the previous question Q11 doing with respect to the full model fitted in Q1 description? Pick only one. - ○ Testing to see if your fitted model is the best model. - ○ Testing to see if your fitted model is better than a model with all the covariates in it. - ○ Testing to see if your fitted model is better than a model with only a single covariate in it. - ○ Testing to see if your fitted model is better than a model with only an intercept in it.
**Question 1:**

Below is the R output of a model where the response is resting heart rate (Rest) and the predictors are Weight (Wgt, in pounds) and Gender (0 for female and 1 for male), with an interaction term between Weight and Gender.

Our population model is: 

\[ Rest_i = \beta_0 + \beta_1 Wgt_i + \beta_2 Gender_i + \beta_3 Wgt_i \cdot Gender_i + \epsilon \]

```
lm(formula = Rest ~ Wgt + Gender + Wgt * Gender)

Coefficients:
              Estimate  Std. Error  t value  Pr(>|t|)
(Intercept)   70.25970  5.67488    12.381   <2e-16 ***
Wgt           -0.01948  0.03138    -0.621   0.535
Gender        16.19178  9.97017    1.624    0.106
Wgt:Gender    -0.10178  0.06803    -1.496   0.136

---

Residual standard error: 9.78 on 228 degrees of freedom
Multiple R-squared: 0.04625, Adjusted R-squared: 0.0337
F-statistic: 3.685 on 3 and 228 DF, p-value: 0.01274
```

**Explanation:**

- **Coefficients:** 
  - **(Intercept):** 70.25970, significant at p < 2e-16.
  - **Wgt (Weight):** Coefficient of -0.01948, not statistically significant (p = 0.535).
  - **Gender:** Coefficient of 16.19178, not statistically significant (p = 0.106).
  - **Wgt:Gender (Interaction):** Coefficient of -0.10178, not statistically significant (p = 0.136).

- **Model Summary:**
  - **Residual standard error:** 9.78, based on 228 degrees of freedom.
  - **Multiple R-squared:** 0.04625, indicating the proportion of variance explained by the model.
  - **Adjusted R-squared:** 0.0337, adjusted for the number of predictors.
  -
Transcribed Image Text:**Question 1:** Below is the R output of a model where the response is resting heart rate (Rest) and the predictors are Weight (Wgt, in pounds) and Gender (0 for female and 1 for male), with an interaction term between Weight and Gender. Our population model is: \[ Rest_i = \beta_0 + \beta_1 Wgt_i + \beta_2 Gender_i + \beta_3 Wgt_i \cdot Gender_i + \epsilon \] ``` lm(formula = Rest ~ Wgt + Gender + Wgt * Gender) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 70.25970 5.67488 12.381 <2e-16 *** Wgt -0.01948 0.03138 -0.621 0.535 Gender 16.19178 9.97017 1.624 0.106 Wgt:Gender -0.10178 0.06803 -1.496 0.136 --- Residual standard error: 9.78 on 228 degrees of freedom Multiple R-squared: 0.04625, Adjusted R-squared: 0.0337 F-statistic: 3.685 on 3 and 228 DF, p-value: 0.01274 ``` **Explanation:** - **Coefficients:** - **(Intercept):** 70.25970, significant at p < 2e-16. - **Wgt (Weight):** Coefficient of -0.01948, not statistically significant (p = 0.535). - **Gender:** Coefficient of 16.19178, not statistically significant (p = 0.106). - **Wgt:Gender (Interaction):** Coefficient of -0.10178, not statistically significant (p = 0.136). - **Model Summary:** - **Residual standard error:** 9.78, based on 228 degrees of freedom. - **Multiple R-squared:** 0.04625, indicating the proportion of variance explained by the model. - **Adjusted R-squared:** 0.0337, adjusted for the number of predictors. -
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