Answer :
This output corresponds to a linear regression model where the statewide fuel consumption is predicted using the number of drivers and the total length of rural roads as explanatory variables. Below is a detailed step-by-step explanation for filling in the model:
1. Model Call:
- The formula for the regression model should be stated clearly. Typically, it would look like this:
```
Call:
lm(formula = road[tex]$fuel ~ road$[/tex]drivers + road[tex]$rural) ``` 2. Residuals: - This section usually shows the distribution of the residuals but isn't fully provided here. Since it's already noted "Min" without further information, we can leave it as is for now. 3. Coefficients: - This part should list the coefficients for each explanatory variable along with their standard errors, t-values, and p-values. The specifics are not given in your problem, so we might represent them symbolically if numerical values are missing: ``` Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) a b c d road$[/tex]drivers e f g h
road[tex]$rural i j k l --- Signif. codes: 0 '' 0.001 ''0.01 ''0.05 '. '0.1 ' '1 ``` 4. Residual standard error: - This value is given as 68 with 23 degrees of freedom. ``` Residual standard error: 68 on 23 degrees of freedom ``` 5. Multiple R-squared and Adjusted R-squared: - Given as 0.402 and 0.35, respectively. ``` Multiple R-squared: 0.402, Adjusted R-squared: 0.35 ``` 6. F-statistic and p-value: - The F-statistic is 7.72 on 2 and 23 degrees of freedom, with a p-value of 0.00272. ``` F-statistic: 7.72 on 2 and 23 DF, p-value: 0.00272 ``` Filling in the model below, we get: ``` Call: lm(formula = road$[/tex]fuel ~ road[tex]$drivers + road$[/tex]rural)
Residuals:
Min
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) a b c d
road[tex]$drivers e f g h road$[/tex]rural i j k l
---
Signif. codes: 0 '' 0.001 ''0.01 ''0.05 ', '0.1' '1'
Residual standard error: 68 on 23 degrees of freedom
Multiple R-squared: 0.402, Adjusted R-squared: 0.35
F-statistic: 7.72 on 2 and 23 DF, p-value: 0.00272
ɜ
ɜ
ɜ Xrural
```
In this output, the placeholders (a, b, c...l) represent specific numerical values for the estimates, standard errors, t-values, and p-values which are not provided in the problem statement. The exact numbers would be used to replace these placeholders if they were available. For the regression equation placeholders at the bottom, it seems to hint at there being three variables to include (with one being `Xrural`). So typically, this might be a part like:
- [tex]\( \beta_0 \)[/tex] (intercept)
- [tex]\( \beta_1 \times \text{road$drivers} \)[/tex]
- [tex]\( \beta_2 \times \text{road$rural} \)[/tex]
So the final model would reflect these terms in a written equation form.
1. Model Call:
- The formula for the regression model should be stated clearly. Typically, it would look like this:
```
Call:
lm(formula = road[tex]$fuel ~ road$[/tex]drivers + road[tex]$rural) ``` 2. Residuals: - This section usually shows the distribution of the residuals but isn't fully provided here. Since it's already noted "Min" without further information, we can leave it as is for now. 3. Coefficients: - This part should list the coefficients for each explanatory variable along with their standard errors, t-values, and p-values. The specifics are not given in your problem, so we might represent them symbolically if numerical values are missing: ``` Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) a b c d road$[/tex]drivers e f g h
road[tex]$rural i j k l --- Signif. codes: 0 '' 0.001 ''0.01 ''0.05 '. '0.1 ' '1 ``` 4. Residual standard error: - This value is given as 68 with 23 degrees of freedom. ``` Residual standard error: 68 on 23 degrees of freedom ``` 5. Multiple R-squared and Adjusted R-squared: - Given as 0.402 and 0.35, respectively. ``` Multiple R-squared: 0.402, Adjusted R-squared: 0.35 ``` 6. F-statistic and p-value: - The F-statistic is 7.72 on 2 and 23 degrees of freedom, with a p-value of 0.00272. ``` F-statistic: 7.72 on 2 and 23 DF, p-value: 0.00272 ``` Filling in the model below, we get: ``` Call: lm(formula = road$[/tex]fuel ~ road[tex]$drivers + road$[/tex]rural)
Residuals:
Min
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) a b c d
road[tex]$drivers e f g h road$[/tex]rural i j k l
---
Signif. codes: 0 '' 0.001 ''0.01 ''0.05 ', '0.1' '1'
Residual standard error: 68 on 23 degrees of freedom
Multiple R-squared: 0.402, Adjusted R-squared: 0.35
F-statistic: 7.72 on 2 and 23 DF, p-value: 0.00272
ɜ
ɜ
ɜ Xrural
```
In this output, the placeholders (a, b, c...l) represent specific numerical values for the estimates, standard errors, t-values, and p-values which are not provided in the problem statement. The exact numbers would be used to replace these placeholders if they were available. For the regression equation placeholders at the bottom, it seems to hint at there being three variables to include (with one being `Xrural`). So typically, this might be a part like:
- [tex]\( \beta_0 \)[/tex] (intercept)
- [tex]\( \beta_1 \times \text{road$drivers} \)[/tex]
- [tex]\( \beta_2 \times \text{road$rural} \)[/tex]
So the final model would reflect these terms in a written equation form.
