Answer all parts of the question please Butler Trucking Company is an independen

ID: 3231052 • Letter: A

Question

Answer all parts of the question please

Butler Trucking Company is an independent trucking company in southern California. A major portion of Bulter's business involves deliveries throughout its local area. To develop better work schedules, the managers want to predict the total daily travel time for their drivers. Initially the managers believed that the total daily travel time would be closely related to the number of miles traveled in making the daily deliveries. To fit the regression model, a simple random sample of 10 driving assignments provided the data in Excel file, "Trucking 1". l. Using the data, Trucking 1 in Excel, develop an estimated linear regression equation and interpret the coefficients 2. What is the value of the sample correlation coefficient? Does it reflect a strong or weak relationship between total daily travel time and number of miles? 3. Compute the coefficient of determination Did the estimated regression equation provide a good fit? 4. How can we explain some of the remaining variability in the dependent variable? 5. Develop an estimated regression equation by adding another independent variable (use the data in Trucking 2) 6. Interpret the coefficients in the estimated regression equation in part 5. 7. Is the estimated regression equation coefficient for daily travel time the same in part 1 and part 5? Interpret the coefficient in each case. 8. Test overall significant using the values in ANOVA table 9. Test individual significant using the values in coefficient table. 0. Which estimated regression equation explains larger amount of the variability in the data? Explain. l. Discuss the benefit of using multivariate independent variable to predict the daily travel time

Explanation / Answer

Question 1

The required regression model for prediction of total daily travel time for drivers is given as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.814905707

R Square

0.664071312

Adjusted R Square

0.622080226

Standard Error

1.001791873

Observations

ANOVA

Significance F

Regression

15.87130435

15.8713

15.81458

0.004080177

Residual

8.028695652

1.003587

Total

23.9

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

1.273913043

1.400744525

0.909454

0.389687

-1.95620962

4.504035707

Miles traveled

0.067826087

0.017055637

3.976755

0.00408

0.028495716

0.107156457

Required linear regression equation is given as below:

Travel time = 1.2739 + 0.0678*Miles traveled

Y = 1.2739 + 0.0678*X

Question 2

The sample correlation coefficient is given as 0.814905707, which indicate a strong positive linear relationship or association between two variables miles traveled and travel time.

Question 3

The coefficient of determination or the value of R square is given as below:

Coefficient of determination = R^2 = 0.814905707*0.814905707 = 0.664071312

This means about 66.41% of the total variation in the dependent variable travel time is explained by the independent variable miles traveled.

This coefficient of determination provides a good fit because more variation is explained by independent variable in the regression equation.

Question 4

We can explain some of the remaining variability in the dependent variable by introducing some more independent variables which would be related to dependent variables. This means we need to find some more factors which are responsible for the effect on the dependent variable travel time.