Helicopter Division of Aerospatiale is studying assembly costs at its Marseilles plant. Past data indicates the accompanying data of number of labor hours per helicopter. Reduction in labor hours over time is often called a "learning curve" phenomenon. Using these data, apply simple linear regression and examine the dual plot. What do you conclude? Construct a scatter chart and use the Excel Trendline feature to identify the best type of curvilinear trendline (but not going beyond a second-order polynomial) that maximizes R. Click the icon to view the Helicopter Data. residuals plot has a nonlinear shape. Therefore, this data cannot be modeled with a linear model. Data table for number of hours per helicopter ermine the best curvilinear trendline that maximizes R TT The best trendline is Power with an R value of. The equation is y = (Dx (Round the coefficient to one decimal place as needed. Round all other values to three decimal places as needed.) Helicopter Number Labor Hours 2000 1400 B. The best trendline is Polynomial with an R? value of The equation is y = (Dx? +x+ (Round to three decimal places as needed.) 1238 1142 1075 1029 985 The best trendline is Exponential with an R? value of The equation is y = (De (Round the coefficient to one decimal place as needed. Round all other values to three decimal places as needed.) 8 957 The best trendline is Logarithmic with an R? value of The equation is y= (D In (x) (Round the coefficient of the logarithm to one decimal place as needed. Round all other values to three decimal places as needed.) Print Done
Helicopter Division of Aerospatiale is studying assembly costs at its Marseilles plant. Past data indicates the accompanying data of number of labor hours per helicopter. Reduction in labor hours over time is often called a "learning curve" phenomenon. Using these data, apply simple linear regression and examine the dual plot. What do you conclude? Construct a scatter chart and use the Excel Trendline feature to identify the best type of curvilinear trendline (but not going beyond a second-order polynomial) that maximizes R. Click the icon to view the Helicopter Data. residuals plot has a nonlinear shape. Therefore, this data cannot be modeled with a linear model. Data table for number of hours per helicopter ermine the best curvilinear trendline that maximizes R TT The best trendline is Power with an R value of. The equation is y = (Dx (Round the coefficient to one decimal place as needed. Round all other values to three decimal places as needed.) Helicopter Number Labor Hours 2000 1400 B. The best trendline is Polynomial with an R? value of The equation is y = (Dx? +x+ (Round to three decimal places as needed.) 1238 1142 1075 1029 985 The best trendline is Exponential with an R? value of The equation is y = (De (Round the coefficient to one decimal place as needed. Round all other values to three decimal places as needed.) 8 957 The best trendline is Logarithmic with an R? value of The equation is y= (D In (x) (Round the coefficient of the logarithm to one decimal place as needed. Round all other values to three decimal places as needed.) Print Done
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Title: Analyzing Assembly Costs with Curvilinear Trendlines**
The Helicopter Division of Aerospatiale is evaluating assembly costs at its Marseilles plant. Historical data provides insights into the labor hours required for each helicopter, as shown in the accompanying table. As labor hours decrease over time—a phenomenon known as the "learning curve"—it's essential to determine whether this data can be best represented by a particular trendline.
**Data Analysis Task:**
- **Objective:** Construct a scatter plot and trendline using Excel to find the most suitable curvilinear trendline, maximizing the R² value, without exceeding a second-order polynomial.
### Data Table:
The following table lists the number of helicopters and corresponding labor hours:
| Helicopter Number | Labor Hours |
|-------------------|-------------|
| 1 | 2000 |
| 2 | 1400 |
| 3 | 1238 |
| 4 | 1142 |
| 5 | 1075 |
| 6 | 1029 |
| 7 | 965 |
| 8 | 957 |
### Observations:
- The residual plot displays a **nonlinear shape**, suggesting a linear model is unsuitable.
### Trendline Options:
1. **Power Trendline:**
- **R² Value:** ___ (Determine during analysis)
- **Equation:** y = (___) x^(___)
2. **Polynomial Trendline:**
- **R² Value:** ___ (Up to second-order)
- **Equation:** y = (___) x² + (___) x + (___)
3. **Exponential Trendline:**
- **R² Value:** ___
- **Equation:** y = (___) e^(___x)
4. **Logarithmic Trendline:**
- **R² Value:** ___
- **Equation:** y = (___) ln(x) + (___)
### Conclusion:
- Use the R² value to assess the fit of each trendline.
- Select the trendline that maximizes R² for accurate modeling of labor hours over time. Ensure all coefficients are rounded appropriately as instructed.
**Next Steps:**
- Apply the best-fitting model for future cost and labor hour predictions.
- Further optimize production efficiency using these analytical insights.
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