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The 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 esidual 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. The residuals plot has a nonlinear shape. Therefore, this data cannot be modeled with a linear model. Determine the best curvilinear trendline that maximizes R. Data table for number of hours per helicopter OA. The best trendline is Logarithmic with an R² value of The equation is y (D tn ( . TT (Round the coefficient of the logarithm to one decimal place as needed. Round all other values to three decimal places as needed.) Helicopter Number Labor HourS 2000 1400 1238 OB. The best trendline is Exponential with an R value of The equation is y= Oe. (Round the coefficient to one decimal place as needed. Round all other values to three decimal places as needed.) ос. 3 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.) 1142 1075 1029 985 957 O D. The best trendline is Polynomial with an R? value of The equation is y D.+ (Round to three decimal places as needed.) Print Done

The 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 esidual 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. The residuals plot has a nonlinear shape. Therefore, this data cannot be modeled with a linear model. Determine the best curvilinear trendline that maximizes R. Data table for number of hours per helicopter OA. The best trendline is Logarithmic with an R² value of The equation is y (D tn ( . TT (Round the coefficient of the logarithm to one decimal place as needed. Round all other values to three decimal places as needed.) Helicopter Number Labor HourS 2000 1400 1238 OB. The best trendline is Exponential with an R value of The equation is y= Oe. (Round the coefficient to one decimal place as needed. Round all other values to three decimal places as needed.) ос. 3 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.) 1142 1075 1029 985 957 O D. The best trendline is Polynomial with an R? value of The equation is y D.+ (Round to three decimal places as needed.) Print Done

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Analyzing Helicopter Assembly Data for Learning Curve Phenomenon The Helicopter Division of Aerospatiale is examining assembly costs at its Marseilles plant. Historical data show the relationship between the helicopter number and labor hours, suggesting a "learning curve" effect where labor hours decrease over time. #### Objective Construct a scatter plot and use Excel's Trendline feature to identify the best curvilinear trendline (not exceeding a second-order polynomial) that maximizes \( R^2 \). #### Data and Analysis A table with the number of hours per helicopter is provided: | Helicopter Number | Labor Hours | |-------------------|-------------| | 1 | 2000 | | 2 | 1400 | | 3 | 1238 | | 4 | 1142 | | 5 | 1075 | | 6 | 1029 | | 7 | 965 | | 8 | 957 | ### Steps for Analysis 1. **Data Visualization**: Construct a scatter plot based on the provided data to visually assess the trend. 2. **Residual Analysis**: Observe the residual plot, which exhibits a nonlinear pattern, suggesting that a linear model is unsuitable. 3. **Model Selection**: Evaluate different trendline models to maximize \( R^2 \). #### Trendline Options - **Option A: Logarithmic** - \( R^2 \) value needed. - Equation: \( y = a \ln(x) + b \). - **Option B: Exponential** - \( R^2 \) value needed. - Equation: \( y = ae^{bx} \). - **Option C: Power** - \( R^2 \) value needed. - Equation: \( y = ax^b \). - **Option D: Polynomial (Second-order)** - \( R^2 \) value needed. - Equation: \( y = ax^2 + bx + c \). **Choose the best model** based on the highest \( R^2 \) value after rounding coefficients as specified. This analysis aids in understanding the reduction in labor hours, indicative of increased efficiency in helicopter production.
Transcribed Image Text:### Analyzing Helicopter Assembly Data for Learning Curve Phenomenon The Helicopter Division of Aerospatiale is examining assembly costs at its Marseilles plant. Historical data show the relationship between the helicopter number and labor hours, suggesting a "learning curve" effect where labor hours decrease over time. #### Objective Construct a scatter plot and use Excel's Trendline feature to identify the best curvilinear trendline (not exceeding a second-order polynomial) that maximizes \( R^2 \). #### Data and Analysis A table with the number of hours per helicopter is provided: | Helicopter Number | Labor Hours | |-------------------|-------------| | 1 | 2000 | | 2 | 1400 | | 3 | 1238 | | 4 | 1142 | | 5 | 1075 | | 6 | 1029 | | 7 | 965 | | 8 | 957 | ### Steps for Analysis 1. **Data Visualization**: Construct a scatter plot based on the provided data to visually assess the trend. 2. **Residual Analysis**: Observe the residual plot, which exhibits a nonlinear pattern, suggesting that a linear model is unsuitable. 3. **Model Selection**: Evaluate different trendline models to maximize \( R^2 \). #### Trendline Options - **Option A: Logarithmic** - \( R^2 \) value needed. - Equation: \( y = a \ln(x) + b \). - **Option B: Exponential** - \( R^2 \) value needed. - Equation: \( y = ae^{bx} \). - **Option C: Power** - \( R^2 \) value needed. - Equation: \( y = ax^b \). - **Option D: Polynomial (Second-order)** - \( R^2 \) value needed. - Equation: \( y = ax^2 + bx + c \). **Choose the best model** based on the highest \( R^2 \) value after rounding coefficients as specified. This analysis aids in understanding the reduction in labor hours, indicative of increased efficiency in helicopter production.
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