**Title: Analyzing Fuel Consumption in Relation to Railcar Number**The Great Plains Railroad is conducting a study on how fuel consumption correlates with the number of railcars on a specific route between Oklahoma City and Omaha. Below are a scatterplot and a residual plot from the regression analysis of these data.**Data Visualization:**1. **Scatterplot:** - **X-axis:** Number of Railcars. - **Y-axis:** Fuel Consumption. - The plot displays a positive linear trend, indicating that as the number of railcars increases, fuel consumption also increases.2. **Residual Plot:** - **X-axis:** Fitted Values. - **Y-axis:** Residuals. - The residuals are scattered randomly around zero, suggesting that the linear model is appropriate for these data.**Statistical Insights:**- **Correlation Coefficient:** \( r = 0.9835 \), indicating a very strong positive linear relationship.- Descriptive statistics for the Number of Railcars: - Mean (\( \bar{x} \)) = 35.6 - Standard Deviation (\( s_x \)) = 10.42- Descriptive statistics for Fuel Consumption: - Mean (\( \bar{y} \)) = 87.2 - Standard Deviation (\( s_y \)) = 22.76**Questions and Discussion:**a) **Scatterplot Description:** - The scatterplot displays a strong positive linear relationship between the number of railcars and fuel consumption.b) **Linear Model Appropriateness:** - A linear model appears suitable given the strong correlation coefficient (r = 0.9835) and the random pattern of residuals around zero.c) **Coefficient of Determination (\( r^2 \)):** - Interpret \( r^2 \) as the percentage of variation in fuel consumption explained by the number of railcars. Given the high \( r \), \( r^2 \) is near 0.967, meaning about 96.7% of the variation is explained by the model.d) **Standard Error Interpretation:** - The value \( s = 4.361 \) implies the typical deviation of the observed fuel consumption from the values predicted by the model is approximately 4.361 units.e) **Equation of Least-Squares Regression Line:** - Using the given

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2. The Great Plains Railroad is interested in studying how fuel consumption is related to the number of railcars for its trains on a certain route between Oklahoma City and Omaha. A scatterplot and residual plot from the regression analysis for these data are shown below. RESIDUALS VERSUS THE FITTED VALUES 120 110- 100 90+ 80- 70 60아 50 20 30 50 50 60 70 80 90 100 1 io 120 40 Fitted Value Number of Railcars After some calculation, we found that the correlation coefficient is r = 0.9835. Our descriptive statistics also tell us that for the Number of Railcars x, i = 35.6 and s, = 10.42. Alongside this information we also know that for Fuel Consumption y, ỹ = 87.2 and s, = 22.76. a) Using the information above, provide a brief description of the scatterplot. b) Would a linear model be appropriate for modeling these data? Explain your reasoning. c) Interpret the coefficient of determination r2. d) Suppose that s = 4.361. Interpret this value in context. e) Using the information above, construct the equation of its Least-Squares Regression Line. Fuel Consumption Residual

2. The Great Plains Railroad is interested in studying how fuel consumption is related to the number of railcars for its trains on a certain route between Oklahoma City and Omaha. A scatterplot and residual plot from the regression analysis for these data are shown below. RESIDUALS VERSUS THE FITTED VALUES 120 110- 100 90+ 80- 70 60아 50 20 30 50 50 60 70 80 90 100 1 io 120 40 Fitted Value Number of Railcars After some calculation, we found that the correlation coefficient is r = 0.9835. Our descriptive statistics also tell us that for the Number of Railcars x, i = 35.6 and s, = 10.42. Alongside this information we also know that for Fuel Consumption y, ỹ = 87.2 and s, = 22.76. a) Using the information above, provide a brief description of the scatterplot. b) Would a linear model be appropriate for modeling these data? Explain your reasoning. c) Interpret the coefficient of determination r2. d) Suppose that s = 4.361. Interpret this value in context. e) Using the information above, construct the equation of its Least-Squares Regression Line. Fuel Consumption Residual

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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