Thank you for visiting A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the linear function that best models the data provided in the table, we need to evaluate the given functions and determine which one fits the data points more accurately. Here's how the process works:
1. Data Points:
- We have the following data points regarding the number of months since the start and the percentage of the house left to build:
- (0, 200)
- (3, 65)
- (3, 99)
- (4, 41)
- (5, 34)
Note: The data point where x = 1 does not have a y-value, so we exclude it from analysis.
2. Possible Linear Models:
- We are given four possible linear models to consider:
- [tex]\( y = -13.5x + 97.8 \)[/tex]
- [tex]\( y = -13.5x + 7.3 \)[/tex]
- [tex]\( y = 97.8x - 13.5 \)[/tex]
- [tex]\( y = 7.3x - 97.8 \)[/tex]
3. Determine Fit:
- We calculate how well each model fits the data points by evaluating the predicted y-values from each model and comparing them to the actual y-values.
- The method used to find the best fit is by calculating the Sum of Squared Differences (SSD) between the actual and predicted values for the given data points.
4. Comparison Results:
- The model: [tex]\( y = -13.5x + 97.8 \)[/tex] resulted in an SSD of 12,264.55.
- The model: [tex]\( y = -13.5x + 7.3 \)[/tex] resulted in an SSD of 80,818.30.
- The model: [tex]\( y = 97.8x - 13.5 \)[/tex] resulted in an SSD of 432,778.21.
- The model: [tex]\( y = 7.3x - 97.8 \)[/tex] resulted in an SSD of 160,221.91.
5. Conclusion:
- The linear model that provides the best fit, with the smallest SSD, is [tex]\( y = -13.5x + 97.8 \)[/tex].
Therefore, the function [tex]\( y = -13.5x + 97.8 \)[/tex] best models the relationship between the number of months and the percentage of the house left to build.
1. Data Points:
- We have the following data points regarding the number of months since the start and the percentage of the house left to build:
- (0, 200)
- (3, 65)
- (3, 99)
- (4, 41)
- (5, 34)
Note: The data point where x = 1 does not have a y-value, so we exclude it from analysis.
2. Possible Linear Models:
- We are given four possible linear models to consider:
- [tex]\( y = -13.5x + 97.8 \)[/tex]
- [tex]\( y = -13.5x + 7.3 \)[/tex]
- [tex]\( y = 97.8x - 13.5 \)[/tex]
- [tex]\( y = 7.3x - 97.8 \)[/tex]
3. Determine Fit:
- We calculate how well each model fits the data points by evaluating the predicted y-values from each model and comparing them to the actual y-values.
- The method used to find the best fit is by calculating the Sum of Squared Differences (SSD) between the actual and predicted values for the given data points.
4. Comparison Results:
- The model: [tex]\( y = -13.5x + 97.8 \)[/tex] resulted in an SSD of 12,264.55.
- The model: [tex]\( y = -13.5x + 7.3 \)[/tex] resulted in an SSD of 80,818.30.
- The model: [tex]\( y = 97.8x - 13.5 \)[/tex] resulted in an SSD of 432,778.21.
- The model: [tex]\( y = 7.3x - 97.8 \)[/tex] resulted in an SSD of 160,221.91.
5. Conclusion:
- The linear model that provides the best fit, with the smallest SSD, is [tex]\( y = -13.5x + 97.8 \)[/tex].
Therefore, the function [tex]\( y = -13.5x + 97.8 \)[/tex] best models the relationship between the number of months and the percentage of the house left to build.
Thank you for reading the article A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
