Math Problem Statement
Compute the standard error of the estimate for quadratic model. compute the MAD for the quadratic model.
Solution
To compute the Standard Error of the Estimate (SEE) and Mean Absolute Deviation (MAD) for the quadratic model, I will extract the data provided in the first image and apply the respective formulas for both the quadratic model.
Let's break this into two steps:
1. Quadratic Regression Model
We have the dataTo compute the Standard Error of the Estimate (SEE) and Mean Absolute Deviation (MAD) for the quadratic model, I will extract the data provided in the first image and apply the respective formulas for both the quadratic model.
Let's break this into two steps:
1. Quadratic Regression Model
We have the
\hline \text{Year (x)} & \text{Amount (y)} \\ \hline 2000 & 22 \\ 2001 & 31 \\ 2002 & 45 \\ 2003 & 71 \\ 2004 & 82 \\ 2005 & 104 \\ 2006 & 139 \\ 2007 & 213 \\ 2008 & 245 \\ \hline \end{array}$$ The quadratic model is typically of the form: $$\hat{y} = ax^2 + bx + c$$ Where $$\hat{y}$$ is the predicted amount, and $$a$$, $$b$$, and $$c$$ are constants determined by regression analysis. ### 2. **Standard Error of the Estimate (SEE) Formula:** The formula for the standard error of estimate is: $$\text{SEE} = \sqrt{\frac{\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}{n-2}}$$ Where: - $$y_i$$ is the actual value. - $$\hat{y}_i$$ is the predicted value from the quadratic model. - $$n$$ is the number of data points. ### 3. **Mean Absolute Deviation (MAD) Formula:** The formula for the Mean Absolute Deviation is: $$\text{MAD} = \frac{1}{n} \sum_{i=1}^{n} | y_i - \hat{y}_i |$$ Next, I will calculate these quantities after fitting the quadratic regression to this dataset. Let me calculate that for you.The calculations for the quadratic model yield the following results: 1. **Standard Error of the Estimate (SEE):** 10.24 2. **Mean Absolute Deviation (MAD):** 7.14 These values represent the average errors between the actual and predicted values for the quadratic model. Would you like further details on the calculations, or do you have any other questions? Here are 5 related questions for further exploration: 1. What is the significance of the Standard Error of the Estimate in a regression model? 2. How does a quadratic regression compare to a linear regression in terms of error? 3. Can SEE be reduced by adding more data points or adjusting the model type? 4. How is the MAD different from other error metrics like Mean Squared Error (MSE)? 5. What does a high SEE or MAD imply about the predictive accuracy of the model? **Tip:** When analyzing models, it's essential to consider both SEE and MAD to get a clearer picture of the accuracy and precision of your predictions.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Statistics
Regression Analysis
Quadratic Regression
Error Metrics
Formulas
Quadratic Regression Model: \(\hat{y} = ax^2 + bx + c\)
Standard Error of the Estimate (SEE): \(\text{SEE} = \sqrt{\frac{\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}{n-2}}\)
Mean Absolute Deviation (MAD): \(\text{MAD} = \frac{1}{n} \sum_{i=1}^{n} | y_i - \hat{y}_i |\)
Theorems
Least Squares Method for Quadratic Regression
Suitable Grade Level
Undergraduate Level (Statistics or Mathematics)
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