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2.) Use the following data to plot a first order and second order model. I have provided code to generate a second order model, repeat this for a first order model, plot both models and the data on a single plot. Comment on which is the better fit based on the plot. X y 5 15 10 22 15 30 20 31 The following code produces a second-order model, enter this code and then repeat this for a first order model with the appropriate changes made, comment on what each line is doing.

2.) Use the following data to plot a first order and second order model. I have provided code to generate a second order model, repeat this for a first order model, plot both models and the data on a single plot. Comment on which is the better fit based on the plot. X y 5 15 10 22 15 30 20 31 The following code produces a second-order model, enter this code and then repeat this for a first order model with the appropriate changes made, comment on what each line is doing.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Code in python please

**Exercise 2: Modeling with Data** **Objective:** Use the data provided to plot both a first order (linear) and a second order (quadratic) model. Compare the two models and the data on a single plot and determine which model fits the data better. **Data Table:** | x | 5 | 10 | 15 | 20 | |----|----|----|----|----| | y | 15 | 22 | 30 | 31 | **Instructions:** 1. **Plot the Models:** - Use the data to create a plot of the first order model. - Use the data to create a plot of the second order model. - Overlay both models on a single graph to compare them with the actual data points. 2. **Model Code:** - Begin with the code provided to generate a second order model. - Adjust the code for a first order model. - Analyze and comment on the function of each line of code. By visualizing and comparing the outputs, you can better understand which model provides a more accurate representation of the data.
Transcribed Image Text:**Exercise 2: Modeling with Data** **Objective:** Use the data provided to plot both a first order (linear) and a second order (quadratic) model. Compare the two models and the data on a single plot and determine which model fits the data better. **Data Table:** | x | 5 | 10 | 15 | 20 | |----|----|----|----|----| | y | 15 | 22 | 30 | 31 | **Instructions:** 1. **Plot the Models:** - Use the data to create a plot of the first order model. - Use the data to create a plot of the second order model. - Overlay both models on a single graph to compare them with the actual data points. 2. **Model Code:** - Begin with the code provided to generate a second order model. - Adjust the code for a first order model. - Analyze and comment on the function of each line of code. By visualizing and comparing the outputs, you can better understand which model provides a more accurate representation of the data.
### Polynomial Regression: Quadratic Equation Model #### Enter the Data ```python x = np.array([5, 10, 15, 20]) y = np.array([15, 22, 30, 31]) ``` #### Quadratic Equation Model (2nd Order Polynomial) In this step, we fit a quadratic polynomial (2nd order) to the data. Equation: \( y = b0 + b1 \times x + b2 \times x^2 \) ```python b = np.polyfit(x, y, 2) print("2nd order polynomial parameters:\nb2 =", b[0], "\nb1 =", b[1], "\nb0 =", b[2]) ``` #### Plot the Model We create a smooth line representing the polynomial model. ```python x1 = np.linspace(5, 20, 100) pylab.plot(x1, np.polyval(b, x1), c = "r", label = "2nd Order Model") ``` #### Plot the Data Visualize the original data points and the fitted polynomial model. ```python pylab.scatter(x, y, c = 'k') pylab.grid() pylab.xlabel("x") pylab.ylabel("y") pylab.legend() ``` ### Explanation of Code - **Data Entry**: Arrays `x` and `y` store the independent and dependent variables, respectively. - **Quadratic Fitting**: `np.polyfit(x, y, 2)` computes the coefficients for a 2nd order polynomial that best fits the data. - **Parameters Display**: The polynomial parameters \( b2, b1, b0 \) are printed to the console. - **Model Plotting**: Uses `np.polyval()` to evaluate the polynomial at points defined by `x1` for smooth plotting. - **Graphical Elements**: - **Data Points**: Displayed as black ('k') scatter points. - **Model Curve**: Represented in red ('r'), labeled as "2nd Order Model". - **Grid and Labels**: Enhance the plot with grid lines, and label axes for clarity. A legend differentiates the model curve from data points.
Transcribed Image Text:### Polynomial Regression: Quadratic Equation Model #### Enter the Data ```python x = np.array([5, 10, 15, 20]) y = np.array([15, 22, 30, 31]) ``` #### Quadratic Equation Model (2nd Order Polynomial) In this step, we fit a quadratic polynomial (2nd order) to the data. Equation: \( y = b0 + b1 \times x + b2 \times x^2 \) ```python b = np.polyfit(x, y, 2) print("2nd order polynomial parameters:\nb2 =", b[0], "\nb1 =", b[1], "\nb0 =", b[2]) ``` #### Plot the Model We create a smooth line representing the polynomial model. ```python x1 = np.linspace(5, 20, 100) pylab.plot(x1, np.polyval(b, x1), c = "r", label = "2nd Order Model") ``` #### Plot the Data Visualize the original data points and the fitted polynomial model. ```python pylab.scatter(x, y, c = 'k') pylab.grid() pylab.xlabel("x") pylab.ylabel("y") pylab.legend() ``` ### Explanation of Code - **Data Entry**: Arrays `x` and `y` store the independent and dependent variables, respectively. - **Quadratic Fitting**: `np.polyfit(x, y, 2)` computes the coefficients for a 2nd order polynomial that best fits the data. - **Parameters Display**: The polynomial parameters \( b2, b1, b0 \) are printed to the console. - **Model Plotting**: Uses `np.polyval()` to evaluate the polynomial at points defined by `x1` for smooth plotting. - **Graphical Elements**: - **Data Points**: Displayed as black ('k') scatter points. - **Model Curve**: Represented in red ('r'), labeled as "2nd Order Model". - **Grid and Labels**: Enhance the plot with grid lines, and label axes for clarity. A legend differentiates the model curve from data points.
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