Problem 22
Question
Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression quadratic for the given points. Then plot the points and graph the least squares regression quadratic. $$ (0,10),(1,9),(2,6),(3,0) $$
Step-by-Step Solution
Verified Answer
The least squares regression equation obtained is in the form of \(ax^2 +bx + c\) where a, b, c are the coefficients determined by regression. The plot illustrates the distribution of the given points and the best fit line described by the equation.
1Step 1: Load the Data into Python and Import Required Libraries
The first step involves inputting the provided data points into Python using an array-like data structure, ideally using a list. Import necessary libraries including 'numpy' for numerical computations and 'matplotlib.pyplot' for data visualization.
2Step 2: Apply Polynomial Regression
For the second step, apply Polynomial regression using 'numpy.polyfit()'. The function requires three parameters: the x-values, y-values, and the degree of the polynomial you want to fit. Given the task is to fit a quadratic equation, the degree will be set to 2
3Step 3: Display the Coefficients of the Quadratic Equation
Display the coefficients of the quadratic regression equation. The equation will be in the form \(ax^2 + bx + c\), and the coefficients a, b, c will be determined by the regression.
4Step 4: Plot the Data Points and the Fitted Curve
In this step, use 'matplotlib.pyplot.plot()' to draw the regression curve along with the data points, which will provide a visual representation of how well the equation fits the data.
5Step 5: Interpret the regression equation and the plot
The last step involves interpreting the regression equation and the plot. The quadratic regression equation provides the best fit curve that minimizes the sum of the residuals between itself and each data point. A trend line can be seen on the plot which gives a better understanding of how data points are distributed.
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