Math Problem Statement

If the relation between x and y is as shown in Table AQ-3.2, then which among the following lines is the best fit?

Solution

The table in the image shows the values of xx and yy, and we are tasked with finding the best fitting line from the options given, each associated with a sum of squared errors (SSE).

Here are the pairs of values provided:

x & y \\ \hline 0 & 1 \\ 1 & 3 \\ 2 & 4 \\ 3 & 5 \\ 4 & 5 \\ 5 & 0 \\ 6 & 8 \\ \end{array}$$ The candidate lines are: - $$y = 2x$$ with SSE = 143 - $$y = x$$ with SSE = 40 - $$y = 3x$$ with SSE = 428 - $$y = 4x$$ with SSE = 895 To determine the best fit, the sum of squared errors (SSE) measures how well a model fits the data. The smaller the SSE, the better the fit. According to the options, the line $$y = x$$ has the smallest SSE (40), indicating it is the best fit for the given data. Therefore, **the best fit line is $$y = x$$**. Let me know if you would like to see any further details or have any other questions! Here are 5 related questions to explore further: 1. How is the sum of squared errors (SSE) calculated? 2. What is the significance of a lower SSE in regression analysis? 3. How would changing the degree of the polynomial affect the fit and SSE? 4. What other methods can be used to assess the quality of a fit? 5. How can outliers influence the calculation of SSE? **Tip:** Always check the residuals (errors) of a regression to ensure no patterns are missed that might suggest a better model.

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Math Problem Analysis

Mathematical Concepts

Regression
Sum of Squared Errors (SSE)
Linear Models

Formulas

y = mx + b (Linear equation)
SSE = Σ(y_observed - y_predicted)^2

Theorems

Least Squares Method

Suitable Grade Level

Grades 9-12

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