Math Problem Statement

What is the shape seen as linear or nonlinear

What is the shape seen as linear or nonlinear?

Solution

The data in the scatter plot shows a linear relationship between the median square footage (x-axis) and the median listing price (y-axis). This can be observed from the straight, dotted trend line, which fits the data points closely. Additionally, the equation y=131.04x+184618y = 131.04x + 184618 indicates a linear function, where yy (median listing price) depends linearly on xx (median square footage).

The high R2R^2 value of 0.9681 further supports this linearity, indicating that approximately 96.81% of the variance in the median listing price is explained by the median square footage.

Would you like further details on the significance of the R2R^2 value or the interpretation of the equation?

Here are some related questions to expand on this topic:

  1. How does the slope of the line (131.04131.04) relate to price per square foot?
  2. What does the R2R^2 value of 0.9681 tell us about the strength of the correlation?
  3. How would this relationship change if the data were nonlinear?
  4. What impact does the intercept (184618) have on the interpretation of prices?
  5. Could there be any external factors affecting this linear relationship?

Tip: A high R2R^2 value suggests a strong fit, but always consider other factors like data outliers that could influence the result.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Scatter Plot Analysis
Correlation

Formulas

Linear Equation: y = mx + b
Coefficient of Determination: R^2

Theorems

Line of Best Fit

Suitable Grade Level

Grades 10-12