Math Problem Statement

The data in the table below represents the square footage and rents​ (dollars per​ month) for apartments in a section of a large city. Complete parts​ (a) through​ (c) below. Square Footage comma x 688 769 811 795 809 901 802 Rent per Month comma Upper R 1545 1605 1620 1640 1635 1730 1650 Question content area bottom Part 1 ​(a) Using a graphing​ utility, draw a scatter diagram of the data treating square footage as the independent variable. What type of relation appears to exist between square footage and​ rent?

Solution

The scatter plot shows a positive relationship between square footage and rent. As square footage increases, the rent generally tends to increase as well. This suggests a positive linear correlation between these two variables.

Would you like more details on interpreting this plot or moving forward with the next parts?

Here are 5 related questions to expand your understanding:

  1. How can you determine the strength of the correlation from the scatter plot?
  2. What factors might affect rent besides square footage?
  3. How can we mathematically describe the relationship between square footage and rent?
  4. What statistical methods can confirm the linear relationship between two variables?
  5. What is the importance of outliers in a scatter plot analysis?

Tip: Always check if the scatter plot suggests a linear, quadratic, or another type of relationship to choose the right model for analysis.

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Math Problem Analysis

Mathematical Concepts

Scatter Plot
Correlation
Linear Relationship

Formulas

Slope formula: (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b

Theorems

Linear Correlation Coefficient
Least Squares Regression

Suitable Grade Level

Grades 10-12