Math Problem Statement

The scatter plot shows the number of hours worked and money spent on entertainment by each of 24 students. (a) As the number of hours increases, the amount of money spent tends to _______. (b) There is a _______ correlation between the number of hours worked and the amount of money spent. (c) Predict how much a student working 8 hours would spend using the line of best fit.

Solution

Let's analyze the problem and answer each part step by step based on the scatter plot and line of best fit:

(a) As the number of hours worked increases, the amount of money spent tends to increase.

This is because the line of best fit slopes upward, indicating a positive relationship between hours worked and money spent.


(b) There is a positive correlation between the number of hours worked and the amount of money spent.

The upward trend in the scatter plot confirms a positive correlation, meaning that as hours worked increase, the money spent also increases.


(c) Using the line of best fit:

To predict the money spent for 8 hours worked, we can estimate from the graph. At approximately 8 hours, the line of best fit aligns with around $20 on the vertical axis.


Final Answers:

  1. (a): Increase
  2. (b): Positive
  3. (c): $20

Do you need further details about interpreting scatter plots, the line of best fit, or correlation? Let me know!

Related Questions:

  1. What does a negative correlation look like on a scatter plot?
  2. How do you calculate the equation of a line of best fit?
  3. What are the possible types of correlation (positive, negative, or none)?
  4. How can you use a line of best fit to make predictions for data?
  5. What does it mean if the points on a scatter plot are widely spread?

Tip:

A line of best fit is used to approximate data trends; it may not pass through all the points but minimizes the overall error.

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Math Problem Analysis

Mathematical Concepts

Scatter Plots
Line of Best Fit
Correlation

Formulas

Slope formula for best fit line: y = mx + b

Theorems

Line of Best Fit
Positive Correlation

Suitable Grade Level

Grades 8-10