Math Problem Statement

S-17. For the following data set, get the regression line, plot the data and the regression line on the same screen, and report the value of the correlation coefficient. x 2 4 6 8 10 y 5 9 15 17 21 S-18. For the following data set, get the regression line, plot the data and the regression line on the same screen, and report the value of the correlation coefficient. x 2 4 6 8 10 y 5 9 20 17 21 S-19. For the following data set, get the regression line, plot the data and the regression line on the same screen, and report the value of the correlation coefficient. x 2 4 6 8 10 y 5 3 0 1 0 S-20. For the following data set, get the regression line, plot the data and the regression line on the same screen, and report the value of the correlation coefficient. x 2 4 6 8 10 y 1 0 21 3 2 S-21. For the following data set, get the regression line, plot the data and the regression line on the same screen, and report the value of the correlation coefficient. x 2 4 6 8 10 y 22 0 2 22 0 accurate answers, show working, and break it down

Solution

Here are the results for each data set:

  1. S-17:

    • Regression line: y=2.00x+1.40y = 2.00x + 1.40
    • Correlation coefficient (RR): 0.99
  2. S-18:

    • Regression line: y=2.00x+2.40y = 2.00x + 2.40
    • Correlation coefficient (RR): 0.90
  3. S-19:

    • Regression line: y=0.60x+5.40y = -0.60x + 5.40
    • Correlation coefficient (RR): -0.88
  4. S-20:

    • Regression line: y=0.25x+3.90y = 0.25x + 3.90
    • Correlation coefficient (RR): 0.09
  5. S-21:

    • Regression line: y=1.10x+15.80y = -1.10x + 15.80
    • Correlation coefficient (RR): -0.30

Would you like further details or have any questions about any of these results?

Here are 5 related questions to explore:

  1. What does the correlation coefficient tell you about the strength and direction of the relationship?
  2. How do positive and negative slopes affect the interpretation of the regression line?
  3. Why is the correlation coefficient for S-17 close to 1?
  4. Can a regression line still be useful when the correlation coefficient is close to zero?
  5. How would the regression change if outliers were added or removed from the data?

Tip: A correlation coefficient near 1 or -1 suggests a strong linear relationship, while values near 0 suggest a weak relationship.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Correlation Coefficient
Algebra

Formulas

Linear Regression Equation: y = mx + b
Correlation Coefficient (R): Pearson formula

Theorems

Least Squares Method for Regression

Suitable Grade Level

Grades 10-12