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:
-
S-17:
- Regression line:
- Correlation coefficient (): 0.99
-
S-18:
- Regression line:
- Correlation coefficient (): 0.90
-
S-19:
- Regression line:
- Correlation coefficient (): -0.88
-
S-20:
- Regression line:
- Correlation coefficient (): 0.09
-
S-21:
- Regression line:
- Correlation coefficient (): -0.30
Would you like further details or have any questions about any of these results?
Here are 5 related questions to explore:
- What does the correlation coefficient tell you about the strength and direction of the relationship?
- How do positive and negative slopes affect the interpretation of the regression line?
- Why is the correlation coefficient for S-17 close to 1?
- Can a regression line still be useful when the correlation coefficient is close to zero?
- 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
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