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Understanding Correlation and Regression: Key Concepts and Predictions

This chapter explores the concepts of correlation and regression, highlighting how two variables relate through ordered pairs and scatter plots. It defines correlation as a numerical measure of strength and direction, expressed via the correlation coefficient (r). The chapter also examines linear regression, introducing the regression line's equation, which predicts dependent variable outcomes based on independent variable values. Using real examples, it demonstrates calculating the regression line from data, such as predicting a home's sale price based on its square footage.

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Understanding Correlation and Regression: Key Concepts and Predictions

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  1. CHAPTER nine Correlation and Regression

  2. Section 9.1 Correlation

  3. Definitions • Correlation is a relationship between 2 variables. • Data is often represented by ordered pairs (x, y) and graphed on a scatter plot • X is the independent variable • Y is the dependent variable

  4. Types of correlation:

  5. CORRELATION COEFFICIENT • A numerical measure of the strength and direction of a linear relationship between 2 variables x and y. • -1 < r < 1 The closer to -1 or 1, the stronger the linear correlation. The closer to 0, the weaker the linear correlation.

  6. Section 9.2 Linear regression

  7. Regression Line The line whose equation best fits the data in a scatter plot. We can use the equation to predict the value y for a given value of x. Recall: basic form of a line is y = mx + b We’ll use this form, but calculate m and b differently…

  8. Finding m and b

  9. Find the equation of the regression line • 18. The square footages and sale prices (in thousands of dollars) of seven homes. Use the line of regression to predict the sale price of a home when x = 1450 sq feet.

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