Questions and Answers
What does the determination coefficient (r^2) indicate?
What is represented by 'a' in linear regression?
slope
What does 'b' represent in a linear regression equation?
y intercept
What does the Pearson correlation coefficient (r) indicate?
Signup and view all the answers
R = -0.5 indicates a strong negative correlation.
Signup and view all the answers
What does r = 1 indicate?
Signup and view all the answers
What does r = -1 indicate?
Signup and view all the answers
What does r = 0 mean?
Signup and view all the answers
What does r < -0.8 indicate?
Signup and view all the answers
What does r > 0.8 indicate?
Signup and view all the answers
What does r = 0.5 indicate?
Signup and view all the answers
What does r^2 = 1 signify?
Signup and view all the answers
What does r^2 = 0 indicate?
Signup and view all the answers
To find a linear regression model, one must run a diagnostic on enter data into ___.
Signup and view all the answers
What does 'transformations of f(x)' refer to?
Signup and view all the answers
What is the equation for a translation up 'k' units?
Signup and view all the answers
What is the equation for a translation down 'k' units?
Signup and view all the answers
What is the equation for a translation right 'h' units?
Signup and view all the answers
What is the equation for a translation left 'h' units?
Signup and view all the answers
What does 'a > 1' indicate in vertical transformations?
Signup and view all the answers
What does '0 < a < 1' indicate in vertical transformations?
Signup and view all the answers
Study Notes
Linear Regression Terms
- r² (Coefficient of Determination): Ranges between 0 and 1, indicates the proportion of variance in the dependent variable explained by the independent variable.
- a (Slope): Represents the rate of change in the dependent variable for each unit change in the independent variable.
- b (Y-Intercept): The point where the line of best fit intersects the Y-axis, indicating the value of the dependent variable when the independent variable is zero.
Correlation Coefficients
- r (Pearson Correlation Coefficient): Ranges from -1 to 1, measuring the strength and direction of a linear relationship between two variables.
- r = 1: Indicates the strongest possible positive correlation between variables.
- r = -1: Represents the strongest possible negative correlation.
- r = 0: Indicates no correlation at all between the variables.
- r < -0.8: Suggests a strong negative correlation.
- r > 0.8: Indicates a strong positive correlation.
- r = -0.5: Suggests a weak negative correlation.
Determination Coefficient Insights
- Determination Coefficient (r²) Explanation: Quantifies the percentage of variation in the dependent variable that can be explained by the independent variable.
- r² = 1: Represents a perfect fit, where all data points lie exactly on the line of best fit.
- r² = 0: Indicates the worst possible fit, with no explanatory power for the model.
Finding Linear Regression Models
- Determining the Linear Regression Model: Involves entering data into statistical software, running diagnostic tests, and comparing r² values for different regression types (linear, quadratic, exponential). The best model is selected based on r² values, and the equation is recorded for predictions.
Transformations of Functions
- Types of Transformations: Include absolute value transformations which alter the position or shape of the graph of a function.
- Translation Up k Units: Represented by the equation ( y = |x| + k ), shifts the graph up by k units.
- Translation Down k Units: Represented by the equation ( y = |x| - k ), shifts the graph down by k units.
- Translation Right h Units: Represented by the equation ( y = |x - h| ), shifts the graph right by h units.
- Translation Left h Units: Represented by the equation ( y = |x + h| ), shifts the graph left by h units.
- Vertical Stretch: Represented when ( a > 1 ) in ( y = a|x| ), stretches the graph vertically.
- Vertical Compression: Occurs when ( 0 < a < 1 ), compressing the graph vertically.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Dive into the essential concepts of linear regression with these flashcards. Learn key terms like the determination coefficient, slope, and Pearson correlation coefficient. Perfect for students looking to master this crucial aspect of Algebra 2.
