Interpreting Linear Regression Equations

Front

What is a linear regression equation?

Back

Tags

CCSS.8.EE.B.5

Front

What does the slope (m) in a linear regression equation represent?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept (b) in a linear regression equation represent?

Back

The y-intercept (b) represents the value of the dependent variable (y) when the independent variable (x) is zero. It is the point where the line crosses the y-axis.

Tags

CCSS.HSF.LE.B.5

Front

What is the coefficient of determination (R²)?

Back

The coefficient of determination (R²) measures how well the regression line fits the data. It ranges from 0 to 1, where a value closer to 1 indicates a strong correlation between the variables.

Tags

CCSS.HSS.ID.B.6B

Front

How do you interpret an R² value of 0.9879?

Back

An R² value of 0.9879 indicates that approximately 98.79% of the variation in the dependent variable can be explained by the independent variable, suggesting a strong correlation.

Front

What is the formula for predicting a value using a linear regression equation?

Back

Tags

CCSS.8.EE.B.5

Front

Back

To find the number of followers (x), substitute y = 200 into the equation: 200 = 1.08x + 119. Solve for x to find the number of followers.

Tags

CCSS.7.EE.B.4A

Front

What does it mean if the linear regression equation is a good representation of the data?

Back

It means that the equation accurately describes the relationship between the variables and can be used to make reliable predictions.

Front

Back

The boiling point at an altitude of 0 feet is 211.7 degrees, as indicated by the y-intercept of the equation.

Tags

CCSS.8.EE.C.8C

Front

How do you interpret the y-intercept in the context of a real-world problem?

Back

The y-intercept provides a baseline value for the dependent variable when the independent variable is zero, helping to understand the starting point of the relationship.

Tags

CCSS.HSF.LE.B.5