Linear Regression and Inverse Function Review

Front

What is linear regression?

Back

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Front

What is the formula for a linear regression equation?

Back

The formula for a linear regression equation is typically expressed as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear regression equation represent?

Back

The slope (m) in a linear regression equation represents the rate of change of the dependent variable (y) for each unit change in the independent variable (x).

Front

What is the y-intercept in a linear regression equation?

Back

The y-intercept (b) in a linear regression equation is the value of y when the independent variable (x) is zero.

Front

How do you interpret a strong positive correlation coefficient (r)?

Back

A strong positive correlation coefficient (r) close to 1 indicates a strong direct relationship between the two variables, meaning as one variable increases, the other variable also tends to increase.

Front

What does it mean to find the inverse of a function?

Back

Finding the inverse of a function means switching the roles of the dependent and independent variables, effectively solving for the original input in terms of the output.

Front

What is the graphical representation of an inverse function?

Back

The graphical representation of an inverse function is a reflection of the original function across the line y = x.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are related such that if f(x) = y, then f^(-1)(y) = x.

Front

What is the significance of the correlation coefficient in linear regression?

Back

The correlation coefficient indicates the strength and direction of the linear relationship between the independent and dependent variables.

Front

How can you determine if a function has an inverse?

Back

A function has an inverse if it is one-to-one, meaning that each output is produced by exactly one input, which can be tested using the horizontal line test.