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 purpose of finding the inverse of a function?

Back

The purpose of finding the inverse of a function is to determine a function that reverses the effect of the original function, effectively switching the roles of the input and output.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function algebraically, replace f(x) with y, switch x and y, and then solve for y. The resulting equation is the inverse function.

Front

What does a positive correlation indicate in a scatter plot?

Back

A positive correlation indicates that as one variable increases, the other variable also tends to increase.

Front

What is the correlation coefficient (r) and what does it signify?

Back

The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables, ranging from -1 to 1.

Front

What does an r value of 0.92 indicate about the relationship between two variables?

Back

An r value of 0.92 indicates a strong positive correlation between the two variables.

Front

If f(x) = x + 5, what is the inverse function f^-1(x)?

Back

The inverse function f^-1(x) is x - 5.

Front

What is the significance of switching x's and y's when finding an inverse function?

Back

Switching x's and y's when finding an inverse function reflects the reversal of the input-output relationship, allowing us to express the original output as a new input.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if a function is one-to-one?

Back

A function is one-to-one if each output is produced by exactly one input, meaning it has an inverse that is also a function.