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 does a correlation coefficient of r = 0.92 indicate?

Back

A correlation coefficient of r = 0.92 indicates a strong positive correlation between the two variables, meaning as one variable increases, the other variable tends to also increase.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables in the equation and solve for y.

Front

What is the inverse of the function f(x) = 2x - 2?

Back

The inverse is f^{-1}(x) = \frac{1}{2}x + 1.

Front

What is a negative correlation?

Back

A negative correlation means that as one variable increases, the other variable tends to decrease.

Front

What is the linear regression equation for a set of data?

Back

The linear regression equation is typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you interpret the slope in a linear regression equation?

Back

The slope indicates the change in the dependent variable for a one-unit change in the independent variable.

Front

What does it mean if a function is not one-to-one?

Back

If a function is not one-to-one, it means that there are at least two different inputs that produce the same output, making it impossible to find an inverse.

Front

What is the inverse of the coordinates (1, 2), (3, 8), (-3, 6)?

Back

The inverse of the coordinates is (2, 1), (8, 3), (6, -3).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is zero, representing the starting point of the line on the y-axis.