Untitled Quiz

Finding an equation (curve) that describes the relationship between two variables based on observed data.

The variable (x) whose value is chosen or controlled in an experiment or study.

The variable (y) whose value changes or is affected by changes in the independent variable.

Equation: y = a + bx. A simple linear relationship between two variables.

Equation: y = ab^x. An exponential relationship.

Equation: y = a + bx + cx^2. A curved relationship.

Equation: y = a + bx + cx^2 + dx^3. Describes a specific growth function.

Values that are fixed within an equation and do not vary.

A linear equation in the form Ax + By + C = 0, where A, B, and C are constants. If B is non-zero, it can be rearranged into the y = mx + c form.

The gradient of a straight line; the rate of change of y as x increases. It determines if the line slopes upward (positive slope), downward (negative slope), or stays horizontal (zero slope).

A specific way to express a linear equation: y = mx + c, where 'm' is the slope (gradient) and 'c' is the y-intercept (y-value when x=0).

A line where y increases when x increases.

A line where y decreases when x increases.

A horizontal line where y remains constant as x changes.

A relationship between two variables where a change in one variable corresponds to a constant change in the other variable.

If a plot of ln(y) against ln(x) is a straight line, it indicates an exponential relationship between y and x.

Using a visual approach to draw a line or curve through a set of data points that best represents the overall trend. The equation of this curve is determined by choosing specific points on the curve.

A mathematical technique used to find the best-fitting curve for a dataset by minimizing the sum of the squared differences between observed data points and the predicted values from the curve's equation.

The underlying concept that the best-fitting curve is the one that minimizes the total squared differences between observed data points and the curve's predicted values.

Values predicted by the equation of the fitted curve for a given set of input values (x).

Actual measurements or data points collected during an experiment or study.

The curve that represents the closest match to the overall trend in a dataset, minimizing the differences between the curve and the actual data points.

Fixed values within a mathematical equation that remain constant regardless of input values (x). These values determine the specific shape and position of the curve.

The best-fitting line minimizes the sum of squared differences between observed data points and the line.

Equations derived from the Least Squares Principle to find the best-fitting line's parameters (a and b).

Visualizing the problem of finding the best-fitting line on a graph. The line minimizes the sum of squared vertical distances between the data points and the line.

The difference between the observed data point's y-value and the corresponding y-value on the line.

The Least Squares method can be used to fit other types of curves besides straight lines, like parabolas or exponentials.

A technique used to find the line that best fits a set of data points by minimizing the sum of the squared distances between the data points and the line.

The process of changing the original variables (x and y) in a data set to simplify calculations or improve the fit of a line.

Shifting the origin of the independent variable (x) by a constant 'c'.

Shifting the origins of both the independent (x) and dependent (y) variables by constants 'c' and 'c'' respectively.

Specific transformations applied when the independent variable (𝑥) has a common difference between successive values and the number of data points (𝑛) is either odd or even.

The constant value that is added to each successive value of the independent variable (𝑥).

Using the fitted line equation to predict the expected value of the dependent variable (y) for a given value of the independent variable (x).

A method for finding the best-fitting curve by minimizing the sum of squared differences between the observed data points and the curve's predicted values.

The equation used to find the best-fitting parabola 𝑦 = 𝑎 + 𝑏𝑥 + 𝑐𝑥 2 by minimizing the sum of squared errors. It's a system of three equations.

The process of finding an exponential curve that best fits a set of data by taking logarithms of both sides and then forming normal equations.

The process of finding the normal equations involves taking partial derivatives with respect to the constants (a, b, c) and setting them equal to zero.

The equations used to find the best-fitting curve of the form 𝑦 = 𝑎𝑏 𝑥 by minimizing the sum of squared errors. They are derived by taking logarithms on both sides.

Taking logarithms on both sides of an exponential equation (𝑦 = 𝑎𝑏 𝑥 ) converts it into a linear form (𝑌 = 𝐴 + 𝑏𝑋) which allows us to use linear regression techniques.

To find the original constant 'a' in the exponential equation 𝑦 = 𝑎𝑏 𝑥 , we need to take the antilogarithm of the constant 'A' found from the solution of the normal equations.