Revise later
SpaceTo flip
If confident
All Flashcards
Define a linear function.
A function of the form (f(x) = b + mx) with a constant rate of change.
Define an exponential function.
A function of the form (f(x) = ab^x) with a changing rate of change dependent on the base 'b'.
Define a quadratic function.
A function of the form (f(x) = ax^2 + bx + c) with a changing rate of change dependent on the coefficient 'a'.
What are residuals in model validation?
The differences between the actual data values and the values predicted by the model. (Residual = Actual - Predicted)
What does a residual represent?
The error or difference between an observed value and the value predicted by a model.
What does 'overestimate' mean in modeling?
When a model's prediction is higher than the actual value.
What does 'underestimate' mean in modeling?
When a model's prediction is lower than the actual value.
Define 'error' in the context of model validation.
The difference between the predicted value and the actual value.
What is a residual plot?
A graph that displays the residuals on the y-axis and the independent variable on the x-axis.
What is model validation?
The process of checking whether a statistical model accurately represents the data and makes reliable predictions.
Explain when a linear model is most appropriate.
When the data exhibits a constant rate of change, forming a straight-line pattern.
Explain when an exponential model is most appropriate.
When the data exhibits growth or decay patterns, with a changing rate of change.
Explain when a quadratic model is most appropriate.
When the data exhibits a parabolic (U-shaped) pattern, with a changing rate of change.
What does a random scatter of residuals indicate?
A good model fit, where the model's errors are randomly distributed around zero.
What does a pattern in the residuals indicate?
A poor model fit, suggesting the model is not accurately capturing the underlying trend in the data.
Why is the context of the problem important when considering overestimation vs. underestimation?
The consequences of over or under predicting can vary greatly depending on the real-world scenario. For example, overestimating hospital resources is preferable to underestimating.
Explain the significance of residuals in determining the appropriateness of a model.
Residuals indicate how well the model fits the data. If residuals are randomly scattered, the model is a good fit; if they form a pattern, the model is not a good fit.
What does the sign of a residual tell you?
A positive residual indicates the model underestimated the actual value; a negative residual indicates the model overestimated the actual value.
How can you visually assess if a linear model is appropriate for a given dataset?
Plot the data points on a scatter plot. If the points appear to form a straight line, a linear model may be appropriate.
How can you visually assess if an exponential model is appropriate for a given dataset?
Plot the data points on a scatter plot. If the points appear to follow a curve that increases or decreases rapidly, an exponential model may be appropriate.
What is the general form of a linear function?
\(f(x) = b + mx)
What is the general form of an exponential function?
\(f(x) = ab^x)
What is the general form of a quadratic function?
\(f(x) = ax^2 + bx + c)
How do you calculate a residual?
\(Residual = Actual - Predicted)
Given data points, how do you determine the equation of an exponential function?
Use two points ((x_1, y_1)) and ((x_2, y_2)) to solve for (a) and (b) in (f(x) = ab^x).
How to determine the equation of a linear function?
Use the slope-intercept form: (y = mx + b), where (m) is the slope and (b) is the y-intercept.
How to determine the equation of a quadratic function from its vertex form?
Use the vertex form: (y = a(x - h)^2 + k), where ((h, k)) is the vertex of the parabola.
How to calculate predicted population in a exponential model?
Use the exponential model equation: (f(x) = ab^x), where (x) is the time, (a) is the initial population, and (b) is the growth factor.
How to calculate predicted population in a linear model?
Use the linear model equation: (f(x) = b + mx), where (x) is the time, (b) is the initial population, and (m) is the rate of change.
How to calculate predicted population in a quadratic model?
Use the quadratic model equation: (f(x) = ax^2 + bx + c), where (x) is the time, and (a), (b), and (c) are constants.