- Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, and exponential models.
- Informally assess the fit of a function by plotting and analyzing residuals.
- Fit a linear function for a scatter plot that suggests a linear association.
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Remarks/ExamplesStudents take a more sophisticated look at using a linear function to model the relationship between two numerical variables. In addition to fitting a line to data, students assess how well the model fits by analyzing residuals.
TEST ITEM SPECIFICATIONS
This benchmark may be assessed using:
- Assessment Limits :
In items that require the student to interpret or use the correlation
coefficient, the value of the correlation coefficient must be given in
- Calculator :
- Clarification :
Students will represent data on a scatter plot.
Students will identify a linear function, a quadratic function, or an
exponential function that was found using regression.
Students will use a regression equation to solve problems in the
context of the data.
Students will calculate residuals.
Students will create a residual plot and determine whether a function
is an appropriate fit for the data.
Students will determine the fit of a function by analyzing the
Students will distinguish between situations where correlation does
not imply causation.
Students will distinguish variables that are correlated because one is
the cause of another.
- Stimulus Attributes :
Items should use real-world data and be set in a real-world context.
- Response Attributes :
Items may require the student to apply the basic modeling cycle.Items may require the student to choose an appropriate level of
accuracy.Items may require the student to choose and interpret the scale in a
Items may require the student to choose and interpret units..
SAMPLE TEST ITEMS (1)
- Test Item #: Sample Item 1
A company creates the equation y = 11.26x-76.1 to model the relationship between the number of pages in its catalog and the number of orders, in thousands, that were received.
To determine how well the equation models the relationship, the company plots the residuals as shown.
Why is the equation not a good model for the relationship?
Type your answer in the space provided.
- Difficulty: N/A
- Type: OR: Open Response