LMT - Linear Models and Tables Module Overview
Linear Models and Tables Module Overview
Introduction
In this module, we will continue to look at functions, particularly linear functions. We will revisit finding rate of change of various application, or real-world, problems. Describing what we see in graphs is an important skill. We will analyze graphs that represent relationships among two variables. This means we are determining if the graph is linear or non-linear, where the graph is increasing, or where the graph is decreasing. All the while, this information will help us make determinations regarding the original data we were given. Sometimes data doesn't fall in a nice straight line, but we can still use linear functions to help us find the line of best fit. This is called linear regression. Finally, we'll wrap this module up by constructing and interpreting two-way tables.
Essential Questions
- How do we construct a function to model linear relationships?
- How do we determine rate of change from a graph or from a table of values?
- How do we analyze a graph qualitatively?
- How do we plot and interpret bivariate data?
- How can we use straight lines to model relationships between two quantitative variables?
- How can we solve problems using linear equations with the bivariate data?
- How do we construct and interpret two-way tables?
Key Terms
The following key terms will help you understand the content in this module.
Model - A mathematical representation of a process, device, or concept by means of a number of variables.
Interpret - To establish or explain the meaning or significance of something.
Initial Value - y-intercept.
Qualitative Variables - A variable whose values are not numerical. Examples include gender (male, female), paint color (red, black, blue), type of bird (cardinal, blue bird, owl), and etc.
Linear - A relationship or function that can be represented by a straight line.
Non-linear: - A relationship which does not create a straight line.
Rate of Change - The ratio of the change in the output value and change in the input value of a function.
Slope: The measure of steepness of a line.
Bivariate Data - Two different response variables that are from the same population.
Quantitative Variables - A variable whose values are numerical. Examples include height, temperature, weight, grades, and etc.
Scatter Plot - The graph of a collection of ordered pairs that allows an exploration of the relationship between the points.
Line of Best Fit - A straight line drawn through the center of a group of data points plotted on a scatter plot.
Clustering - The partitioning of a data set into subsets (clusters), so that the data in each subset (ideally) share some common trait - often similarity or proximity for some defined distance measure.
Outlier - An element of a data set that distinctly stands out from the rest of the data.
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