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This PDF package contains five projects involving the plotting and analysis of (x, y) data.
Each project is guided (see preview thumbnail images above) and includes five assessment questions.
In each project, students are presented with a table containing (x, y) data for one of the scenarios listed below. The project then guides the students through these activities:
1). Plot the (x, y) data on a scatter plot.
2). Fit a trend line and uncertainty band by eye.
3). Use the graphed trend line to make a prediction. Use the uncertainty band to estimate the uncertainty of the prediction.
4). Find the slope and y-intercept of the trend line.
5). Use the equation of the trend line to compute a predicted value.
6). Think about concepts related to estimation, prediction, uncertainty.
7). Consider the appropriateness of applying a linear model to the data set.
8). Think about and interpret trend-line slopes and y-intercepts.
Project 1: Weights and Heights of Adult Women
Project 2: Egg Production and Age - Golden Comet Hens
Project 3: Chirp Rate and Temperature - Field Crickets
Project 4: Vehicle Percent Value and Vehicle Age
Project 5: Birth Weights and Mature Weights of Various Whale Species
TO THE INSTRUCTOR
These guided projects ask students to develop lines-of-best-fit and associated uncertainty bands for various sets of bivariate data.
The lines-of-best-fit and the uncertainty bands are developed qualitatively by eye rather than by standardized computational means.
Please let your students know that:
1). There exist standardized computational methods (linear least-squares fitting and median-median fitting, for example) for developing a line-of-best-fit and its associated uncertainty band.
2). The “by eye” development of the uncertainty band used in these projects is crude and represents an upper limit of the uncertainties of predictions made from the line-of-best-fit. Formal and standardized uncertainty estimates, such as the error of the estimate, will not be so broad as the “by eye” estimate we use in these projects. These crude uncertainty bands are particularly crude when i). only one or two (x, y) pairs lie far off the line, and ii). as the number of data points increases.
3). While the “by eye” uncertainty bands developed in these projects are crude, they are still very useful for quickly estimating an upper limit of the uncertainty of a particular prediction.