Authentic Learning Task (ALT) #2: The Predictive Powers of Ice Cream |
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Overview This ALT introduces order in the Design of Experiments (DOE) process through regression and pre-selection of factors and levels to test. This ALT asks you to consider the independent variables identified as significant in a factorial design procedure, and use them to generate data to put into a regression procedure. The purpose of the regression equation is to predict values of the dependent variable from the significant independent variables. In this ALT, the dependent variable to be observed is the time required to freeze ice cream for two levels of milk fat and two levels of rock salt added to ice in a plastic bag ice cream freezer. You use Excel to generate the prediction equation. After completing this ALT, you should be able to demonstrate the following competencies:
Materials and Equipment Safety and Disposal Pre-Activity In this activity, the relationship between the dependent variable (freeze time) and the independent variables (rock salt and % fat in the milk) will be determined by the use of scatter diagrams and regression equations. In order to prepare for this activity, complete the learning object
on scatter
Self Assessment For the following data, found in the attached file, compares the measurements of a chemical (x1– dependent variable) and a reagent (x2 – independent Variable) used to obtain the result by creating scatter chart and determining the regression line. The answers are available on the Solution sheet. Click here to access sample. Additional Analysis – ANOVA (Analysis of Variance) The Data Analysis Package in Excel has a regression subroutine that produces the equation for the line correlation coefficient and tests the “goodness” of the predictor line fit using Analysis of Variance (ANOVA). The underlying principal is the allocation of variation to the “theoretical” and the unassigned variation which is typically called “error”. The Fisher test (F test) is used to determine if the “Null Hypothesis” that there is “No difference” between the variation predicted by the model when compared to the random or unassigned variation typically known as “error.” By rejecting the null hypothesis that the variation is the same between the predicted and error, we conclude that the model explains the difference. An example problem comparing the measurements collected from two operators of the same thirty parts using both the approach developed in the first section using scatter plots and the regression equation is reworked using the Regression subroutine in the Data Analysis Package found in Excel. The problem is also reworked using a web based software package Statcrunch found at www.statcrunch.com. What conclusion can you make concerning the operators? Are they
consistent and are there any offsets (bias) in their measurements? To learn more about ANOVA, the following websites and simulators
are helpful. (We will be revisiting this topic in a later activity.)
Click here
for a glossary of terms. Activity In your team, perform the following steps to complete the activity:
Post-Activity Your team should now post its results from the activity to the Discussion Board. Assignment Assessment Statistical Experiments Home Page
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