# Linear Modeling and Titrating of Drug Dosages

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#### Updated on Mar 18, 2013

Grade Level: 6th to 8th; Type: Mathematics/Computer Science

### Objective

This experiment will introduce students to linear modeling and demonstrate its applicability to everyday situations like dosing medications.

### Research Questions

• Can all recommended drug dosages be fit to a linear model?
• How can linear models be used to titrate dosages of medicine?

### Introduction

In this experiment, students will obtain recommended drug dosages from everyday pharmaceutical products and evaluate if they can be fit to a linear model. Students will then use their linear models to titrate dosages for specific patient subgroups.

### Terms to Know

• Linear modeling
• Line of best fit
• Titrating drug doses
• Trendline

### Materials

• Several over-the-counter medications. Select medications that have dosages listed for several weight ranges.
• Computer
• Graphing software (eg, Microsoft Excel)

### Experimental Procedure

1. Graph the dosages that you find for a medication on a scatter plot. The listed weights should be used as the X-values and dosage should be used as the Y-values.
2. After the data points are plotted, add a trendline to your data. For example, if you are using Microsoft Excel, right-click on a data point on the graph and select “Add Trendline.” In the box that appears, select “Linear,” “Display equation on chart,” and “Display R-squared value on chart.” Your graph should now contain a line of best fit.
3. Look at the R-squared value. How close is it to 1? This number represents how well your data fits the linear model. The closer it is to 1, the better your data fits in the model.
4. Use the equation that is generated to determine specific dosages for patients. For example, the recommended dosages for infant acetaminophen are
• 6-11 lbs: 1.25 mL
• 2-17 lbs: 2.5 mL
• 8-23 lbs: 3.75 mL
5. A scatter plot can be generated with 3 data points:
• Data point 1: X-value=6lbs; Y-value=1.25 mL
• Data point 2: X-value=12 lbs; Y-value=2.5 mL
• Data point 3: X-value=18 lbs; Y-value=3.75 mL
6. When a linear trendline is applied to this data, you get the equation: y=0.2083x.
7. According to the drug bottle, an infant weighing 13 lbs falls in the 12-17 lbs. range and should receive 1.25 mL. However, your equation allows you to calculate a titrated dosage for an infant at this weight.
• y=0.2083 x 13 lbs.
• y=2.7079 mL
8. Repeats steps 1 to 4 for other medications. Try calculating titrated dosages for several of the drugs that you select. Can the same equation be used to model the dosages of every drug that you find?

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