1. What are the variables on the x- and y-axes in Figure 1 from the Flannigan et al. (2014) study?

2. What is the name of the type of variable represented by x and y in Figure 1? Is x or y the score to be predicted?

3. What is the purpose of simple linear regression analysis and the regression equation?

4. What is the point where the regression line meets the y-axis called? Is there more than one term for this point and what is the value of x at that point?

5. In the formula y = bx + a, is a or b the slope? What does the slope represent in regression analysis?

6. Using the values a = 3.161 and b = 0.502 with the novel formula in Figure 1, what is the predicted weight in kilograms for a child at 5 months of age? Show your calculations.

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7. What are the variables on the x-axis and the y-axis in Figures 2 and 3? Describe these variables and how they might be entered into the regression novel formulas identified in Figures 2 and 3.

8. Using the values a = 7.241 and b = 0.176 with the novel formula in Figure 2, what is the predicted weight in kilograms for a child at 4 years of age? Show your calculations.

9. Does Figure 1 have a positive or negative slope? Provide a rationale for your answer. Discuss the meaning of the slope of Figure 1.

10. According to the study narrative, why are estimated child weights important in a pediatric intensive care (PICU) setting? What are the implications of these findings for practice?

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1. The x variable is age in months, and the y variable is weight in kilograms in Figure 1.

2. x is the independent or predictor variable. y is the dependent variable or the variable that is to be predicted by the independent variable, x.

3. Simple linear regression is conducted to estimate or predict the values of one dependent variable based on the values of one independent variable. Regression analysis is used to calculate a line of best fit based on the relationship between the independent variable x and the dependent variable y. The formula developed with regression analysis can be used to predict the dependent variable (y) values based on values of the independent variable x.

4. The point where the regression line meets the y-axis is called the y intercept and is also represented by a (see Figure 14-1). a is also called the regression constant. At the y intercept, x = 0.

5. b is the slope of the line of best fit (see Figure 14-1). The slope of the line indicates the amount of change in y for each one unit of change in x. b is also called the regression coefficient.

6. Use the following formula to calculate your answer: y = bx + a

y = 0.502 (5) + 3.161 = 2.51 + 3.161 = 5.671 kilograms

Note: Flannigan et al. (2014) expressed the novel formula of weight in kilograms = (0.502 × age in months) + 3.161 in the title of Figure 1.

7. Age in years is displayed on the x-axis and is used for the APLS UK formulas in Figures 2 and 3. Figure 2 includes children 1 to 5 years of age, and Figure 3 includes children 6 to 12 years of age. However, the novel formulas developed by simple linear regression are calculated with age in months. Therefore, the age in years must be converted to age in months before calculating the y values with the novel formulas provided for Figures 2 and 3. For example, a child who is 2 years old would be converted to 24 months (2 × 12 mos./year = 24 mos.). Then the formulas in Figures 2 and 3 could be used to predict y (weight in kilograms) for the different aged children. The y-axis on both Figures 2 and 3 is weight in kilograms (kg).

8. First calculate the child’s age in months, which is 4 × 12 months/year = 48 months.

y = bx + a = 0.176 (48) + 7.241 = 8.448 + 7.241 = 15.689 kilograms

Note the x value needs to be in age in months and Flannigan et al. (2014) expressed the novel formula of weight in kilograms = (0.176 × age in months) + 7.241.

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9. Figure 1 has a positive slope since the line extends from the lower left corner to the upper right corner and shows a positive relationship. This line shows that the increase in x (independent variable) is associated with an increase in y (dependent variable). In the Flannigan et al. (2014) study, the independent variable age in months is used to predict the dependent variable of weight in kilograms. As the age in months increases, the weight in kilograms also increases, which is the positive relationship illustrated in Figure 1.

10. According to Flannigan et al. (2014, p. 927), “The gold standard for prescribing therapies to children admitted to Paediatric Intensive Care Units (PICU) requires accurate measurement of the patient’s weight. . . . An accurate weight may not be obtainable immediately because of instability and on-going resuscitation. An accurate tool to aid the critical care team estimate the weight of these children would be a valuable clinical tool.” Accurate patient weights are an important factor in preventing medication errors particularly in pediatric populations. The American Academy of Pediatrics (AAP)’s policy on Prevention of Medication Errors in the Pediatric Inpatient Setting can be obtained from the following website: https://www.aap.org/en-us/advocacy-and-policy/federal-advocacy/Pages/Federal-Advocacy.aspx#SafeandEffectiveDrugsandDevicesforChildren. The Centers for Medicare & Medicaid Services, Partnership for Patients provides multiple links to Adverse Drug Event (ADE) information including some resources specific to pediatrics at http://partnershipforpatients.cms.gov/p4p_resources/tsp-adversedrugevents/tooladversedrugeventsade.html.

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Follow your instructor’s directions to submit your answers to the following questions for grading. Your instructor may ask you to write your answers below and submit them as a hard copy for grading. Alternatively, your instructor may ask you to use the space below for notes and submit your answers online at http://evolve.elsevier.com/Grove/Statistics/ under “Questions to Be Graded.”

Name: _______________________________________________________ Class: _____________________

Date: ___________________________________________________________________________________

1. According to the study narrative and Figure 1 in the Flannigan et al. (2014) study, does the APLS UK formula under- or overestimate the weight of children younger than 1 year of age? Provide a rationale for your answer.

2. Using the values a = 3.161 and b = 0.502 with the novel formula in Figure 1, what is the predicted weight in kilograms (kg) for a child at 9 months of age? Show your calculations.

3. Using the values a = 3.161 and b = 0.502 with the novel formula in Figure 1, what is the predicted weight in kilograms for a child at 2 months of age? Show your calculations.

4. In Figure 2, the formula for calculating y (weight in kg) is Weight in kg = (0.176 × Age in months) + 7.241. Identify the y intercept and the slope in this formula.

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5. Using the values a = 7.241 and b = 0.176 with the novel formula in Figure 2, what is the predicted weight in kilograms for a child 3 years of age? Show your calculations.

6. Using the values a = 7.241 and b = 0.176 with the novel formula in Figure 2, what is the predicted weight in kilograms for a child 5 years of age? Show your calculations.

7. In Figure 3, some of the actual mean weights represented by blue line with squares are above the dotted straight line for the novel formula, but others are below the straight line. Is this an expected finding? Provide a rationale for your answer.

8. In Figure 3, the novel formula is (weight in kilograms = (0.331 × Age in months) − 6.868. What is the predicted weight in kilograms for a child 10 years old? Show your calculations.

9. Was the sample size of this study adequate for conducting simple linear regression? Provide a rationale for your answer.

10. Describe one potential clinical advantage and one potential clinical problem with using the three novel formulas presented in Figures 1, 2, and 3 in a PICU setting.

(Grove 139-150)

Grove, Susan K., Daisha Cipher. *Statistics for Nursing Research: A Workbook for Evidence-Based Practice, 2nd Edition*. Saunders, 022016. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

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