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.