Seventeen subjects (nine women and eight men) from an outpatient, hospital-based

Question

Seventeen subjects (nine women and eight men) from an outpatient, hospital-based treatment program for obesity volunteered.
Within 10 days after the baseline measures (i.e., pretest measures) were obtained, the subjects began the 12-week VLCD [very low calorie diet] portion of the…program… At the end of the 12 weeks, all measurements were repeated in the laboratory.

Figure 1 demonstrates the relationship between age and percent of weight loss as fat. The correlation coefficient for this relationship was r = -.49.

Correlation between hydrostatic weighing and bioelectrical impedance was r = .63 for the 16 pretests and r = .84 for the 17 posttests. (Hydrostatic measurement of one male subject was not possible on the pretest because of discomfort in the water. Correlation for the combined pretest and posttest trials (n=33) was r = .837. (See Figure 2)
Please answer the following questions:

1. Which figure illustrates a direct relationship? Which figure has a negative slope? Explain.

2. What is the value of the intercept in Figure 2? Is the relationship depicted in Figure 1 or Figure 2 stronger? Explain.

3. Use the equation for the straight line shown in Figure 1 to predict the percentage of weight lost as fat for a person who is 60 years of age. Also, use same equation to predict the percentage of weight lost as fat for a person who is 20 years of age. Compare your above answers. Do your answers make sense considering that the relationship is inverse? Explain.

4. Use the equation for the straight line shown in Figure 2 to predict the percentage of body fat as measure by BIA for a person who has 50% body fat as measured by hydrodensitometry. In addition, suppose the slope in Figure 2 had been 1.50 instead of 0.77. With a slope of 1.50, would the line rise (from left to right) more steeply or less steeply than the line show in Figure 2? Explain.

5. The equation in which figure will yield more accurate predictions? Explain.

100 90 -913-40 80 70 60 0 0 20 30 40 50 60 70 Age (yean) Figure I. Relationship of age to fat loss 50 5 40 30 20 10 -544+7 10 20 30 40 50 % Body fat as measured by hydrondensitometry Figure 2. Hydrodensitomctry vs. bioelectrical impedance.

Explanation / Answer

Figure 1: y= 91.3-0.4x and r= -0.49 and Figure 2: Y= 5.44+0.77 and r= 0.837

1) Figure 2 illustrates direct relationship . Figure 1 has a negative slope.

2) The value of the intercept in Figure 2 is 5.44.Therelationship exhibited in Figure 2 is stronger. Since the points are close toline.

3) For x= 60

y= 91.3-0.4*60= 91.3-24= 67.3 kg amount of weight loss

x=20

y= 91.3-0.4*20 =91.3-8= 83.3 kg amount of weight loss

Yes answer make sense . At young age amount of weight loss is more than as compared to older age.

4) to predict the percentage of body fat as measure by BIA for a person who has 50% body fat as measured by hydrodensitometry is

y= 5.44+0.77x

x= 50%= 0.5

y= 5.44+0.77*50

y= 5.44+38.5= 43.94% body fat

With a slope of 1.50, the line would rise (from left to right) more steepy.

5) Figure 2 ismore accurate because the points are are more closer to the line also r is close to 1 for figure 2

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