I give good rates to correct answer !! Question #2 / 25 The well-known psycholog
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I give good rates to correct answer !! Question #2 / 25 The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from 0 to 10, measures the "general anxiety" of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod's assessment of anxiety is based on a variety of measurements, both physiological and psychological.) We're interested in making predictions about individuals' sleep behavior based on their GAS scores. The bivariate data below give the GAS score (denoted by x) and the number of hours of sleep last night (denoted by y) for each of the fifteen adults in a study. The least-squares regression line for these data has equation y 8.38-0.27x. This line, along with a scatter plot of the sample data, is shown in Figure 1. Sleep time, y GAS score, X(in hours) 8.5 7.1 5.8 8.4 5.1 6.3 6.3 10- 1.5 0.9 8.8 2.1 8.1 6.4 7.0
Explanation / Answer
1. Mean of the GAS scores = 5.1067; Mean of the sleep times = 7.02.
Below are the same scores sorted in increasing order of sleep times:
As we can see, sleep times greate than the mean sleep time are ranged 7.1 to 8.6 and the corresponding GAS scores range 0.9 to 3.9, which are smaller than the mean GAS score of 5.1067
So we can conclude that sleep times that are greater than the mean sleep time tend to be paired with GAS scores that are less than the mean GAS score.
2. The regression equation is: sleep time = 8.38 - 0.27 x GAS score.
So for an increase of one in GAS score, there is a decrease of 0.27 hours in sleep time.
3. For a GAS score of 8.1, sleep time = 8.38 - 0.27 x 8.1 = 6.193 ~ 6.19
4. From the given table, observed sleep time was 5.1 hours for a GAS score of 8.1
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