The least-squares regression equation is “hat\" y = 8.44 - 0.33x for a doctor Dr
ID: 3217930 • Letter: T
Question
The least-squares regression equation is “hat" y = 8.44 - 0.33x for a doctor Dr. Elbod's Generalized Anxiety (GA) scale. The GA scale is a scale from 0 to 10,
x denotes the number of hours of sleep last night
y denotes the value for each of the 12 adults participating in a study.
Use this equation (“hat" y = 8.44 - 0.33x ) to predict tonight's sleep time for a woman whose GA score is 6.2
To predict the interval for her sleep time and confidence interval for the mean sleep time of individuals with a 6.2 GA score, the following for our data has been computed:
GIVEN: mean square error (MSE) 0.607;
GIVEN: 1/12 + ((6.2 - x bar)^2) / (Summation 12, i=1 (x sub1 - x bar)^2)) = 0.1017;
where x sub 1, x sub 2, …’ x sub 12 denote the GA scores in the sample, and x bar denotes their mean.,
Answer:
1. When the GA score is 6.2 what is the 90% prediction for an individual value for sleep time (in hours)
(Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.)
ANSWER: Lower Limit ______
Answer Upper Limit _______
2. When the GA score is 6.2. Consider(but do not actually compute) the 90% interval for the mean sleep time, answer:
How would this confidence interval compare to the prediction interval computed above (assuming that both intervals are computed from the same sample data)?
Choose one response to answer the question below.
a). The confidence interval would be positioned to the left of the predication interval
b). The confidence interval would be positioned to the right of the predication interval
c). The confidence interval would have the same center as, but would be wider than, the ….
d). The confidence interval would be identical to the prediction interval.
e). The confidence interval would have the same center as, but would be narrower than, ….
3. For the GA score values in this sample, 2.8 is more extreme than 6.2 is, that is, 2.8 is farther from the sample mean GA score than 6.2 is.
How would the 90% prediction interval from the mean sleep time when the GA score is 2.8 compare to the 90% prediction interval for the mean sleep time when the GA score is 6.2?
Choose one response to answer the question below.
a). The interval computed from a GA score of 2.8 would be narrower, but have the same
a). The interval computed from a GA score of 2.8 would be wider, but have the same
a). The intervals would be identical
a). The interval computed from a GA score of 2.8 would be wider, and have a different
a). The interval computed from a GA score of 2.8 would be narrower, and have a different
Explanation / Answer
from above std error =0.607*(0.1017)1/2 =0.1936
for 10 df and 90% CI, t=1.8125
for x=6.2 predictive value =6.3874
hence Lower Limit =predicted value -t*std error =6.0366
upper limit = 6.7382
e). The confidence interval would have the same center as, but would be narrower than, …
3)a).The interval computed from a GA score of 2.8 would be wider, and have a different
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