The well-known psychologist Dr. Elbod has established what he calls his Generali
ID: 2947661 • Letter: T
Question
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 participating in a study. A scatter plot of the data is shown in Figure 1. Also given are the products of the GAS scores and sleep times for each of the fifteen adults. (These products, written in the column labelled "xy," may aid in calculations.) Sleep time, y (in hours) 6.6 5.2 5.6 GAS score, x 5.1 8.0 33.66 41.6 50.96 29.11 48.6 11.62 27.3 56.07 22.4 34 14.76 7.3 44.8 38.43 56.8 10 6.0 8.3 7.8 6.3 7.0 8.5 8.2 7.3 6.4 1.4 8.9 3.2 4.0 1.8 1.0 7.0 6.3 8.0 Send data to Excel Figure 1 Answer the following Carry your intermediate computations to at least four decimal places, and round your answer as specified below. (If necessary consult a list of formulas.) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places Clear Undo HelpExplanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 8.4191645 - 0.26727994 x
Sample size: 15
R (correlation coefficient) = -0.71585483
R-sq = 0.51244813
Estimate of error standard deviation: 0.73325111
Parameter estimates:
Analysis of variance table for regression model:
Hence,
Slope = -0.27
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 8.4191645 0.41839021 ? 0 13 20.122757 <0.0001 Slope -0.26727994 0.072306967 ? 0 13 -3.6964618 0.0027Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.