I give good feedback to correct answers ! Thanks The well-known psychologist Dr.
ID: 3366130 • Letter: I
Question
I give good feedback to correct answers ! Thanks 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 ona 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 score, x(in hours) xy 6.8 8.1 6.1 6.6 5.8 5.1 8.4 7.2 6.9 20.4 47.79 39.65 25.74 52.78 40.29 31.08 5.76 55.89 10 3.0 5.9 6.5 3.9 9.1 7.9 3.7 0.8 8.1
Explanation / Answer
Solution
Back-up Theory
The linear regression model Y = ?0 + ?1X + ?, ………………………………………..(1)
where ? is the error term, which is assumed to be Normally distributed with mean 0 and variance ?2.
Estimated Regression of Y on X is given by: Y = ?0cap + ?1capX, ……………………….(2)
where
slope coefficient, ?1cap = Cov(x,y)/Var(X) ……………………………………………..(3)
Mean X = Xbar = (1/n)sum of xi …………………………………….……………….(4)
Mean Y = Ybar = (1/n)sum of yi ……………………………………….……………….(5) Var(X) = (1/n)sum of (xi – Xbar)2 …………………………………..………………………………..(6)
Cov(x, y) = (1/n)sum of {(xi – Xbar)(yi – Ybar)} ……………………………………………….………(7)
All above sums are over i = 1, 2, …., n, n = sample size ………………………………(8)
Calculations
Slope Coefficient = - 1.6547 ANSWER
i
xi
yi
xi^2
xi.yi
1
3
6.8
9
20.4
2
5.9
8.1
34.81
47.79
3
6.5
6.1
42.25
39.65
4
3.9
6.6
15.21
25.74
5
9.1
5.8
82.81
52.78
6
7.9
5.1
62.41
40.29
7
3.7
8.4
13.69
31.08
8
0.8
7.2
0.64
5.76
9
8.1
6.9
65.61
55.89
10
1.4
8.4
1.96
11.76
11
7.1
6.4
50.41
45.44
12
3.3
7.5
10.89
24.75
13
2.2
8.2
4.84
18.04
14
9
5.4
81
48.6
15
5
6.4
25
32
Sum
76.9
103.3
500.53
499.97
Mean
5.1267
20.66
78.2078
19.9988
Variance
51.9251
-85.9181
i
xi
yi
xi^2
xi.yi
1
3
6.8
9
20.4
2
5.9
8.1
34.81
47.79
3
6.5
6.1
42.25
39.65
4
3.9
6.6
15.21
25.74
5
9.1
5.8
82.81
52.78
6
7.9
5.1
62.41
40.29
7
3.7
8.4
13.69
31.08
8
0.8
7.2
0.64
5.76
9
8.1
6.9
65.61
55.89
10
1.4
8.4
1.96
11.76
11
7.1
6.4
50.41
45.44
12
3.3
7.5
10.89
24.75
13
2.2
8.2
4.84
18.04
14
9
5.4
81
48.6
15
5
6.4
25
32
Sum
76.9
103.3
500.53
499.97
Mean
5.1267
20.66
78.2078
19.9988
Variance
51.9251
-85.9181
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