The data being used for the quiz are based on data that were collected after the
ID: 3364058 • Letter: T
Question
The data being used for the quiz are based on data that were collected after the 2009 war ended that was between Israel and the Hamas militias in the Gaza Strip. Responses were obtained from a group of students whom were exposed to rocket attacks during that period. The variables in the study include:
ID: Used to indicate the ID# of the participant
Age: The age of the individuals that responded to the survey
Gender: The gender of the individuals that responded to the survey
0 = Female
1 = Male
Parents in range; Indicates whether or not the participant’s parents decided to stay in the range of the rockets
0 = Not in range
1 = In range
Anger: Respondents were asked to estimate the level of anger they felt during the war
Fear: Respondents were asked to estimate the level of fear they felt during the war
Perceived Threat: Respondents estimated the likelihood/probability that they would experience risky events within the next 12 months
7.0
How much of the variation in perceived threat can be explained by:
NOTE: Please convert your answer to a percent (XX.XX%)
a. age: ______
b. both age and the level of anger someone felt during the war: ______
Generate the regression equation for the Model 2.
ID age gender parents.in.range anger fear perceived.threat 1 35 0 0 4.57.0
64.90 2 40 0 0 7.0 7.0 86.78 3 28 1 0 5.0 5.0 87.97 4 25 1 0 2.0 2.0 44.63 5 26 1 0 5.5 2.0 98.83 6 33 0 1 6.5 2.0 61.45 7 21 1 1 4.0 4.0 42.38 8 29 1 1 5.0 2.5 99.61 9 21 0 1 3.0 3.5 83.61 10 20 1 1 5.5 4.5 76.94 11 39 1 0 6.0 1.5 49.23 12 31 1 1 4.0 2.0 5.16 13 34 0 1 3.0 3.0 64.15 14 34 0 1 4.0 6.0 25.56 15 26 1 0 2.5 5.5 84.39Explanation / Answer
Solution:
Part a
First of all we have to find the percentage of variation in the dependent variable perceived threat due to age only. The value of R square or the coefficient of determination is given as 0.031, this means about 3.1% of the variation in the dependent variable perceived threat is explained by the independent variable age (see model 1 below).
Part b
Now, we have to find the percentage of variation in the dependent variable perceived threat due to age and level of anger. For this model, the coefficient of determination or the value of R square is given as 0.17, this means about 17% of the variation in the dependent variable perceived threat is explained by independent variables age and level of anger (see model 2 below).
Regression outputs for both models are given as below:
Model 1
Regression Statistics
Multiple R
0.176181409
R Square
0.031039889
Adjusted R Square
-0.043495504
Standard Error
28.02079623
Observations
15
ANOVA
df
SS
MS
F
Significance F
Regression
1
326.9780148
326.978
0.416445
0.529941664
Residual
13
10207.14528
785.165
Total
14
10534.12329
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
87.40171677
35.40008693
2.468969
0.028189
10.92447868
163.8789549
age
-0.758904415
1.176002581
-0.64533
0.529942
-3.299503527
1.781694697
Model 2
Regression Statistics
Multiple R
0.413411623
R Square
0.17090917
Adjusted R Square
0.032727365
Standard Error
26.97799261
Observations
15
ANOVA
df
SS
MS
F
Significance F
Regression
2
1800.378269
900.1891
1.236843
0.324797494
Residual
12
8733.745025
727.8121
Total
14
10534.12329
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
76.22194993
34.97666897
2.179223
0.049963
0.014334916
152.4295649
age
-1.566981323
1.266695017
-1.23706
0.239726
-4.326872674
1.192910028
anger
7.775799935
5.465052511
1.422823
0.180261
-4.131526578
19.68312645
Regression Statistics
Multiple R
0.176181409
R Square
0.031039889
Adjusted R Square
-0.043495504
Standard Error
28.02079623
Observations
15
ANOVA
df
SS
MS
F
Significance F
Regression
1
326.9780148
326.978
0.416445
0.529941664
Residual
13
10207.14528
785.165
Total
14
10534.12329
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
87.40171677
35.40008693
2.468969
0.028189
10.92447868
163.8789549
age
-0.758904415
1.176002581
-0.64533
0.529942
-3.299503527
1.781694697
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