1. A social psychologist wanted to test the hypothesis that people with similar
ID: 3174117 • Letter: 1
Question
1. A social psychologist wanted to test the hypothesis that people with similar interests will be attracted to one another. To test this, 15 women who had participated in a computer dating program were surveyed. Each of these individuals had already been on one date and each was asked to indicate how much she was attracted to that person on a scale of 1 (not attracted) to 10 (very attracted). Before being matched, subjects had responded to a 10-item questionnaire about their interests and habits, as had their eventual partners. For purposes of the study, the similarity between assigned partners differed. Some individuals were assigned partners who responded the same way on all 1o questions, some were assigned to partners who responded the same way on only 9 of the questions, and so on, all the way down to 1 similar questionnaire response. Thus, similarity between partners could range from 1 to 10, with low scores indicating little similarity and high scores indicating a great deal of similarity
Individual
Attraction
Similarity
1
10
8
2
8
6
3
6
4
4
4
2
5
2
3
6
10
6
7
8
8
8
6
5
9
7
9
10
4
5
11
1
3
12
3
1
13
5
3
14
7
5
15
9
7 Please calculate the coefficient of determination and show work
Individual
Attraction
Similarity
1
10
8
2
8
6
3
6
4
4
4
2
5
2
3
6
10
6
7
8
8
8
6
5
9
7
9
10
4
5
11
1
3
12
3
1
13
5
3
14
7
5
15
9
7 Please calculate the coefficient of determination and show work
Explanation / Answer
coefficient of determination R2=r*r=0.6042, is the parameter of the regression analysis and was done as
here attraction is defiened as dependendent variable (y) and similarity as indpendent variable (x)
after fitting regression y=a+bx =1.3846+0.9231
a=(sum(y)*sum(x2)-sum(x)*sum(xy))/(n*sum(x2)-(sum(x))2)=1.3846
b=(n*sum(xy)-sum(x)*sum(y))/ (n*sum(x2)-(sum(x))2) =0.9231
the correlation(r) betwee x and y
r=(n*sum(xy)-sum(x)*sum(y))/sqrt(n*sum(x2)-(sum(x))2)*(n*sum(y2)-sum(y))2=0.7777
and for simple linear regression (in this case)
coefficient of determination R2=r*r=0.6042
Individual Attraction (y) Similarity(x) y2 x2 xy 1 10 8 100 64 80 2 8 6 64 36 48 3 6 4 36 16 24 4 4 2 16 4 8 5 2 3 4 9 6 6 10 6 100 36 60 7 8 8 64 64 64 8 6 5 36 25 30 9 7 9 49 81 63 10 4 5 16 25 20 11 1 3 1 9 3 12 3 1 9 1 3 13 5 3 25 9 15 14 7 5 49 25 35 15 9 7 81 49 63 sum= 90 75 650 453 522Related Questions
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