Ben is interested in flirting. He wants to know what kinds of people are likely

Question

Ben is interested in flirting. He wants to know what kinds of people are likely to be good (and bad) at flirting. He thinks that self-confidence will be correlated with flirting ability, but he’s not sure which way it will go. High self-confidence should make for good flirters, but if people are too self-confident, it might hurt their flirting performance. So he gives a number of students a self-confidence measure (Y) and then watches them try to flirt with people at an off-campus bar (X). Both scales range from 1 (low) to 7 (high). He records the following scores:

Self-Confidence (X)

Flirting (Y)

4

5

6

3

6

5

7

6

6

7

3

1

6

4

2

3

3

2

3

4

Compute the correlation for these scores (13 pts). SHOW YOUR WORK! Use as much space as necessary.

Self-Confidence (X)

Flirting (Y)

4

5

6

3

6

5

7

6

6

7

3

1

6

4

2

3

3

2

3

4

Explanation / Answer

Correlation

r( X,Y) =Co V ( X,Y) / S.D (X) * S.D (y)                              
r( X,Y) = Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )                                
                              
Co v ( X, Y ) = 1 /10 (203) - [ 1/10 *46 ] [ 1/10 *40] = 1.9                              
S. D ( X ) = Sqrt( 1/10*240-(1/10*46)^2) = 1.685                              
S .D (Y) = Sqrt( 1/10*190-(1/10*40)^2) = 1.732                              
r(x,y) = 1.9 / 1.685*1.732 = 0.651                              
                              
If r = 0.651> 0 ,Perfect Positive Correlation                              

( X) ( Y) X^2 Y^2 X*Y 4 5 16 25 20 6 3 36 9 18 6 5 36 25 30 7 6 49 36 42 6 7 36 49 42 3 1 9 1 3 6 4 36 16 24 2 3 4 9 6 3 2 9 4 6 3 4 9 16 12 46 40 240 190 203 = TOTALS

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