Studying Correlation. Create a graph of this data X= number of people at the party Y= number of $10...

Studying Correlation

Create a graph of this data

X= number of people at the party

Y= number of $10 gifts received

Positive Correlation

As x increases—y increases


X= DAYS OF RAIN IN A ROW

Y= NUMBER OF PEOPLE BUYING SUNTAN LOTION

Negative correlation

As x increases—y decreases


No correlation

X= NUMBER OF PEOPLE ON THE BEACH READING HARRY POTTER

Y= NUMBER OF CHILDREN IN THEIR FAMILY

Do all three graphs show the same type of correlation?

What kind of correlation is shown by each?

Negative Correlation

Positive Correlation

No Correlation

A line of best fit can show the relationship between the two variables.

CORRELATION COEFFICIENT +.89


Y= number OF $10 received in gifts

Use the line of best fit to predict the number of $10 gifts when 8 people are at the party.

X= # of people at the party

Y= # OF $10 received in gifts CORRELATION

COEFFICIENT=+.89

Use the line of best fit to predict how many people will be present at the party to receive 4-$10 gifts.

CORRELATION COEFFICIENT=.89


Y= number of $10 received in gifts

CORRELATION COEFFICIENT = -.91



A line of best fit can show the relationship between the two variables.

Use the line of best fit to predict how many people will buy suntan lotion when there have been four days of rain in a row.




Use the line of best fit to see how many days of rain there have been in a row if 2 people buy suntan lotion.




Is there a correlation between these two variables?

We say that this line has no correlation.

X= NUMBER OF PEOPLE ON THE BEACH READING HARRY POTTER

Y= NUMBER OF CHILDREN IN THEIR FAMILY

CALCULATING COVARIANCE

First Step: Find the Standard Deviation

3.5x

x x-mean (x-mean)2

1 -2.5 6.252 -1.5 2.253 -0.5 0.254 0.5 0.255 1.5 2.256 2.5 6.25

y y-mean (y-mean)2

1 -2.67 7.12893 -0.67 0.44892 -1.67 2.78895 1.33 1.76895 1.33 1.76896 2.33 5.4289

3.67y

3.5x

x x-mean (x-mean)2

1 -2.5 6.252 -1.5 2.253 -0.5 0.254 0.5 0.255 1.5 2.256 2.5 6.25

2( ) 17.56

2.92 1.78

x

x xs

N


y y-mean (y-mean)2

1 -2.67 7.12893 -0.67 0.44892 -1.67 2.78895 1.33 1.76895 1.33 1.76896 2.33 5.4289

3.67y

2( ) 19.336

3.22 1.79

y

y ys

N

x y x-mean y-mean (x-mean)(y-mean)1 1 -2.5 -2.67 6.6752 3 -1.5 -0.67 1.0053 2 -0.5 -1.67 0.8354 5 0.5 1.33 0.6655 5 1.5 1.33 1.9956 6 2.5 2.33 5.825

( )( )

176(1.78)(1.79)

1719.

.11

0 89

x y

x x y y

Ns s

1.78

1.79x

y

s

s

( )( ) 17x x y y

Second Step: Find the correlation


4.57x 2.71y

x x-mean (x-mean)2

1 -3.57 12.74492 -2.57 6.60493 -1.57 2.46495 0.43 0.18496 1.43 2.04497 2.43 5.90498 3.43 11.7649

y y-mean (y-mean)2

4 1.29 1.66414 1.29 1.66414 1.29 1.66413 0.29 0.08411 -1.71 2.92412 -0.71 0.50411 -1.71 2.9241


4.57x

2( ) 41.747

5.96 2.44

x

x xs

N

x x-mean (x-mean)2

1 -3.57 12.74492 -2.57 6.60493 -1.57 2.46495 0.43 0.18496 1.43 2.04497 2.43 5.90498 3.43 11.7649


2.71y

2( ) 11.437

1.63 1.28

y

y ys

N

y y-mean (y-mean)2

4 1.29 1.66414 1.29 1.66414 1.29 1.66413 0.29 0.08411 -1.71 2.92412 -0.71 0.50411 -1.71 2.9241

Finding the Measure of Covariability

( )( )

19.867(2.44)(1.28)

0.9119.8621.84

x y

x x y y

Ns s

2.44

1.28x

y

s

s

( )( ) 19.86x x y y

x y x-mean y-mean (x-mean)(y-mean)1 4 -3.57 1.29 -4.60532 4 -2.57 1.29 -3.31533 4 -1.57 1.29 -2.02535 3 0.43 0.29 0.12476 1 1.43 -1.71 -2.44537 2 2.43 -0.71 -1.72538 1 3.43 -1.71 -5.8653

NOW IT IS YOUR TURN

Find the Peason’s Correlation Coefficient

Student Number Pre-Test Course Grade

1 45 92

2 23 86

3 50 97

4 46 95

5 33 87

6 21 76

7 13 72

8 30 84

9 34 85

10 50 98

PT PT - Mean (PT-Mean)2 CG CG-Mean (CG-Mean)2

45 92

23 86

50 97

46 95

33 87

21 76

13 72

30 84

34 85

50 98

First find the Standard Deviation for each variable

PT PT-Mean (PT-Mean)2 CG CG-Mean (CG-Mean)2

45 10.5 110.25 92 4.8 23.0423 -11.5 132.25 86 -1.2 1.4450 15.5 240.25 97 9.8 96.0446 11.5 132.25 95 7.8 60.8433 -1.5 2.25 87 -0.2 0.0421 -13.5 182.25 76 -11.2 125.4413 -21.5 462.25 72 -15.2 231.0430 -4.5 20.25 84 -3.2 10.2434 -0.5 0.25 85 -2.2 4.8450 15.5 240.25 98 10.8 116.64

34.5x

2( ) 1552.510

155.25 12.45

x

x xs

N

87.2y

2( ) 669.610

66.96 8.18

y

y ys

N

PT PT - Mean CG CG-Mean (PT-Mean)(CG-Mean)

45 92

23 86

50 97

46 95

33 87

21 76

13 72

30 84

34 85

50 98

Second: Calculate the Pearson’s Correlation Coefficient

PT PT-Mean CG CG-Mean (PT-Mean)(CG-Mean)45 10.5 92 4.8 50.423 -11.5 86 -1.2 13.850 15.5 97 9.8 151.946 11.5 95 7.8 89.733 -1.5 87 -0.2 0.321 -13.5 76 -11.2 151.213 -21.5 72 -15.2 326.830 -4.5 84 -3.2 14.434 -0.5 85 -2.2 1.150 15.5 98 10.8 167.4

( )( )

96710(12.45)(8.18)

9671018.

54

91

0.

x y

x x y y

Ns s

12.45

8.18x

y

s

s

( )( ) 967x x y y

Make a GraphPre-test vs. Course Grade

Studying Correlation

Studying Correlation. Create a graph of this data X= number of people at the party Y= number of $10...

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