Question

Questions 6 to 10 are based on the problem below:

Compute the Pearson
Correlation Coefficient, *r*, for the following data

X |
Y |

2 |
3 |

3 |
1 |

6 |
5 |

4 |
4 |

5 |
2 |

The Pearson
Correlation, *r* is

Answer #1

Solution:

X | Y | XY | X^2 | Y^2 |

2 | 3 | 6 | 4 | 9 |

3 | 1 | 3 | 9 | 1 |

6 | 5 | 30 | 36 | 25 |

4 | 4 | 16 | 16 | 16 |

5 | 2 | 10 | 25 | 4 |

n | 5 |

sum(XY) | 65.00 |

sum(X) | 20.00 |

sum(Y) | 15.00 |

sum(X^2) | 90.00 |

sum(Y^2) | 55.00 |

Numerator | 25.00 |

Denominator | 50.00 |

r | 0.5000 |

r square | 0.2500 |

Xbar(mean) | 4.0000 |

Ybar(mean) | 3.0000 |

SD(X) | 1.4142 |

SD(Y) | 1.4142 |

b | 0.5000 |

a | 1.0000 |

r = 0.5000

The Pearson Correlation, *r* is
**0.5000**

Compute the Pearson Correlation coefficient for the following
data (SSx= 10, and SSy= 10 )
X
Y
2
3
3
1
6
5
4
4
5
2

Determine the Pearson product-moment correlation coefficient for
the following data.
x 1 11 9 6 4 3 2
y 10 4 5 5 7 7 8
(Do not round the intermediate values. Round your answer to 3
decimal places.)
Correlation coefficient, r =

Determine the Pearson product-moment correlation coefficient for
the following data.
x 1 10 9 7 5 3 2
y 8 4 6 5 7 7 8
(Do not round the intermediate values. Round your answer to 3
decimal places.)
Correlation coefficient, r =

Compute the Pearson correlation for the following data.
X Y
7 3
3 1
6 5
4 4
5 2

(c) Compute the sample correlation coefficient r for each of the
following data sets and show that r is the same for both. (Use 3
decimal places.) (i) x 6 5 9 y 2 1 5 (ii) x 2 1 5 y 6 5 9 r (i)
(ii)

Compute the sample correlation coefficient r for each
of the following data sets and show that r is the same for
both. (Use 3 decimal places.)
(i)
x
3
4
9
y
3
3
5
(ii)
x
3
3
5
y
3
4
9
r
(i)
(ii)

Calculate the linear correlation coefficient for the data
below.
Calculate
the linear correlation coefficient for the data below.
x : 4, 6, 13, 10, 8, 7, 9, 11, 12, 5
y : 17, 12, 0, 5, 9, 10, 7, 2, 1, 14

Based on the data shown below, calculate the correlation
coefficient (to three decimal places)
x
y
5
65.8
6
68.4
7
73.6
8
70.8
9
75.8
10
77.4
r=r=

Based on the data shown below, calculate the correlation
coefficient (rounded to three decimal places)
x
y
1
8.32
2
12.24
3
11.46
4
15.78
5
20.2
6
20.42
7
23.94
8
27.96
9
27.48
10
31.5
11
33.82
12
38.24

compute r,r2 and 1-r2 for the problem
below .What does r,r2 and 1-r2 mean ? Is the
correlation strong or weak ?
You are given the following data:
X(Independent
Variable)
Y(Dependent
variable)
Month Advertising Expenditure (in Millions of
$) Sales Revenue (in Millions of
$)
July
1
3
August
2
7
September
3
5
October
4
11
November
5
14

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