Step: 1

Correlation is a measure of the strength of the relationship between two variables. It is used to predict the value of one variable given the value of the other.

Step: 2

Causation is the act of causing one variable to happen due to the other variable's effect.

Step: 3

Eating junk food makes you obese therefore there is a causal factor present.

Correct Answer is : causal factor is present between the two

Step: 1

Correlation is a measure of the strength of the relationship between two variables. It is used to predict the value of one variable given the value of the other.

Step: 2

Causation is the act of causing one variable to happen due to the other variable's effect

Step: 3

Eating junk food makes you obese therefore there is a causal factor present.

Correct Answer is : correlation doesn′t imply causation

Step: 1

Correlation is a measure of the strength of the relationship between two variables. It is used to predict the value of one variable given the value of the other.

Step: 2

Causation is the act of causing one variable to happen due to the other variable's effect.

Step: 3

There is direct relation of correlation and causation as student's scores increases his cumulative GPA also increases.

Correct Answer is : There is both correlation and causation.

Step: 1

Step: 2

Causation is the act of causing one variable to happen due to the other variable's effect.

Step: 3

In the problem, the age of truck and the cost of repairs are the two variables.

Step: 4

If the age of truck is more, then the cost of repairs is also more. So, there exists a causal factor between the two.

Step: 5

Therefore, both correlation and causation exists.

Correct Answer is : There is both correlation and causation.

Step: 1

Step: 2

Causation is the act of causing one variable to happen due to the other variable's effect.

Step: 3

In the problem, the money spent on R & D and the firm's annual profits are the two variables.

Step: 4

If the money spent on R & D is more, then the firm's annual profit is also more. So, there exists a causal factor between the two.

Step: 5

Therefore, both correlation and causation exists.

Correct Answer is : There is both correlation and causation.

Student | Hours of study( | Test scores ( |

A | 6 | 48 |

B | 12 | 72 |

C | 8 | 65 |

D | 10 | 70 |

E | 12 | 78 |

F | 7 | 65 |

G | 12 | 82 |

H | 6 | 50 |

I | 14 | 85 |

J | 15 | 90 |

Step: 1

Prepare a table for values x , y , x ^{2}, y ^{2}, xy .

Step: 2

Correlation coefficient,r = n ( Σ x y ) - ( Σ x ) ( Σ y ) [ n ( Σ x 2 ) - ( Σ x ) 2 ] [ n ( Σ y 2 ) - ( Σ y ) 2 ]

[Formula]

Step: 3

[Substitute the values from the table and simplify.]

Step: 4

Step: 5

Therefore, there is a strong positive relationship between the hours of study and test scores .

[When r is close to ± 1, the relationship between the variables is strong and when r is away from ± 1, it is a weak relationship.]

Correct Answer is : 0.953; strong positive relationship

-2 | -1 | 0 | 1 | 2 | |

64 | 1 | 0 | 1 | 64 |

Step: 1

Make a table with values for x , y , x ^{2}, y ^{2}, xy .

Step: 2

Correlation coefficient, r = n ( Σ x y ) - ( Σ x ) ( Σ y ) [ n ( Σ x 2 ) - ( Σ x ) 2 ] [ n ( Σ y 2 ) - ( Σ y ) 2 ] = 0

[Substitute the values from the table and simplify.]

Step: 3

Therefore, x and y are uncorrelated.

Step: 4

But, we can see that x and y are connected and are such that y = x ^{6}

Step: 5

Therefore, two uncorrelated variables need not be independent, i.e., they can be dependent also.

Correct Answer is : true; there exists a relation between x and y i.e., y = x ^{6}

Height(in inches) | 60 | 62 | 64 | 66 | 66 |

Shoe size(in inches) | 7 | 8 | 9 | 10 | 11 |

Step: 1

Make a table with values for x , y , x ^{2}, y ^{2}, xy .

Step: 2

Correlation coefficient, r = n ( Σ x y ) - ( Σ x ) ( Σ y ) [ n ( Σ x 2 ) - ( Σ x ) 2 ] [ n ( Σ y 2 ) - ( Σ y ) 2 ]

[Substitute the values from the table.]

Step: 3

[Simplify.]

Step: 4

Step: 5

Therefore, there is a strong positive relationship between the heights and their shoe sizes of 5 people .

[When r is close to ± 1, the relationship between the variables is strong and when r is away from ± 1, it is a weak relationship.]

Correct Answer is : 1; strong positive relationship

Average temperature(in °F) | 42.3 | 40.2 | 41.8 | 42.9 | 43.1 | 42.6 | 40.7 |

Average precipitation(in cm) | 0.85 | 1.72 | 0.69 | 2.77 | 2.46 | 1.89 | 0.64 |

Step: 1

Make a table with values for x , y , x ^{2}, y ^{2}, xy .

Step: 2

Correlation coefficient, r = n ( Σ x y ) - ( Σ x ) ( Σ y ) [ n ( Σ x 2 ) - ( Σ x ) 2 ] [ n ( Σ y 2 ) - ( Σ y ) 2 ]

[Substitute the values from the table.]

Step: 3

[Simplify.]

Step: 4

The correlation coefficient, r is 0.54.

Correct Answer is : 0.54

34 | 31 | 35 | 30 | 32 | 35 | 32 | 33 | |

35 | 32 | 30 | 31 | 34 | 30 | 33 | 35 |

Step: 1

Make a table with values for x , y , x ^{2}, y ^{2}, xy .

Step: 2

Correlation coefficient, r = n ( Σ x y ) - ( Σ x ) ( Σ y ) [ n ( Σ x 2 ) - ( Σ x ) 2 ] [ n ( Σ y 2 ) - ( Σ y ) 2 ]

[Substitute the values from the table.]

Step: 3

[Simplify.]

Step: 4

Step: 5

Therefore, there is weak negative relationship between the variables.

[When r is close to ± 1, the relationship between the variables is strong and when r is away from ± 1, it is a weak relationship.]

Correct Answer is : - 0.1506; weak negative relationship

Student | A | B | C | D | E | F | G | H | I | J |

Midterm scores( | 76 | 68 | 66 | 83 | 90 | 72 | 79 | 92 | 96 | 87 |

Final scores( | 71 | 75 | 79 | 77 | 84 | 68 | 82 | 98 | 88 | 93 |

Step: 1

Prepare a table for values x , y , x ^{2}, y ^{2}, xy .

Step: 2

[Substitute the values from the table.]

Step: 3

[Simplify.]

Step: 4

The correlation coefficient, r = 0.752

Correct Answer is : 0.752

Temperature °C( | Ice Cream Sales ( |

14.2° | $210 |

16.4° | $320 |

11.9° | $185 |

15.2° | $328 |

18/5° | $410 |

22.1° | $518 |

19.4° | $416 |

Step: 1

Prepare a table for values x , y , x ^{2}, y ^{2}, xy .

Step: 2

[Substitute the values from the table.]

Step: 3

[Simplify.]

Step: 4

Step: 5

Therefore, there is a strong positive relationship between the temperature and ice cream sales. [When r is close to ± 1, the relationship between the variables is strong and when r is away from ± 1, it is a weak relationship.]

Correct Answer is : 0.975

Speed( | Time( |

50 | 50 |

55 | 40 |

60 | 42 |

65 | 35 |

70 | 36 |

Step: 1

Prepare a table for values x , y , x ^{2}, y ^{2}, xy .

Step: 2

Correlation coefficient, r = n ( Σ x y ) - ( Σ x ) ( Σ y ) [ n ( Σ x 2 ) - ( Σ x ) 2 ] [ n ( Σ y 2 ) - ( Σ y ) 2 ]

[Formula.]

Step: 3

[Substitute the values from the table and simplify.]

Step: 4

Step: 5

The correlation coefficient, r is 1.321.

Correct Answer is : 1.321

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