Positive and Negative Correlation Worksheet

**Page 1**

1.

What type of correlation does $x$ and $y$ have?

a. | either positive or negative correlation | ||

b. | negative correlation | ||

c. | no correlation | ||

d. | positive correlation |

So,

Correct answer : (3)

2.

The scatter plot shows the population of California from 1997 to 2002. What kind of correlation exists between them?

a. | Inverse correlation | ||

b. | No correlation | ||

c. | Negative correlation | ||

d. | Positive correlation |

So, there exists a positive correlation between the years and the population of California.

Correct answer : (4)

3.

What kind of correlation does the statement describe?

"As the number of workers increases, the number of days required to complete a work decreases (assume each person work at same rate.)"

"As the number of workers increases, the number of days required to complete a work decreases (assume each person work at same rate.)"

a. | Strongly positive correlation | ||

b. | Positive correlation | ||

c. | Negative correlation | ||

d. | No correlation |

As one set of data increases, the other set of data tends to decrease. So, the statement describes a negative correlation.

Correct answer : (3)

4.

Positive correlation means ______.

a. | points can be approximated by a line with a negative slope | ||

b. | points can be approximated by a line with a positive slope | ||

c. | points that cannot be approximated by a line | ||

d. | points can be approximated by a curve |

Correct answer : (2)

5.

Negative correlation means _______.

a. | points that can be approximated by a line with a positive slope | ||

b. | points that cannot be approximated by a line | ||

c. | points that can be approximated by a line with a negative slope | ||

d. | points can be approximated by a curve |

Correct answer : (3)

6.

Points that cannot be approximated by a line have

a. | negative correlation | ||

b. | positive correlation | ||

c. | either positive or negative correlation | ||

d. | no correlation |

Correct answer : (4)

7.

The annual income of Sam is shown in the table. If $y$ represents the annual income and $t$ the number of years since 1990, choose an equation of the line that closely fits the data.

Year | 1990 | 1991 | 1992 | 1993 | 1994 |

Income($) | 16000 | 17000 | 20000 | 22000 | 24000 |

a. | $y$ = 2000$t$ - 16000 | ||

b. | $y$ = 2000$t$ | ||

c. | $y$ = 16000$t$ + 2000 | ||

d. | $y$ = 2000$t$ + 16000 |

Two points on the line are (0, 16000) and (3, 22000).

[Slope of the line.]

Write the equation of the line using a

[Slope-intercept form.]

[Replace

The equation of the best fitting line for the annual income of Sam is

Correct answer : (4)

8.

Choose the best fitting line for the data shown in the table and estimate the value of $y$ when $x$ is 10.

$x$ | 0 | 3 | 6 | 9 | 12 |

$y$ | 26.58 | 26.31 | 25.92 | 25.66 | 25.34 |

a. | $y$ = 3$x$ + 26.58; 25.48 | ||

b. | $y$ = 0.11$x$ + 26.58; 27.68 | ||

c. | $y$ = 26.58$x$; 2.658 | ||

d. | $y$ = - 0.11$x$ + 26.58; 25.48 |

Two points on the line are (0, 26.58) and (6, 25.92).

[Slope of the line.]

[Slope-intercept form.]

[Replace

[Replace

At

Correct answer : (4)

9.

The number of women competing in a beauty contest from 1995 to 1999 is shown in the table. Is it reasonable to represent the data by an equation of the best fitting line?

Year | 1995 | 1996 | 1997 | 1998 | 1999 |

Number of Women | 25 | 68 | 107 | 155 | 200 |

a. | No | ||

b. | Yes |

From the scatter plot, you can see that the data fall almost exactly on a line.

The equation of the best fitting line for the given data is possible.

Correct answer : (2)

10.

State whether $x$ and $y$ suggest a linear relationship in the graph.

a. | Yes | ||

b. | No |

So,

Correct answer : (1)