# Positive and Negative Correlation Worksheet

Positive and Negative Correlation Worksheet
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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

#### Solution:

From the scatter plot, you see that the points cannot be approximated by a line.

So, x and y have no correlation.

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

#### Solution:

From the scatter plot, you can see that the points can be approximated by a line with positive slope.

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

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.)"
 a. Strongly positive correlation b. Positive correlation c. Negative correlation d. No correlation

#### Solution:

As the number of workers increases, the number of days required to complete the work decreases. This is true since each person is working at same rate.

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

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

#### Solution:

Positive correlation means that the points can be approximated by a line with a positive slope.

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

#### Solution:

Negative correlation means that the points can be approximated by a line with a negative slope.

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

#### Solution:

Points that cannot be approximated by a line have no correlation.

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

#### Solution:

Plot the points and draw the line that best fits the points.

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

m = y2-y1x2-x1 =22000-160003-0 =60003 = 2000
[Slope of the line.]

Write the equation of the line using a y-intercept of b = 16000 and a slope of m = 2000.

y = mt + b
[Slope-intercept form.]

y = 2000t + 16000
[Replace m with 2000 and b with 16000.]

The equation of the best fitting line for the annual income of Sam is y = 2000t + 16000.

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

#### Solution:

Plot the points of the data and draw the line that best fits the points.

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

m = y2 -y1x2 -x1 =25.92 - 26.586 - 0 = - 0.11
[Slope of the line.]

y = mx + b
[Slope-intercept form.]

y = - 0.11x + 26.58
[Replace m with - 0.11 and b by 26.58.]

y = - 0.11(10) + 26.58 = 25.48
[Replace x with 10.]

At x = 10, the value of y is 25.48.

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

#### Solution:

Draw a scatter plot of the data to decide whether the data can be represented by a linear model.

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.

10.
State whether $x$ and $y$ suggest a linear relationship in the graph.

 a. Yes b. No

#### Solution:

From the scatter plot, you can see that the points can be approximated by a line.

So, x and y have a linear relationship.