﻿ Scatter Plot and Correlation Worksheet | Problems & Solutions

# Scatter Plot and Correlation Worksheet

Scatter Plot and Correlation Worksheet
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1.
Determine the relationship between the age and the playing hours in a week.
 Age ($x$) Playing hours ($y$) 6 20 7 17 8 18 9 17 10 17 11 13 12 16 14 14 15 13 16 12 17 5 18 9

 a. curvilinear relationship b. positive relationship c. no relationship d. negative relationship

#### Solution:

Plot the scatter diagram

From the scatter diagram, we can say that the playing hours decreases as the age increases.

So, the relationship is a negative relationship.

2.
Determine the relationship between the values of X and Y.
 X Y 0 5 1 2 2 1 3 2 4 5 5 10

 a. positive relationship b. curvilinear relationship c. no relationship d. negative relationship

#### Solution:

Plot the scatter diagram for X and Y.

From the scatter diagram, we can say that the points form a curve.

So, the relationship is a curvilinear relationship.

3.
Determine the relationship between the amount spent on cars(in million \$) and the years. The data of a particular state are shown in the table.
 Year ($x$) Amount ($y$) 1996 700 1997 750 1998 825 1999 975 2000 760 2001 1000 2002 904 2003 1144 2004 1403

 a. positive relationship b. curvilinear relationship c. negative relationship d. no relationship

#### Solution:

Plot the scatter diagram.

From the scatter diagram, we can say that the amount spent on cars increases yearly.

So, the relationship is a positive relationship.

4.
At different speeds of a car, the time for a particular journey are shown in the table. What is the relationship between the speed(in miles per hour) of the car and the time taken(in hours) by the car?
 Speed ($x$) Time ($y$) 50 50.4 55 40 60 42 65 35 70 36 75 37.5 80 31.5 85 32.5 90 28 95 25

 a. positive relationship b. curvilinear relationship c. negative relationship d. no relationship

#### Solution:

Plot the scatter diagram

From the scatter diagram, we can say that the speed of car increases with time.

So, the relationship is a negative relationship.

5.
Determine the relationship of the newspaper readers(in millions) in different years from 1996 to 2004.
 Year ($x$) Newspaper readers ($y$) 1996 63.3 1997 65.1 1998 67.6 1999 72.2 2000 71.8 2001 70.5 2002 75.4 2003 74.9 2004 80.2

 a. no relationship b. curvilinear relationship c. negative relationship d. positive relationship

#### Solution:

Plot the scatter diagram.

From the scatter diagram, we can say that the newspaper readers increased yearly.

So, the relationship is a positive relationship.

6.
Determine the relationship between the variables X and Y.
 X Y 0 0 1 0.5 2 0.7 3 0.9 4 1

 a. negative relationship b. no relationship c. curvilinear relationship d. positive relationship

#### Solution:

Plot the scatter diagram for X and Y.

From the scatter diagram, we can say that y increased as x increased.

So, the relationship is a positive relationship.

7.
Which of the following statement(s) is/are true?
I. Correlation is used to determine the existence of a relationship between variables.
II. Correlation is used to describe the type of relationship between variables.
III. Regression is used to determine the existence of a relationship between variables.
IV. Regression is used to describe the type of relationship between variables.
 a. III only b. IV only c. I and IV only d. II and III only

#### Solution:

Correlation is used to determine the existence of a relationship between variables.

Regression is used to describe the type of relationship between variables.

Therefore, I and IV are correct.

8.
Which of the following statement(s) is/are true?
I. A relationship between two variables is called simple relationship.
II. When both variables increase or decrease at the same time then that relationship is called negative relationship.
III. Multiple relationship exists between two variables.
IV. When one variable increases the other decreases, then the relationship is called negative relationship.
 a. II and III only b. IV only c. III only d. I and IV only

#### Solution:

A relationship between two variables is called simple relationship.

When one variable increases the other decreases, this relationship is called negative relationship.

Therefore, I and IV are correct.

9.
Which of the following statement(s) is/are false?
I. A relationship between many variables is called multiple relationship.
II. A relationship between three variables only is called multiple relationship.
III. When both variables increase or decrease at the same time, then the relationship is called positive relationship.
IV. A relationship between two variables is called simple relationship.
 a. I only b. II only c. III and IV only d. III only

#### Solution:

A relationship between many variables is called multiple relationship.

When both variables increase or decrease at the same time then that relationship is called positive relationship.

A relationship between two variables is called simple relationship.

So, I, III and IV are correct.

Therefore II is wrong.

10.
Which of the following statement(s) is/are true?
I. The variable that cannot be controlled or manipulated is dependent variable.
II. Independent variable is plotted on the y-axis.
III. A relationship between four variables only is called multiple relationship.
IV. The relationship between the independent and the dependent variables is shown through a scatter plot.
 a. II and III only b. I and IV only c. III only d. I only

#### Solution:

The variable that cannot be controlled or manipulated is dependent variable.

The relationship between the independent and the dependent variables is shown through a scatter plot.

Therefore, I and IV are correct.