math
Chapter 3
Relationships
Between
Quantitative
Variables
Copyright ©2011 Brooks/Cole, Cengage Learning
1
Principle Idea:
The description and confirmation of relationships between variables are very important in research.
Copyright ©2011 Brooks/Cole, Cengage Learning
2
Three Tools we will use …
• Scatterplot, a two-dimensional graph of data values
• Correlation, a statistic that measures the strength and direction of a linear relationship between two quantitative variables.
• Regression equation, an equation that describes the average relationship between a quantitative response and explanatory variable.
Copyright ©2011 Brooks/Cole, Cengage Learning
3
3.1 Looking for Patterns with Scatterplots
Questions to Ask about a Scatterplot
• What is the average pattern? Does its form look like a straight line or curved?
• What is the direction of the pattern?
• How much do individual points vary from the average pattern? (How strong is the relationship?) • Are there any unusual data points?
Copyright ©2011 Brooks/Cole, Cengage Learning
4
Direction/Form
• Direction:
– Two variables have a positive association when the
– Two variables have a negative association when the
– Two variables have a linear relationship when the
Copyright ©2011 Brooks/Cole, Cengage Learning
5
Example 3.1 Height and Handspan
Data shown are the first 12 observations of a data set that includes the heights
(in inches) and fully stretched handspans
(in centimeters) of
167 college students.
Copyright ©2011 Brooks/Cole, Cengage Learning
6
Example 3.1 Height and Handspan
The handspan and height measurements have a
Copyright ©2011 Brooks/Cole, Cengage Learning
7
Example 3.2 Driver Age and Maximum
Legibility Distance of Highway Signs
• A research firm determined the maximum distance at which each of 30 drivers could read a newly designed sign.
– Age range of 30 participants: 18 to 82 yrs. old
• We
Relationships
Between
Quantitative
Variables
Copyright ©2011 Brooks/Cole, Cengage Learning
1
Principle Idea:
The description and confirmation of relationships between variables are very important in research.
Copyright ©2011 Brooks/Cole, Cengage Learning
2
Three Tools we will use …
• Scatterplot, a two-dimensional graph of data values
• Correlation, a statistic that measures the strength and direction of a linear relationship between two quantitative variables.
• Regression equation, an equation that describes the average relationship between a quantitative response and explanatory variable.
Copyright ©2011 Brooks/Cole, Cengage Learning
3
3.1 Looking for Patterns with Scatterplots
Questions to Ask about a Scatterplot
• What is the average pattern? Does its form look like a straight line or curved?
• What is the direction of the pattern?
• How much do individual points vary from the average pattern? (How strong is the relationship?) • Are there any unusual data points?
Copyright ©2011 Brooks/Cole, Cengage Learning
4
Direction/Form
• Direction:
– Two variables have a positive association when the
– Two variables have a negative association when the
– Two variables have a linear relationship when the
Copyright ©2011 Brooks/Cole, Cengage Learning
5
Example 3.1 Height and Handspan
Data shown are the first 12 observations of a data set that includes the heights
(in inches) and fully stretched handspans
(in centimeters) of
167 college students.
Copyright ©2011 Brooks/Cole, Cengage Learning
6
Example 3.1 Height and Handspan
The handspan and height measurements have a
Copyright ©2011 Brooks/Cole, Cengage Learning
7
Example 3.2 Driver Age and Maximum
Legibility Distance of Highway Signs
• A research firm determined the maximum distance at which each of 30 drivers could read a newly designed sign.
– Age range of 30 participants: 18 to 82 yrs. old
• We