Statistical Sciences 2244A/B Chapter Notes - Chapter 3: Lean Body Mass, Dependent And Independent Variables, Scatter Plot
22 May 2018
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Stats 2244
Chapter 3
VIDEO
- Ex: we are interested in the relationship bw height and weight in children
- Displayed in a table, the data doesn’t reveal much about the relationship bw the variables
- A scatterplot must be created
o A scatter plot is a visual display of the relationship bw 2 quantitative variables
o on the y axis you put the response variable
o on the x axis you put the explanatory variable – influences or explains changes in the
response variable
- association is the term used to refer to a relationship bw variables
- that a strong associations bw variables does not necessarily mean that changes in one variable
cause changes in the other
- ASSOCIATION DOES NOT IMPLY CAUSATION
- Correlation is a numerical measure of the strength and direction of the linear relationship bw
two quantitative variables
o Correlation is denoted by the letter r and it’s a value bw -1 and 1
o The sign indicates the direction of the relationship
o The closer the correlation is to +1 or -1, the stronger the linear relationship is
o Note: -ive linear relationships can be equally strong
- The strength of the linear relationship bw 2 variables is important bc it helps determine
whether the explanatory variable can be used to accurately depict values of the response
variable
CHAPTER 3.1
Explanatory and response variables
- Response variable, explanatory variable
o A response variable measure an outcome of a study
o An explanatory variable may explain or influence changes in a response variable
- You will often find explanatory variables called independent variables and response variables
called dependent variables
CHAPTER 3.3
Interpreting scatterplots
- Examining a scatterplot
o In any graph of data, look for the overall pattern and for striking deviations from that
pattern
o You can describe the overall pattern of a scatterplot by the direction, form and strength
of the relationship
o An important kind of deviation is an outlier, an individual value that falls outside the
overall pattern of the relationship
- Positive association, negative association
o Two variables are positively associated when above-average values of one tend to
accompany above average values of the other and below average values also tend to
occur together
o Two variables are negatively associated when above average values of one tend to
accompany below average values of the other and vice versa
CHAPTER 3.4
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Adding categorical variables to scatterplots
- Categorical variables in scatterplots
o To add a categorical variable to a scatterplot, use a different plot color or symbol for
each category
VIDEO: interpreting scatterplots
- Example scatterplot for relationship
- If relationship exists, describe its…
o Direction
▪ Positively sloped: as X increases, Y increases
▪ Negatively sloped: as X increases, Y decreases
o Form
▪ Linear: shape suggests a straight line
▪ Nonlinear: shape suggests curvature (quadratic, cubic, exponential etc)
o Strength
▪ Strong: points concentrate about the form
▪ Weak: points very loosely scattered about the form
- Examples: examine scatterplot for pattern
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find more resources at oneclass.com
- Example:
o Can we apply this relationship bw lean body mass and resting metabolic rate to other
subjects?
▪ First ask if the subjects in this study are a representative sample from a larger
group of subject
▪ Look for confounding factors
- Examples:
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find more resources at oneclass.com
Document Summary
Ex: we are interested in the relationship bw height and weight in children. The strength of the linear relationship bw 2 variables is important bc it helps determine whether the explanatory variable can be used to accurately depict values of the response variable. Response variable, explanatory variable: a response variable measure an outcome of a study, an explanatory variable may explain or influence changes in a response variable. You will often find explanatory variables called independent variables and response variables called dependent variables. Categorical variables in scatterplots: to add a categorical variable to a scatterplot, use a different plot color or symbol for each category. A scatterplot displays the direction, form, and strength of the relationship between two quantitative variables. The formula for r begins by standardizing the observations. Suppose, for example, that x is height in centimeters and yis weight in kilograms and that we have height and weight measurements for n people.
