Scatterplots

Scatterplots

Types of Data

• Categorical (Qualitative) Data: eye color, favorite subject, zip code, favorite animal

• Numerical (Quantitative) Data: Height, weight, number of students in a class

• To determine if data is categorical or numerical, ask if a meaningful average exists.

Scatterplots

• Only for numerical/quantitative data

Independent variable (x) vs. Dependent variable (y)

• Think of it in terms of cause and effect: the independent variable (x) causes the dependent variable (y)

• y "depends" on x

• The dependent variable is always graphed on the vertical y-axis and the independent variable is always graphed on the horizontal x-axis

Multiple Choice

Carey and Justin are raising money to purchase books for the library. The more money they raise, the more books they will be able to purchase for the library.

Which of the variables is dependent?

• amount of money raised

• number of books

Multiple Choice

The higher the temperature of water, the faster the egg will cook. Select the independent variable.

• Faster Egg Cooks

• Higher Temperature

Multiple Choice

Molly investigated if the age of students caused them to be better drivers. What is the independent variable?

• Type of car

• Skill of driving

• Age of student

Multiple Choice

What type of association does this graph have?

• positive 
• negative
• none
• all of the above

Multiple Choice

Which best describes the form of this scatterplot?

• linear
• nonlinear
• scattered

Multiple Choice

What type of association does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

What type of association does this scatter plot represent?

• positive linear association
• negative linear association
• no association
• nonlinear association

Outliers

• Extreme values that are either very large or very small with respect to the rest of the data points

Correlation coefficient

• measures the strength of the relationship between the two variables (how closely they are spread around regression line

•  $-1\le r\le1$  

• 1 is a perfect positive linear correlation

• -1 is a perfect negative linear correlation

• No linear correlation is close to zero

• The closer to 1/-1, the stronger the relationship

• A strong correlation does not necessarily mean there is causation

Multiple Choice

Estimate the correlation coefficient

• r = 1

• r = -1

• r ≈ -0.8

• r ≈ 0.8

• r ≈ -0.5

Multiple Choice

Estimate the correlation coefficient.

• r is close to 1

• r is close to -1

• r is close to 0

• r is close to -0.5

• r is close to 0.5

Multiple Choice

Estimate the correlation coefficient.

• r is close to zero

• r is close to -1

• r is close to 1

• r is close to -1.5

• r is close to 1.5