Understanding Relationships in Scatter Plots, Lecture notes of Advanced Data Analysis

An introduction to analyzing scatter plots to determine the relationship between two variables. Students will learn about positive and negative relationships, slope, and how to make predictions based on strong and weak relationships. The document also covers deciding cause and effect and includes exercises for practice.

Typology: Lecture notes

2021/2022

Uploaded on 08/05/2022

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Name ___________________________ Date __________________ Period_________
Relationships on a Scatter Plot
Goals:
Students will analyze scatter plots to determine:
-Are variables X and Y related?
-Are variables X and Y linearly related? If so How?
-Does the variation in Y change depending on X?
A scatter plot reveals relationships between two variables. Such relationships manifest themselves by
any non-random structure in the plot. Various common types of relationships are demonstrated in the
examples.
Part I – Positive and Negative
Positive relationship
a clear line that goes up.
Inverse or Negative relationship
a line that goes down.
No relationship
no clear pattern, or line is perfectly
horizontal or vertical
The following are descriptions of slope of a line or pattern on a scatter plot. Identify the relationship
that best fits each description.
1) Positive slope ____________________
2) Negative slope ____________________
3) -36.5 ____________________
4) 0.0036 _____________________
5) 23.6 _____________________
6) _____________________
7) In a positive relationship, if the X variable increases what happens to the Y variable?
8) In a negative relationship, if the X variable increases what happens to the Y variable?
9) State a general rule for using slope to determine the relationship on a scatter plot.
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Name ___________________________ Date __________________ Period_________

Relationships on a Scatter Plot

Goals: Students will analyze scatter plots to determine: -Are variables X and Y related? -Are variables X and Y linearly related? If so How? -Does the variation in Y change depending on X?

A scatter plot reveals relationships between two variables. Such relationships manifest themselves by any non-random structure in the plot. Various common types of relationships are demonstrated in the examples.

Part I – Positive and Negative

Positive relationship a clear line that goes up.

Inverse or Negative relationship a line that goes down.

No relationship no clear pattern, or line is perfectly horizontal or vertical

The following are descriptions of slope of a line or pattern on a scatter plot. Identify the relationship that best fits each description.

  1. Positive slope ____________________

  2. Negative slope ____________________

3) -36.5 ____________________

4) 0.0036 _____________________

5) 23.6 _____________________

6) _____________________

  1. In a positive relationship, if the X variable increases what happens to the Y variable?

  2. In a negative relationship, if the X variable increases what happens to the Y variable?

  3. State a general rule for using slope to determine the relationship on a scatter plot.

Part II A scatter plot is a plot of the values of Y versus the corresponding values of X:

  • Vertical axis: variable Y--usually the dependent variable
  • Horizontal axis: variable X--usually the independent variable

Strong relationship a clear line or predictable pattern.

Weak relationship the line is there but it is “fuzzy”

No relationship no clear pattern, or line is perfectly horizontal or vertical

  1. Since graphs are scientific models and we use models to make predictions, then explain how strong and weak relationships affect the ability to make predictions.

  2. If there is a strong positive relationship explain how the dependent variable changes with a change in the independent variable?

  3. If there is no relationship explain how the dependent variable changes with a change in the independent variable?

  4. In terms of the dependent and independent variable what does a shallow slope mean?

  5. In terms of the dependent and independent variable what does a steep slope mean?

Exercises

  1. Classify the relationship of the dependent and independent variable in the following graphs by circling the correct terms:

Positive or Negative

Strong or Weak

No Relationship

Positive or Negative

Strong or Weak

No Relationship

Positive or Negative

Strong or Weak

No Relationship

Positive or Negative

Strong or Weak

No Relationship

  1. Draw sample graphs that could be described as the following: a) Strongly Related b) Strong Negatively Related c) Weak Positively Related