Scatter Plots and Trend Lines

Construct and interpret scatter plots and use trend lines to make predictions.

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Scatter Plots and Trend Lines

What Is a Scatter Plot?

A scatter plot shows the relationship between two sets of numerical data. Each point represents one data pair.

Correlation

| Pattern | Type | Example | |---------|------|---------| | Points go up | Positive correlation | Height and weight | | Points go down | Negative correlation | TV time and grades | | No pattern | No correlation | Shoe size and IQ |

Strength of Correlation

  • Strong: Points are close together, nearly forming a line
  • Weak: Points are spread out
  • None: No pattern at all

Trend Lines (Lines of Best Fit)

A trend line is a straight line that best represents the data in a scatter plot.

Properties:

  • Passes through or near most points
  • Has roughly equal numbers of points above and below
  • Follows the general direction of the data

Making Predictions

Use the trend line equation to predict values:

If the trend line is y=2x+10y = 2x + 10 and x=15x = 15: y=2(15)+10=40y = 2(15) + 10 = 40

Interpolation vs. Extrapolation

  • Interpolation: Predicting within the data range (reliable)
  • Extrapolation: Predicting outside the data range (less reliable)

Clusters, Gaps, and Outliers

  • Cluster: A group of points close together
  • Gap: A space with no data points
  • Outlier: A point far from the general pattern

Two-Way Tables

For categorical data, use two-way tables to find relationships:

| | Likes Math | Doesn't Like Math | Total | |---|---|---|---| | Grade 7 | 30 | 20 | 50 | | Grade 8 | 35 | 15 | 50 | | Total | 65 | 35 | 100 |

Caution: Correlation does NOT mean causation! Just because two variables are related doesn't mean one causes the other.

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