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Wednesday

Wednesday - Linear Relationships in Data

I can analyze scatter plots, lines of best fit, and association.

Why It Matters

Data Often Contains Variation

Instead of focusing on one point, we look for the overall pattern to understand what the data suggests.

Association

Positive, negative, or little/no association describes the overall direction.

Regression

A regression line models the overall trend and can help us make predictions.

Residual

Residual=Actual-Predicted

Guided Examples

Read the Trend, Then Interpret Carefully

Example 1

Imagine a scatter plot comparing hours studied with test scores.

The points generally move upward from left to right and stay close to a line.

Strong positive scatter plot Points rise from left to right and stay close to a trend line.

Step-by-step interpretation:

  1. Positive association The graph moves upward from left to right.
Example 2

A regression model is y=5x+60. For x=4, suppose the actual observed value is 83.

Find and interpret the residual.

Step-by-step solution:

  1. y=5(4)+60=80 Find the predicted value.

Wednesday Practice

Use the Overall Pattern

Choose carefully, then use feedback to decide what to try next.

Problem 1

A scatter plot has points tightly grouped around an upward-sloping line. Describe the association.

Choose one

Problem 2

A residual is positive. Is the actual value above or below the predicted value?

Choose one

Problem 3

Ice cream sales and swimming pool attendance both increase during hot weather. Does eating ice cream cause people to swim?

Choose one

Problem 4

A model y=2x+5 predicts y=25 when x=10. The actual value is 27. Find the residual.

Problem 5

What does a regression line help us do?

Choose one

Wednesday Reflection

Which strategy helps you interpret data?

End of Wednesday

Choose Where to Go Next