Scatter Plots and Correlations

Analyzing scatter plots and identifying correlations

What is a Scatter Plot?

A scatter plot displays the relationship between two quantitative variables.

Positive Correlation:

Negative Correlation:

No Correlation:

Strong: Points are tightly clustered around a line Weak: Points are loosely scattered Moderate: Between strong and weak

A trend line that best represents the data pattern.

The line minimizes the distance from all points.

Equation form: $y = mx + b$

A scatter plot shows hours studied vs. test scores. As hours increase, scores increase. What type of correlation is this?

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When one variable increases and the other also increases, we have a positive correlation.

The points would slope upward from left to right.

Answer: Positive correlation

A trend line for temperature (°F) vs. ice cream sales has the equation $y = 50x - 1000$ . Predict sales when temperature is 80°F.

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Substitute $x = 80$ into the equation:

$y = 50(80) - 1000$ $y = 4000 - 1000$ $y = 3000$

Answer: Predicted sales: $3,000

Describe the correlation: As outdoor temperature increases, heating bills decrease.

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One variable (temperature) increases while the other (heating bills) decreases.

This is a negative correlation.

The relationship makes sense: warmer weather means less heating needed!

Answer: Negative correlation

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