Data Relationships Insight

Name:

Date:

Scatterplot and line of best fit illustration

📊 Part 1: Understanding Linear Models

1. A linear model shows the relationship between hours of exercise per week (x) and resting heart rate (y): y = -2x + 75

a) What does the slope (-2) tell us in this context?

b) What does the y-intercept (75) represent?

2. Look at the scatterplot descriptions below. Which would be MOST appropriate for linear modelling?

Points form a curved U-shape pattern

Points are scattered randomly with no pattern

Points form a straight diagonal line from bottom-left to top-right

Points form distinct clusters in different areas

3. For the research question "Does daily screen time affect sleep quality scores?", identify:

Independent variable: _________________

Dependent variable: _________________

Expected direction of association: _________________ (positive/negative/none)

🔍 Part 2: Data Collection and Ethics

4. You want to collect data on students' study hours and test scores. List TWO ethical considerations you must address:

1. ________________________________________________

2. ________________________________________________

5. Why is data cleaning important before creating scatterplots? Give TWO specific examples of data cleaning actions:

6. When describing the association between two variables, we consider three characteristics. Complete the sentence:

The three characteristics are: __________, __________, and __________.

🎯 Part 3: Application and Extension

7. For diverse learners: Match each slope value to its meaning (draw lines to connect):

Slope = 0

Slope = 3

Slope = -0.5

Gentle negative relationship

No relationship

Strong positive relationship

8. Extension Challenge: A line of best fit has the equation y = 1.5x + 10. If one data point is at (4, 20), calculate the residual (difference between actual and predicted values).

9. Advanced Extension: Describe a real-world scenario where a linear model would NOT be appropriate and suggest what type of relationship might exist instead: