Scatter Plots Notes and Worksheets - Lindsay Bowden - Free Printable

Let's go through each question on the Linear Scatter Plots Practice worksheet and solve them step by step with explanations.

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Question 1: Use the scatter plot to answer the questions below.

#### a. What type of correlation is shown?
Looking at the scatter plot:
- The points are somewhat scattered but show a general upward trend from left to right.
- As the $x$ values increase, the $y$ values tend to increase as well.

✔ Answer: Positive correlation

> *Explanation:* A positive correlation means that as one variable increases, the other tends to increase too.

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#### b. Estimate the correlation coefficient.
The correlation coefficient ($r$) measures the strength and direction of a linear relationship. It ranges from -1 to 1.

- Since the points are not perfectly linear, but there’s a clear upward trend, the correlation is moderate to strong.
- The data isn’t tightly clustered around a line, so it’s not close to 1.

✔ Estimated correlation coefficient: About 0.6 to 0.7

> *Explanation:* A value like 0.6–0.7 indicates a moderate positive correlation — not perfect, but clearly trending upward.

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Question 2: Soccer Team Practice Data

Given data:

| Hours Practiced (x) | 0 | 1 | 2 | 3 | 4 | 5 |
|---------------------|---|---|---|---|---|---|
| Average Goals per Game (y) | 0 | 0.4 | 1 | 1.5 | 2 | 2.5 |

We need to:
- Plot the data
- Answer the questions

#### a. What type of correlation is shown?

Plotting the points:
- (0, 0), (1, 0.4), (2, 1), (3, 1.5), (4, 2), (5, 2.5)

These form a perfect straight line increasing from left to right.

✔ Answer: Perfect positive correlation

> *Explanation:* As practice hours increase, goals scored increase consistently in a linear fashion.

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#### b. Estimate the correlation coefficient.

Since all points lie exactly on a straight line with a positive slope, the correlation is perfect.

✔ Answer: r = 1

> *Explanation:* When all data points fall exactly on a straight line with a positive slope, the correlation coefficient is +1.

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Question 3: Surveyor Interviewing People at Grocery Store

A surveyor found that people who spent more money had more pets and concluded that spending causes more pet ownership.

#### a. What type of correlation did the surveyor find?

She observed that higher spending was associated with more pets.

✔ Answer: Positive correlation

> *Explanation:* As one variable (spending) increases, the other (number of pets) also increases.

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#### b. Was the surveyor’s conclusion correct? Why or why not?

No, the conclusion is not necessarily correct.

✔ Answer: No, because correlation does not imply causation.

> *Explanation:* Just because two variables are correlated doesn't mean one causes the other. There could be a third factor (like income level) causing both higher spending and more pets. For example, wealthier people might spend more at the store and also afford more pets.

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Question 4: Parents' Children and Sleep Data

Scatter plot shows:
- x-axis: Number of children (0 to 5)
- y-axis: Hours of sleep per night (2 to 10)

#### a. Is there a correlation between number of children and hours of sleep?

Looking at the scatter plot:
- As the number of children increases, hours of sleep tend to decrease.
- The points show a downward trend, though not perfectly linear.

✔ Answer: Yes, there is a negative correlation.

> *Explanation:* More children are associated with fewer hours of sleep, suggesting a negative relationship.

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#### b. Name one thing that could have affected this data.

There are many possible confounding factors.

✔ Answer: Age of the parents (e.g., younger parents may sleep less due to stress or lack of experience), or infant care responsibilities, or job demands, etc.

> *Example:* Parents with infants may sleep less regardless of how many children they have, or older children may require less attention, allowing for more sleep.

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✔ Final Answers Summary:

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#### Question 1:
a. Positive correlation
b. Approximately 0.6–0.7

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#### Question 2:
a. Perfect positive correlation
b. r = 1

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#### Question 3:
a. Positive correlation
b. No, because correlation does not imply causation. Other factors like income could influence both spending and pet ownership.

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#### Question 4:
a. Yes, there is a negative correlation.
b. One possible factor: Age of the children (infants require more attention and disrupt sleep).

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Let me know if you'd like help plotting the graph for Question 2!