Scatter Plot Worksheet For questions 1-3 a. Identify the ... - Free Printable

Let's go through each part of the Scatter Plot Worksheet step by step and solve it with explanations.

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Questions 1–3: Identify correlation and describe a real-life situation

#### 1.
Graph: Points form a downward diagonal line from top-left to bottom-right.

- a. Correlation: Negative correlation
As $ x $ increases, $ y $ decreases.

- b. Real-life example:
*The number of hours spent watching TV vs. grades in school.*
As time spent watching TV increases, grades tend to decrease.

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#### 2.
Graph: Points are scattered randomly with no clear pattern.

- a. Correlation: No correlation (or weak/no correlation)
There is no apparent relationship between $ x $ and $ y $.

- b. Real-life example:
*A person’s shoe size vs. their IQ.*
These two variables are unrelated—no meaningful connection.

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#### 3.
Graph: Points form an upward diagonal line from bottom-left to top-right.

- a. Correlation: Positive correlation
As $ x $ increases, $ y $ increases.

- b. Real-life example:
*Number of hours studied vs. test scores.*
More study time tends to lead to higher test scores.

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Question 4: Make a scatter plot

We are given data on homeowners and vacation homeowners in Maintown over several years.

| Year | Homeowners | Vacation Homeowners |
|------------|------------|---------------------|
| 1997–98 | 2,080 | 973 |
| 1996–97 | 1,987 | 967 |
| 1995–96 | 1,948 | 1,041 |
| 1994–95 | 1,897 | 1,043 |
| 1993–94 | 1,862 | 1,125 |
| 1992–95 | 1,832 | 1,126 |

> Note: The last row says "1992–95", which seems like a typo. Probably meant 1992–93? But we’ll use as-is for plotting.

We'll plot:
- X-axis: Number of Homeowners
- Y-axis: Number of Vacation Homeowners

But since both values are large, we can scale or just plot directly.

Let’s analyze the trend:

| Homeowners | Vacation Homeowners |
|------------|---------------------|
| 2080 | 973 |
| 1987 | 967 |
| 1948 | 1041 |
| 1897 | 1043 |
| 1862 | 1125 |
| 1832 | 1126 |

Observation:
- As homeownership decreases, vacation homeownership increases.
- So there's a negative correlation.

Now, let’s sketch this on a grid (you'd draw it on paper).

Steps to create the scatter plot:
1. Label axes:
- X-axis: Homeowners (range ~1800 to 2100)
- Y-axis: Vacation Homeowners (range ~960 to 1130)
2. Plot each point:
- (2080, 973)
- (1987, 967)
- (1948, 1041)
- (1897, 1043)
- (1862, 1125)
- (1832, 1126)
3. Draw a trend line: It should slope downward from left to right.

✔ Trend line: Negative slope — as more people own homes, fewer own vacation homes? Wait — actually, here, as regular homeownership decreases, vacation ownership increases.

So, possibly:
- People who don’t own homes may be investing in vacation homes?
- Or maybe the town is becoming more tourist-oriented.

But note: This could also reflect economic shifts — perhaps as home prices rise, some people buy second homes instead of primary ones.

Real-life interpretation:
*As the number of primary homeowners declines, more people invest in vacation homes — possibly due to rising housing costs or tourism development.*

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Questions 5–7: Decide if linear; find equation of trend line

We need to determine if the data follows a linear pattern and, if so, find the equation of the trend line ($ y = mx + b $).

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#### 5.
Graph: Points cluster around a straight line from bottom-left to top-right.

- Yes, linear pattern.
- Let’s estimate two points:
- Point A: (0, 1) → when $ x = 0 $, $ y \approx 1 $
- Point B: (2, 14) → when $ x = 2 $, $ y \approx 14 $

Wait — check actual points:
- At $ x = 0 $, $ y \approx 1 $
- At $ x = 1 $, $ y \approx 6 $
- At $ x = 2 $, $ y \approx 11 $
- At $ x = 3 $, $ y \approx 14 $

So roughly:
- From (0,1) to (3,14): change in $ y = 13 $, change in $ x = 3 $
- Slope $ m = \frac{13}{3} \approx 4.33 $

But better to pick two clear points:
- (0, 1) and (3, 14)

$ m = \frac{14 - 1}{3 - 0} = \frac{13}{3} \approx 4.33 $

Using point-slope: $ y - 1 = \frac{13}{3}(x - 0) $

So:
$$
y = \frac{13}{3}x + 1
$$

Or approximately:
$$
y = 4.33x + 1
$$

✔ Answer: Yes, linear. Equation: $ y = \frac{13}{3}x + 1 $

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#### 6.
Graph: Points are scattered, no clear pattern.

- Some points at top, some at bottom, no consistent direction.
- No trend line possible.

✔ Answer: No, not linear.

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#### 7.
Graph: Points form a clear upward trend.

Plotting:
- Points seem to go from (−5, 0) to (5, 10) roughly.
- Let’s pick two points:
- (−4, 1)
- (4, 9)

Change in $ y = 9 - 1 = 8 $, change in $ x = 4 - (-4) = 8 $

Slope $ m = \frac{8}{8} = 1 $

Now use point (−4, 1):

$ y - 1 = 1(x + 4) $
$ y = x + 4 + 1 $
$ y = x + 5 $

Check with another point: (0, 5)? Is (0,5) on graph? Yes, looks like it.

And (4,9): $ 4 + 5 = 9 $ ✔

So equation: $ y = x + 5 $

✔ Answer: Yes, linear. Equation: $ y = x + 5 $

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✔ Final Answers Summary

#### 1.
a. Negative correlation
b. Hours studying vs. test score (inverse: less study → lower score)

#### 2.
a. No correlation
b. Shoe size vs. IQ

#### 3.
a. Positive correlation
b. Study time vs. test scores

#### 4.
- Scatter plot: Plot (Homeowners, Vacation Owners)
- Trend line: Downward slope → negative correlation
- Interpretation: As regular homeownership decreases, vacation homeownership increases (possibly due to tourism or investment shift)

#### 5.
- Yes, linear
- Equation: $ y = \frac{13}{3}x + 1 $ or $ y \approx 4.33x + 1 $

#### 6.
- No, not linear

#### 7.
- Yes, linear
- Equation: $ y = x + 5 $

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Let me know if you’d like a visual sketch or help drawing these plots!