Line of Best Fit Worksheet PDF | Download Free PDF | Scatter Plot ... - Free Printable

Let’s solve each problem step by step.

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Problem 1: Study Hours vs. Exam Score

We’re given this table:

| Hours (x) | 0 | 1 | 2 | 3 |
|-----------|---|---|---|---|
| Score (y) | 60| 70| 80| 90|

a) Draw a scatterplot — You’d plot points: (0,60), (1,70), (2,80), (3,90). They form a straight line going up.

b) Equation for the line of best fit

Look at how y changes as x increases:
- When x goes from 0 to 1 → y goes from 60 to 70 → +10
- From 1 to 2 → 70 to 80 → +10
- From 2 to 3 → 80 to 90 → +10

So slope = 10.

When x=0, y=60 → that’s the y-intercept.

→ Equation: y = 10x + 60

c) Predict score if studied 4 hours

Plug x=4 into equation:

y = 10(4) + 60 = 40 + 60 = 100

d) Is this prediction reasonable?

Yes — because the pattern is perfectly linear so far, and 100 is a possible test score (assuming max is 100 or more). Also, it follows the same increase of 10 points per hour.

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Problem 2: Height vs. Shoe Size

Table:

| Height (in) | 58 | 62 | 65 | 68 | 70 | 72 |
|-------------|----|----|----|----|----|----|
| Shoe size | 6 | 7 | 8 | 9 | 10 | 11 |

a) Scatterplot — Plot points: (58,6), (62,7), (65,8), (68,9), (70,10), (72,11). Looks like a straight line going up.

b) Equation for line of best fit

Check the change:

From 58 to 62 → height +4, shoe size +1 → slope = 1/4 = 0.25

Check another pair: 62 to 65 → +3 height, +1 shoe → slope = 1/3 ≈ 0.33? Wait — not consistent?

Wait — let’s check all steps:

Actually, look again:

Height: 58 → 62 → 65 → 68 → 70 → 72
Shoe: 6 → 7 → 8 → 9 → 10 → 11

Differences in height:
62-58=4 → shoe +1
65-62=3 → shoe +1
68-65=3 → shoe +1
70-68=2 → shoe +1
72-70=2 → shoe +1

Not constant slope? But maybe we can still find a good line.

Alternatively, notice: every time shoe size increases by 1, height increases roughly 2–4 inches. Let’s try to find average rate.

Total change: from first to last point:

Δheight = 72 - 58 = 14
Δshoe = 11 - 6 = 5
Slope = Δshoe / Δheight = 5/14 ≈ 0.357

But maybe better to use two middle points or do linear regression? Since this is likely meant to be simple, perhaps they expect us to see it's almost linear.

Wait — actually, looking closely:

If you assume shoe size = m * height + b

Try using first and last point:

Point A: (58,6)
Point B: (72,11)

Slope m = (11 - 6)/(72 - 58) = 5/14 ≈ 0.357

Now plug into point-slope:

y - 6 = (5/14)(x - 58)

Multiply out:

y = (5/14)x - (5/14)*58 + 6

Calculate (5/14)*58 = (290)/14 ≈ 20.714

Then y = (5/14)x - 20.714 + 6 = (5/14)x - 14.714

That’s messy. Maybe there’s a simpler pattern.

Wait — what if we reverse? Think of height as function of shoe size?

Shoe size s, height h.

s: 6→h:58
s:7→62
s:8→65
s:9→68
s:10→70
s:11→72

Now differences:

s+1 → h increases:
6→7: +4
7→8: +3
8→9: +3
9→10: +2
10→11: +2

Average increase per shoe size: total h increase = 72-58=14 over 5 steps → 14/5 = 2.8

So slope ≈ 2.8 when predicting height from shoe size.

But question says “equation for line of best fit” — probably expects us to use calculator or approximate.

Since this is likely for middle/high school, and data looks very close to linear, let’s pick two points that are easy.

Use (6,58) and (11,72):

Slope m = (72 - 58)/(11 - 6) = 14/5 = 2.8

Equation: h - 58 = 2.8(s - 6)

h = 2.8s - 16.8 + 58 = 2.8s + 41.2

Check with s=7: 2.8*7=19.6 +41.2=60.8 → actual is 62 → close

s=8: 2.8*8=22.4+41.2=63.6 → actual 65 → off by 1.4

Hmm.

Alternative: Use (8,65) and (10,70)

m=(70-65)/(10-8)=5/2=2.5

h - 65 = 2.5(s - 8)

h = 2.5s - 20 + 65 = 2.5s + 45

Check s=6: 2.5*6=15+45=60 → actual 58 → off by 2

s=11: 2.5*11=27.5+45=72.5 → actual 72 → very close

Maybe best to go with overall trend.

Actually, let’s calculate properly using least squares? Too advanced.

Perhaps the problem expects us to notice that for every 1 increase in shoe size, height increases about 2.8 inches on average.

But let’s look back — maybe I misread the table.

Original table:

Height (in): 58, 62, 65, 68, 70, 72
Shoe size: 6, 7, 8, 9, 10, 11

Let me list pairs:

(58,6), (62,7), (65,8), (68,9), (70,10), (72,11)

Notice: shoe size = (height - 52)/2 ? Let's test:

For height 58: (58-52)/2 = 6/2=3 → no, should be 6.

Wait: 58 - 52 = 6 → matches shoe size 6
62 - 55 = 7? No.

Another idea: shoe size = (height - 46)/2 ?

58-46=12/2=6 ✔️
62-46=16/2=8 ✘ should be 7