b Do you think everybody has the same kind of pencil?
C
c The slope describes rise over run. What does the rise represent? How about the run?
D
d Substitute 11.5 instead of ℓ.
E
e What does a pencil usually have at the end of it?
A
aAssociation: Linear
Correlation: Strong and positive Outlier: At x=2.3
B
b See solution.
C
c See solution.
D
d4.3 grams
E
e See solution.
Practice makes perfect
a Examining the diagram, we see that there is a positive association between the length of the paint and the pencil's weight — as the length of the paints increases, so does the weight of the pencil increase. Also, it appears that this association is linear with an outlier at x≈2.3.
b There could be many reasons why the data has an outlier. Perhaps this particular pencil was of a different and heavier sort than the others?
c In Sam's line of best fit we can identify the slope as 0.25. If we rewrite this as a fraction it is easier to talk about what the slope represents.
m=0.25⇔m=41
The numerator shows the number of steps you take in the vertical direction when you take the number of steps given by the denominator in the horizontal direction.
m=41⇔m=runrise
Therefore, the slope tells us that the pencil's weight is expected to increase by 1 gram for every four centimeters of paint.
d By substituting 11.5 instead of ℓ in the equation from Part C, we can predict the weight of the teacher's pencil.
The weight of the pencil should be about 4.3 grams.
e The y-intercept shows the weight of the pencil when the length of the paint is 0 cm. This must mean that the pencil without any paint left still weighs 1.4 grams. Obviously, the wood underneath the paint has weight.
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