Question

cca lesson 4.1.1 homework
name

4-4.
sam collected data by measuring the pencils of her classmates. she recorded the length of the painted part of each pencil and its weight. her data is shown on the graph at right. homework help

a. describe the association between weight and length of the painted part of the pencil. remember to describe the form, direction, strength, and outliers.

b. make a conjecture (a guess) about why sam’s data had an outlier.

c. sam created a line of best fit: ( w = 1.4 + 0.25l ) where ( w ) is the weight of the pencil in grams and ( l ) is the length of the painted part on the pencil in centimeters. what does the slope represent in this context?

d. sam’s teacher has a pencil where the painted part is 11.5 long. predict the weight of the teacher’s pencil.

e. interpret the meaning of the ( y )-intercept in context.

graph: a scatter plot with length (cm) on the x - axis (ranging from 0 to 14) and weight (g) on the y - axis (ranging from 0 to 6). the points show a general positive trend with one outlier.

Explanation:

Step1: Analyze scatter plot form/direction

The points (excluding outlier) follow a straight trend, and as length ($l$) increases, weight ($w$) increases.

Step2: Analyze strength and outliers

Points cluster tightly around a line; one point (low length, high weight) is far from the cluster.

Step3: Conjecture outlier cause

The outlier has high weight but short painted length, so it could be a thick pencil or have extra weight (e.g., eraser, metal band) unrelated to painted length.

Step4: Interpret slope of line

The line is $w=1.4+0.25l$. Slope is the coefficient of $l$, so it's the weight increase per cm of painted length.

Step5: Predict teacher's pencil weight

Substitute $l=11.5$ into the line equation:
$w = 1.4 + 0.25(11.5)$
$w = 1.4 + 2.875$
$w = 4.275$

Step6: Interpret y-intercept

The y-intercept is the value of $w$ when $l=0$, so it's the base weight of a pencil with no painted part.

Answer:

a. The association is linear, positive, strong, and has one outlier (a pencil with a short painted length but unusually high weight).
b. The outlier could be a pencil that is thicker than the others, or has an extra heavy eraser/metal component, making it heavy even with a short painted section.
c. The slope of 0.25 means that for each additional centimeter of painted length on the pencil, the pencil's weight increases by 0.25 grams.
d. 4.275 grams
e. The y-intercept of 1.4 represents the estimated base weight (in grams) of a pencil that has no painted part (the weight of the unpainted wood, eraser, etc.).