Algebra 1 Common Core Student Edition, Grade 8-9

Got It? 3. a. Predict th e cost of atten d in g in th e 2016-2017 academ ic year.

b. Reasoning W hat does th e slope of th e line of b est fit in Problem 3 tell

you ab o u t th e rate of change in the cost?

Causation is w hen a change in one quantity causes a change in a second quantity.

A correlation betw een quantities does n o t always im ply causation.

JM n k
Causal re lationships
always have a
correlation. However,
tw o data sets that have a
correlation may not have
a causal re lationship.

Pr o b l em 4 Identifying Whet her Relat ionships Are Causal

In the following situations, is there likely to be a correlation? If so, does the

correlation reflect a causal relationship? Explain.

Q the number of loaves of bread baked and the amount of flour used

There is a positive correlation and also a causal relationship. As the num ber of loaves of

bread baked increases, the am ount of flour used increases.

0 the number of mailboxes and the number of firefighters in a city

There is likely to be a positive correlation because b o th the n u m b e r of mailboxes

an d th e n u m b e r of firefighters te n d to increase as th e p o p u latio n of a city increases.

However, installing m ore m ailboxes will n o t cause th e n u m b e r of firefighters to

increase, so th ere is no causal relationship.

Got It? 4. In th e following situations, is th ere likely to be a correlation? If so, does the

correlation reflect a causal relationship? Explain.

a. th e cost of a family’s vacation an d th e size of th eir house

b. th e tim e sp en t exercising an d th e n u m b e r of Calories b u rn e d

Lesso n Ch eck

Do y o u k n o w H OW?

Use the table.

Average Maximum Daily Temperature

in January fo r N o rth e rn L a titu d es

L a titu d e (° N) 35 33 30 25 43 40 39

Temperature (°F) 46 52 67 76 32 37 44

Source: U.S. D e p a rtm e n t o f C om m erce

1. Make a scatter plot of the data. W hat type of
   relationship does th e scatter plot show?


2. Draw a tren d line an d write its equation.


3. Predict the average m axim um daily tem p eratu re in
   January at a latitude of 50° N.

\

Do y o u UN DERSTAN D? ^ PRACTICES

0 4. Vocabulary Given a set of d ata pairs, how w ould you

decide w h e th e r to u se interpolation or extrapolation

to find a certain value?

5. Com pare and Contrast How are a tren d line an d the
   line of b est fit for a set of d ata pairs similar? How are
   they different?

0 6. E r r o r A n a l y s i s Refer to the table below. A stu d en t

says th a t the d ata have a negative correlation

because as x d e c r e a s e s , y also decreases. W hat is the

stu d e n t’s error?

a^107541 0

a^1 0-2-4-7 -9

340 Chap t er 5 Linear Funct ions