Thirteen students entered the business program at Sante Fe College 2 years ago. The following table indicates what each student scored on the high school SAT math exam and their grade-point averages (GPAs) after students were in the Sante Fe program for 2 years. Student A B C D E F G
SAT Score 421 375 585 693 608 392 418
GPA 2.93 2.87 3.03 3.42 3.66 2.91 2.12
Student H I J K L M
SAT Score 484 725 506 613 706 366
GPA 2.50 3.24 1.97 2.73 3.88 1.58
The least-squares regression equation that shows the best relationship between GPA and the SAT score is:.

y=1.003009+0.003453x

or

GPA=1.003009+0.003453(SAT Score)

Step-by-step explanation:

The least square regression equation can be written as

y=a+bx

In the given scenario y is the GPA and x is SAT score because GPA depends on SAT score.

SAT score (X)GPA (Y)X²         XY

421           2.931772411233.53

375          2.87         1406251076.25

585          3.033422251772.55

693          3.42  4802492370.06

608          3.663696642225.28

392          2.91  1536641140.72

418           2.12  174724886.16

484          2.5    2342561210

725             3.24  525625  2349

506          1.97  256036996.82

613           2.73  3757691673.49

706          3.884984362739.28

366           1.58  133956578.28

sumx=6892

sumy=36.84

sumx²=3862470

sumxy=20251.42

n=13

b=9367.18/2712446

b=0.003453

a=ybar-b(xbar)

ybar=sum(y)/n

ybar=2.833846

xbar=sum(x)/n

xbar=530.1538

a=2.833846-0.003453*(530.1538)

a=1.003009

Thus, required regression equation is

y=1.003009+0.003453x.

The least-squares regression equation that shows the best relationship between GPA and the SAT score is

GPA=1.003009+0.003453(SAT Score)

step-by-step explanation:

ddd

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)