Question

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:_____.

Answer 1

Answer:

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           2.93 177241 1233.53

375          2.87         140625 1076.25

585          3.03 342225 1772.55

693          3.42  480249 2370.06

608          3.66 369664 2225.28

392          2.91  153664 1140.72

418           2.12  174724 886.16

484          2.5    234256 1210

725             3.24  525625  2349

506          1.97   256036 996.82

613           2.73  375769 1673.49

706          3.88 498436 2739.28

366           1.58  133956 578.28

sumx=6892

sumy=36.84

sumx²=3862470

sumxy=20251.42

n=13

$b=\frac{(nsumxy)-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }$

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)