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=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)