In an area of the Midwest, records were kept on the relationship between the rai
ID: 3223072 • Letter: I
Question
In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Find the equation of the regression line for the given data.
Rain fall (in inches), x
10.5
8.8
13.4
12.5
18.8
10.3
7.0
15.6
16.0
Yield (bushels per acre), y
50.5
46.2
58.8
59.0
82.4
49.2
31.9
76.0
78.8
^
^
^
^
^
+ 4.379
A) y = 4.379x + 4.267
B) y = -4.379x + 4.267
C) y = 4.267x
D) y = 4.267x - 4.379
Rain fall (in inches), x
10.5
8.8
13.4
12.5
18.8
10.3
7.0
15.6
16.0
Yield (bushels per acre), y
50.5
46.2
58.8
59.0
82.4
49.2
31.9
76.0
78.8
^
^
^
^
^
+ 4.379
A) y = 4.379x + 4.267
B) y = -4.379x + 4.267
C) y = 4.267x
D) y = 4.267x - 4.379
Explanation / Answer
Solution:
AnswerA:
Explanation
We will find an equation of the regression line in 4 steps.
Step 1: Find XY and X2 as it was done in the table below.
Step 2: Find the sum of every column:
X=112.9 , Y=532.8 , XY=7187.81 , X2=1531.39
Step 3: Use the following equations to find a and b:
a=YX2XXY/nX2(X)2
=532.81531.39112.97187.81/91531.39112.924.267
b=nXYXY/nX2(X)2=9(7187.81)112.9(532.8/)91531.39(112.9)24.379
Step 4: Substitute a and b in regression equation formula
y = a + bx= 4.267 + 4.379x
ANSWER A
X Y XY XX 10.5 50.5 530.25 110.25 8.8 46.2 406.56 77.44 13.4 58.8 787.92 179.56 12.5 59.0 737.5 156.25 18.8 82.4 1549.12 353.44 10.3 49.2 506.76 106.09 7.0 31.9 223.3 49 15.6 76.0 1185.6 243.36 16.0 78.8 1260.8 256Related Questions
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