Answer:
Y= 19.86 - 0.42b
Step-by-step explanation:
Step 1: Write the formula
Regression Line: Y = a + bx
a=<u>(Total Y) x (Total X^2) - (Total X) x (Total XY)</u>
n x (total X^2) - (Total X)^2
b= <u>n x (Total XY) - (Total X) x (Total Y)</u>
n x (total X^2) - (Total X)^2
Step 2: Make a table to find all values
X Y X^2 Y^2 XY
5 17.19 25 295.4961 85.95
6 19.12 36 365.5744 114.72
7 16.75 49 280.5625 117.25
8 15.58 64 242.7364 124.64
9 16.21 81 262.7641 145.89
10 14.14 100 199.9396 141.1
11 14.97 121 224.1009 164.67
12 16.2 144 262.44 194.4
68 130.16 620 2133.614 1088.62 TOTAL
Step 3: Substitute all values in the equation to find a and b
a=<u>(Total Y) x (Total X^2) - (Total X) x (Total XY)</u>
n x (total X^2) - (Total X)^2
a= <u>(130.16 x 620) - (68 x 1088.62)</u>
8 x (620) - (68)^2
a = <u>80699.2 - 74026.16</u>
336
a = 19.86
b = <u>n x (Total XY) - (Total X) x (Total Y)</u>
n x (total X^2) - (Total X)^2
b = <u>8 x (1088.62) - (68 x 130.16)</u>
8 x (620) - (68)^2
b =<u> 8708.96 - 8850.88 </u>
336
b = -0.42
Step 4 : Apply values of a and b in the formula of the regression line.
Regression Line: Y = a + bx
Y= 19.86 + b (-0.42)
Y= 19.86 - 0.42b
