Based on the data shown below, calculate the regression line
(each value to two decimal places)
y =_____ x + ______
x | y |
---|---|
5 | 8.4 |
6 | 9.4 |
7 | 8.6 |
8 | 7.2 |
9 | 8.6 |
10 | 9.6 |
11 | 10.6 |
12 | 9.8 |
13 | 11.3 |
14 | 13.6 |
15 | 11.1 |
16 | 15 |
17 | 15.5 |
18 | 13.1 |
solution,
X | Y | XY | X^2 | Y^2 |
5 | 8.4 | 42 | 25 | 70.56 |
6 | 9.4 | 56.4 | 36 | 88.36 |
7 | 8.6 | 60.2 | 49 | 73.96 |
8 | 7.2 | 57.6 | 64 | 51.84 |
9 | 8.6 | 77.4 | 81 | 73.96 |
10 | 9.6 | 96 | 100 | 92.16 |
11 | 10.6 | 116.6 | 121 | 112.36 |
12 | 9.8 | 117.6 | 144 | 96.04 |
13 | 11.3 | 146.9 | 169 | 127.69 |
14 | 13.6 | 190.4 | 196 | 184.96 |
15 | 11.1 | 166.5 | 225 | 123.21 |
16 | 15 | 240 | 256 | 225 |
17 | 15.5 | 263.5 | 289 | 240.25 |
18 | 13.1 | 235.8 | 324 | 171.61 |
n | 13 |
sum(XY) | 1631.10 |
sum(X) | 143.00 |
sum(Y) | 138.70 |
sum(X^2) | 1755.00 |
sum(Y^2) | 1560.35 |
Numerator | 1370.20 |
Denominator | 1573.81 |
r | 0.8706 |
r square | 0.7580 |
Xbar(mean) | 11.0000 |
Ybar(mean) | 10.6692 |
SD(X) | #NAME? |
SD(Y) | #NAME? |
b | 0.5791 |
a | 4.2989 |
= bx + a
= 0.5791x + 4.2989
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