as per company policies i am answering 4 parts only.
x | y | x^2 | y^2 | xy |
5 | 21 | 25 | 441 | 105 |
7 | 23 | 49 | 529 | 161 |
8 | 24 | 64 | 576 | 192 |
8 | 23 | 64 | 529 | 184 |
9 | 22 | 81 | 484 | 198 |
12 | 25 | 144 | 625 | 300 |
13 | 27 | 169 | 729 | 351 |
sum x | sum y | sum x^2 | sum y^2 | sum xy | n |
62 | 165 | 596 | 3913 | 1491 | 7 |
b)
excel output:
c)
scatter plot given below
d)
slope, b1=
{n*sum(xy) - sum(x)*sum(y)} / {n*sum(x^2) - [sum(x)]^2
}
{7*1491 - 62*165} / {7*596 - [62]^2 }
0.6311
intercept, bo=
{sum(y)*sum(x^2) - sum(x)*sum(xy)} / {n*sum(X^2) -
[sum(X)]^2}
{165*596 - 62*1491} / {7*596 - [62]^2}
18.0
regression equation:
y = bo + b1*x
y = 17.9817 + 0.6311*x
e)
when x= 18
yhat = 17.9817+0.6311*18
Yhat = 29
f)
corr coef, r =
(n*sum(XY) - sum(X)*sum(Y)) / ( sqrt(n*sum(x^2)-[sum(x)]^2) *
sqrt(n*sum(y^2)-[sum(y)]^2) )
(7*1491-62*165) / ( sqrt(7*596-[62]^2) * sqrt(7*3913-[165]^2)
)
0.887113891
coef of determination, R^2
0.887113890631588^2
0.787
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