X | Y | (x-x̅)² | (y-ȳ)² | (x-x̅)(y-ȳ) |
7 | 5 | 6.950 | 25.000 | -13.182 |
10 | 5 | 31.769 | 25.000 | -28.182 |
2 | 14 | 5.587 | 16.000 | -9.455 |
0 | 15 | 19.041 | 25.000 | -21.818 |
4 | 8 | 0.132 | 4.000 | 0.727 |
7 | 11 | 6.950 | 1.000 | 2.636 |
9 | 9 | 21.496 | 1.000 | -4.636 |
1 | 14 | 11.314 | 16.000 | -13.455 |
7 | 8 | 6.950 | 4.000 | -5.273 |
0 | 11 | 19.041 | 1.000 | -4.364 |
1 | 10 | 11.314 | 0.000 | 0.000 |
ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
total sum | 48 | 110 | 140.545 | 118.0 | -97 |
mean | 4.36 | 10.00 | SSxx | SSyy | SSxy |
sample size , n = 11
here, x̅ = 4.36 , ȳ
= 10.00
SSxx = Σ(x-x̅)² = 140.55
SSxy= Σ(x-x̅)(y-ȳ) = -97.0
a)
correlation coefficient , r = Sxy/√(Sx.Sy) = -0.75
--------------------------
b)
Ho: ρ = 0
Ha: ρ ╪ 0
n= 11
alpha,α = 0.05
correlation , r= -0.7532
t-test statistic = t = r*√(n-2)/√(1-r²) =
-3.43535
p-value = 0.0074
--------------------------
c)
option c)
d)
r²= -0.7532² =0.57
e)
option b)
f)
slope , ß1 = SSxy/SSxx =
-0.69017
intercept, ß0 = y̅-ß1* x̄ =
13.01164
so, regression line is Ŷ =
13.01 + -0.69 *x
g)
Ŷ = 13.01 + -0.69 * x
Ŷ = 13.01 + -0.69 * 4 = 10(answer)
h)
option b)
i)
option d)
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