Answers
for weekly disposable income-
| X(age) | Y(weekly disposable income) | (x-x̅)² | (y-ȳ)² | (x-x̅)(y-ȳ) |
| 30 | 500 | 400 | 130401.2 | 7222.222 |
| 35 | 550 | 225 | 96790.12 | 4666.667 |
| 40 | 600 | 100 | 68179.01 | 2611.111 |
| 45 | 500 | 25 | 130401.2 | 1805.556 |
| 50 | 900 | 0 | 1512.346 | 0 |
| 55 | 1000 | 25 | 19290.12 | 694.4444 |
| 60 | 1000 | 100 | 19290.12 | 1388.889 |
| 65 | 1200 | 225 | 114845.7 | 5083.333 |
| 70 | 1500 | 400 | 408179 | 12777.78 |
| ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
| total sum | 450 | 7750 | 1500 | 988888.9 | 36250 |
| mean | 50 | 861.111111 | SSxx | SSyy | SSxy |
sample size , n = 9
here, x̅ = 50 ȳ = 861.1111111
SSxx = Σ(x-x̅)² = 1500
SSxy= Σ(x-x̅)(y-ȳ) = 36250
slope , ß1 = SSxy/SSxx = 24.16666667
intercept, ß0 = y̅-ß1* x̄ = -347.2222222
so, regression line is Ŷ = -347.2222 + 24.1667 *x
correlation coefficient , r = Sxy/√(Sx.Sy) = 0.9412
R² = (Sxy)²/(Sx.Sy) = 0.8859
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a)
slope = 24.167
intercept= -347.2222
eqn is
Ŷ = -347.2222 + 24.1667 *x
b) for every unit increase in age, weekly disposable income will get increase by 24.1667
c) R² = 0.8859
88.59% variations in observations of variable Y(weekly disposable income) is explained by variable X(age)
d)
age,X=58
Ŷ = -347.2222 + 24.1667 *58=1054.444
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for weekly consumption per capita-
| X | Y | (x-x̅)² | (y-ȳ)² | (x-x̅)(y-ȳ) |
| 30 | 50 | 400 | 241.9753 | 311.1111 |
| 35 | 55 | 225 | 111.4198 | 158.3333 |
| 40 | 60 | 100 | 30.8642 | 55.55556 |
| 45 | 60 | 25 | 30.8642 | 27.77778 |
| 50 | 50 | 0 | 241.9753 | 0 |
| 55 | 70 | 25 | 19.75309 | 22.22222 |
| 60 | 75 | 100 | 89.19753 | 94.44444 |
| 65 | 80 | 225 | 208.642 | 216.6667 |
| 70 | 90 | 400 | 597.5309 | 488.8889 |
| ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
| total sum | 450 | 590 | 1500 | 1572.222 | 1375 |
| mean | 50 | 65.5555556 | SSxx | SSyy | SSxy |
sample size , n = 9
here, x̅ = 50 ȳ = 65.55555556
SSxx = Σ(x-x̅)² = 1500
SSxy= Σ(x-x̅)(y-ȳ) = 1375
slope , ß1 = SSxy/SSxx = 0.916666667
intercept, ß0 = y̅-ß1* x̄ = 19.72222222
so, regression line is Ŷ = 19.7222 + 0.9167 *x
correlation coefficient , r = Sxy/√(Sx.Sy) = 0.8954
R² = (Sxy)²/(Sx.Sy) = 0.8017
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a)
slope = 0.9167
intercept= 19.7222
eqn is
Ŷ = 19.7222 + 0.9167 *x
b) for every unit increase in age, weekly per capita consumption will get increase by 0.9167
c) R² = 0.8017
80.17% variations in observations of variable Y is explained by variable X(age)
d)
age,X=58
Ŷ = 19.7222 + 0.9167 *58 = 72.889