## 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

------------------------------

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