1. **Stating the problem:** We have data of 10 TNI soldiers with their monthly income (Pendapatan) and consumption (Konsumsi) in million rupiahs. We want to analyze the relationship between income and consumption. 2. **Organizing the data:** | Soldier | Income ($x$) | Consumption ($y$) | |--------|--------------|------------------| | A | 6 | 5.5 | | B | 8 | 7 | | C | 4 | 4 | | D | 6 | 5 | | E | 7 | 6.5 | | F | 9 | 8 | | G | 11 | 10 | | H | 10 | 9.5 | | I | 8 | 7.5 | | J | 9 | 9 | 3. **Goal:** Find the linear regression equation $y = mx + b$ that models consumption based on income. 4. **Calculate means:** $$\bar{x} = \frac{6+8+4+6+7+9+11+10+8+9}{10} = \frac{78}{10} = 7.8$$ $$\bar{y} = \frac{5.5+7+4+5+6.5+8+10+9.5+7.5+9}{10} = \frac{71}{10} = 7.1$$ 5. **Calculate slope $m$:** $$m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$$ Calculate numerator: $$(6-7.8)(5.5-7.1) + (8-7.8)(7-7.1) + (4-7.8)(4-7.1) + (6-7.8)(5-7.1) + (7-7.8)(6.5-7.1) + (9-7.8)(8-7.1) + (11-7.8)(10-7.1) + (10-7.8)(9.5-7.1) + (8-7.8)(7.5-7.1) + (9-7.8)(9-7.1)$$ $$= (-1.8)(-1.6) + (0.2)(-0.1) + (-3.8)(-3.1) + (-1.8)(-2.1) + (-0.8)(-0.6) + (1.2)(0.9) + (3.2)(2.9) + (2.2)(2.4) + (0.2)(0.4) + (1.2)(1.9)$$ $$= 2.88 - 0.02 + 11.78 + 3.78 + 0.48 + 1.08 + 9.28 + 5.28 + 0.08 + 2.28 = 36.9$$ Calculate denominator: $$(6-7.8)^2 + (8-7.8)^2 + (4-7.8)^2 + (6-7.8)^2 + (7-7.8)^2 + (9-7.8)^2 + (11-7.8)^2 + (10-7.8)^2 + (8-7.8)^2 + (9-7.8)^2$$ $$= (-1.8)^2 + (0.2)^2 + (-3.8)^2 + (-1.8)^2 + (-0.8)^2 + (1.2)^2 + (3.2)^2 + (2.2)^2 + (0.2)^2 + (1.2)^2$$ $$= 3.24 + 0.04 + 14.44 + 3.24 + 0.64 + 1.44 + 10.24 + 4.84 + 0.04 + 1.44 = 39.6$$ So, $$m = \frac{36.9}{39.6} \approx 0.932$$ 6. **Calculate intercept $b$:** $$b = \bar{y} - m \bar{x} = 7.1 - 0.932 \times 7.8 = 7.1 - 7.27 = -0.17$$ 7. **Regression equation:** $$y = 0.932x - 0.17$$ 8. **Interpretation:** For each additional million rupiah in income, consumption increases by approximately 0.932 million rupiah. **Final answer:** The linear regression model relating consumption to income is: $$\boxed{y = 0.932x - 0.17}$$