1. **Problem Statement:** Given the data for income $X$ and consumption $Y$, find the coefficients $a$ and $b$ of the simple linear regression model $$Y = a + bX$$ and predict consumption if income increases by 10. 2. **Formula and Explanation:** The formulas for the regression coefficients are: $$b = \frac{n\sum XY - \sum X \sum Y}{n\sum X^2 - (\sum X)^2}$$ $$a = \bar{Y} - b\bar{X}$$ where $n$ is the number of data points, $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively. 3. **Calculations:** - $n = 6$ - $\sum X = 40 + 50 + 60 + 70 + 80 + 90 = 390$ - $\sum Y = 25 + 35 + 40 + 50 + 60 + 75 = 285$ - $\sum XY = 40\times25 + 50\times35 + 60\times40 + 70\times50 + 80\times60 + 90\times75 = 1000 + 1750 + 2400 + 3500 + 4800 + 6750 = 20200$ - $\sum X^2 = 40^2 + 50^2 + 60^2 + 70^2 + 80^2 + 90^2 = 1600 + 2500 + 3600 + 4900 + 6400 + 8100 = 27100$ Calculate $b$: $$b = \frac{6 \times 20200 - 390 \times 285}{6 \times 27100 - 390^2} = \frac{121200 - 111150}{162600 - 152100} = \frac{10050}{10500} = 0.9571$$ Calculate means: $$\bar{X} = \frac{390}{6} = 65$$ $$\bar{Y} = \frac{285}{6} = 47.5$$ Calculate $a$: $$a = 47.5 - 0.9571 \times 65 = 47.5 - 62.21 = -14.71$$ 4. **Prediction:** If income increases by 10 (from any base), the predicted increase in consumption is: $$\Delta Y = b \times 10 = 0.9571 \times 10 = 9.571$$ So, consumption increases by approximately 9.57 (thousand rupiah). **Final regression equation:** $$Y = -14.71 + 0.9571X$$ **Answer:** $a = -14.71$, $b = 0.9571$, predicted consumption increase for $\Delta X = 10$ is approximately 9.57.