1. **State the problem:** We need to find the linear regression equation $y = mx + b$ for the data points $(4, -8)$, $(5, -14)$, $(7, -24)$, $(11, -43)$, and $(13, -60)$, rounding coefficients to the nearest hundredth. 2. **Formula for linear regression coefficients:** - Slope: $$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ - Intercept: $$b = \frac{\sum y - m \sum x}{n}$$ where $n$ is the number of points. 3. **Calculate sums:** - $n = 5$ - $\sum x = 4 + 5 + 7 + 11 + 13 = 40$ - $\sum y = -8 - 14 - 24 - 43 - 60 = -149$ - $\sum x^2 = 4^2 + 5^2 + 7^2 + 11^2 + 13^2 = 16 + 25 + 49 + 121 + 169 = 380$ - $\sum xy = (4)(-8) + (5)(-14) + (7)(-24) + (11)(-43) + (13)(-60) = -32 - 70 - 168 - 473 - 780 = -1523$ 4. **Calculate slope $m$:** $$m = \frac{5(-1523) - 40(-149)}{5(380) - 40^2} = \frac{-7615 + 5960}{1900 - 1600} = \frac{-1655}{300} = -5.52$$ 5. **Calculate intercept $b$:** $$b = \frac{-149 - (-5.52)(40)}{5} = \frac{-149 + 220.8}{5} = \frac{71.8}{5} = 14.36$$ 6. **Write the regression equation:** $$y = -5.52x + 14.36$$ This is the linear regression equation rounded to the nearest hundredth.