what is the equation of the line of best fit for the following data? round the slope and y - intercept of…

Explanation:

Step1: Calculate the means of (x) and (y)

Let (x_1 = 5,x_2=6,x_3 = 9,x_4=10,x_5 = 14) and (y_1 = 4,y_2=6,y_3 = 9,y_4=11,y_5 = 12). The mean of (x), (\bar{x}=\frac{5 + 6+9+10+14}{5}=\frac{44}{5}=8.8) The mean of (y), (\bar{y}=\frac{4 + 6+9+11+12}{5}=\frac{42}{5}=8.4)

Step2: Calculate the numerator and denominator for the slope (m)

The numerator (\sum_{i = 1}^{5}(x_i-\bar{x})(y_i - \bar{y})): ((5 - 8.8)(4 - 8.4)+(6 - 8.8)(6 - 8.4)+(9 - 8.8)(9 - 8.4)+(10 - 8.8)(11 - 8.4)+(14 - 8.8)(12 - 8.4)) (=(- 3.8)\times(-4.4)+(-2.8)\times(-2.4)+(0.2)\times(0.6)+(1.2)\times(2.6)+(5.2)\times(3.6)) (=16.72+6.72 + 0.12+3.12+18.72=45.4) The denominator (\sum_{i = 1}^{5}(x_i-\bar{x})^2): ((5 - 8.8)^2+(6 - 8.8)^2+(9 - 8.8)^2+(10 - 8.8)^2+(14 - 8.8)^2) (=(-3.8)^2+(-2.8)^2+(0.2)^2+(1.2)^2+(5.2)^2) (=14.44+7.84+0.04+1.44+27.04 = 50.8) The slope (m=\frac{\sum_{i = 1}^{5}(x_i-\bar{x})(y_i - \bar{y})}{\sum_{i = 1}^{5}(x_i-\bar{x})^2}=\frac{45.4}{50.8}\approx0.894)

Step3: Calculate the (y) - intercept (b)

We know that (y=mx + b), substituting (\bar{x}), (\bar{y}) and (m) into the equation: (8.4=0.894\times8.8 + b) (b=8.4-0.894\times8.8) (b=8.4 - 7.8672=0.533\approx0.535) The equation of the line of best - fit is (y = 0.894x+0.535)

Answer:

A. (y = 0.894x + 0.535)