create a linear model for the data in the table.\nwrite a linear model for the data in the table.\ny =…

Explanation:

Step1: Calculate the mean of x and y

Let $x_i$ and $y_i$ be the data - points. $n = 7$ $\bar{x}=\frac{3 + 6+9+10+11+13+17}{7}=\frac{69}{7}\approx9.857$ $\bar{y}=\frac{6 + 11+14+17+18+21+27}{7}=\frac{114}{7}\approx16.286$

Step2: Calculate the slope (m)

$m=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sum_{i = 1}^{n}(x_i-\bar{x})^2}$ $\sum_{i = 1}^{7}(x_i-\bar{x})(y_i - \bar{y})=(3 - 9.857)(6 - 16.286)+(6 - 9.857)(11 - 16.286)+(9 - 9.857)(14 - 16.286)+(10 - 9.857)(17 - 16.286)+(11 - 9.857)(18 - 16.286)+(13 - 9.857)(21 - 16.286)+(17 - 9.857)(27 - 16.286)$ $=(- 6.857)\times(-10.286)+(-3.857)\times(-5.286)+(-0.857)\times(-2.286)+(0.143)\times(0.714)+(1.143)\times(1.714)+(3.143)\times(4.714)+(7.143)\times(10.714)$ $=70.51+20.37+1.96 + 0.10+1.96+14.81+76.51$ $=186.22$ $\sum_{i = 1}^{7}(x_i-\bar{x})^2=(3 - 9.857)^2+(6 - 9.857)^2+(9 - 9.857)^2+(10 - 9.857)^2+(11 - 9.857)^2+(13 - 9.857)^2+(17 - 9.857)^2$ $=(-6.857)^2+(-3.857)^2+(-0.857)^2+(0.143)^2+(1.143)^2+(3.143)^2+(7.143)^2$ $=47.02+14.88+0.73+0.02+1.31+9.88+51.02$ $=124.86$ $m=\frac{186.22}{124.86}\approx1.491$

Step3: Calculate the y - intercept (b)

$b=\bar{y}-m\bar{x}$ $b = 16.286-1.491\times9.857$ $b = 16.286 - 14.797$ $b = 1.489$

Answer:

$y = 1.491x+1.489$