if amelia wants to make the maximum amount of money working only 22 hours per week, which company should she…

Explanation:

Step1: Find the hourly - rate formula for linear regression

For a linear regression model $y = mx + b$, where $y$ is earnings, $x$ is hours, $m$ is the slope (hourly - rate) and $b$ is the y - intercept. The slope $m=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}$. But we can also estimate the slope using two - point formula $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. For Company A: Let's take two points $(x_1,y_1)=(5,340)$ and $(x_2,y_2)=(20,460)$. Then $m_A=\frac{460 - 340}{20 - 5}=\frac{120}{15}=8$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(5,340)$ and $m = 8$, we get $y=8x+300$. When $x = 22$, $y_A=8\times22 + 300=176+300 = 476$. For Company B: Let's take two points $(x_1,y_1)=(4,125)$ and $(x_2,y_2)=(20,450)$. Then $m_B=\frac{450 - 125}{20 - 4}=\frac{325}{16}=20.3125$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(4,125)$ and $m = 20.3125$, we get $y=20.3125x+43.75$. When $x = 22$, $y_B=20.3125\times22+43.75=446.875 + 43.75=490.625$. $y_B-y_A=490.625 - 476=14.625\approx14$.

Answer:

Company B: Using linear regression models from both data sets, she determines that it pays about $14 more.