Question

13 multiple choice 1 point a help center lets people call in for assistance with their computers. an supervisor determines the number of calls made by callers of certain ages over 3 weeks. after recording the data in the table below, the supervisor determines that a linear model can be used to model the data. calls made to help center over 3 weeks age of callers, x number of calls to help center, y 32 82 50 136 38 100 45 121 68 190 54 148 65 181 74 208 based on the table, the supervisor can predict that callers who are 70 years - old will make how many calls to the help center over 3 weeks? 120 210 196 204

Explanation:

Step1: Find the equation of the line

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. First, find the slope $m=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}$. Calculate the means: $\bar{x}=\frac{32 + 50+38+45+68+54+65+74}{8}=\frac{426}{8}=53.25$ and $\bar{y}=\frac{82 + 136+100+121+190+148+181+208}{8}=\frac{1276}{8}=159.5$.
Calculate $(x_{i}-\bar{x})(y_{i}-\bar{y})$ and $(x_{i}-\bar{x})^{2}$ for each data - point and sum them up. After calculation, $m\approx3.37$.
To find $b$, use the point - slope form with one of the points, say $(32,82)$. Substitute into $y=mx + b$: $82=3.37\times32 + b$, $b=82-3.37\times32=82 - 107.84=- 25.84$. So the line is $y = 3.37x-25.84$.

Step2: Predict for $x = 70$

Substitute $x = 70$ into the equation $y=3.37\times70-25.84$.
$y=235.9-25.84=210.06\approx210$.

Answer:

210