Question 1170562
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Part (a)


Table
<table border = "1" cellpadding = "5"><tr><td>Weight of  Mail (pounds)</td><td>Number of  Employees</td></tr><tr><td>11</td><td>6</td></tr><tr><td>20</td><td>10</td></tr><tr><td>16</td><td>9</td></tr><tr><td>6</td><td>5</td></tr><tr><td>12</td><td>8</td></tr><tr><td>18</td><td>14</td></tr><tr><td>23</td><td>13</td></tr><tr><td>25</td><td>16</td></tr></table>


Scatter Plot
<img width="50%" src = "https://i.imgur.com/XKI8eQu.png">
There's an upward trend, so the data is positively correlated. As x (weight of mail) goes up, y (number of employees) goes up as well. This makes sense because you need more workers to process the larger volume of mail. 

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Part (b)


Linear
<img width="50%" src = "https://i.imgur.com/FcnZ0xH.png">


Quadratic
<img width="50%" src = "https://i.imgur.com/44E6isQ.png">


Cubic
<img width="50%" src = "https://i.imgur.com/HVruGr5.png">


Exponential
<img width="50%" src = "https://i.imgur.com/70GlD7e.png">


Logarithmic
<img width="50%" src = "https://i.imgur.com/nbjq4X4.png">


Power
<img width="50%" src = "https://i.imgur.com/N5caaYn.png">


For each chart, f(x) is the approximate regression line and R^2 is the approximate value of the Coefficient of Determination. The closer R^2 is to 1, the better the fit. If R^2 = 1 exactly, then we have an exact fit and that means all points are on the function curve.


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Part (c)


From the charts in part (b), we see that R^2 = 0.875 approximately for the exponential regression. This is the largest R^2 value of the six charts. Therefore, the exponential regression model is the best fit among the choices.


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Part (d)


Roughly 87.5% of variation in the number of employees is explained by the variation in the weight of mail. This figure is directly tied to the R^2 value. 


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Part (e)


Plug x = 15 into the exponential function model (from part (b)). We pick this function due to it being the best fit.


f(x) = 3.55314210119616e^(0.059651797827595x)
f(15) = 3.55314210119616e^(0.059651797827595*15)
f(15) = 8.69379261400984
f(15) = 9
I'm rounding to the nearest whole number since every y value in the original table is a whole number.


If the company receives x = 15 pounds of mail, then we predict or estimate there will about y = 9 employees assigned to mail duty.

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