Question 1207185
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Use technology of your choice to determine these regression equations<ul><li>linear: f(x) = 17.4249142857x + 379.5919047619</li><li>quadratic: g(x) = 0.2559714286x^2 + 11.0256285714x + 400.9228571429</li><li>exponential: h(x) = 400.0011431092e^(0.0295586331x)</li></ul>The decimal values are approximate.
The 'e' is a special constant roughly equal to 2.718
h(x) is roughly equivalent to 400.0011431092*1.0299998258^x


From here, use spreadsheet software to construct the following table
<table border = "1" cellpadding = "5"><tr><td colspan=2>Given</td><td colspan=3>Absolute Error</td></tr><tr><td>x</td><td>y</td><td>linear</td><td>quadratic</td><td>exponential</td></tr><tr><td>0</td><td>400</td><td>20.408095</td><td>0.922857</td><td>0.001143</td></tr><tr><td>5</td><td>463.71</td><td>3.006476</td><td>1.259714</td><td>0.000563</td></tr><tr><td>10</td><td>537.57</td><td>16.271048</td><td>0.793714</td><td>0.002821</td></tr><tr><td>15</td><td>623.19</td><td>17.775619</td><td>0.710857</td><td>0.002834</td></tr><tr><td>20</td><td>722.44</td><td>5.65019</td><td>1.384</td><td>0.004115</td></tr><tr><td>25</td><td>837.51</td><td>22.295238</td><td>0.964286</td><td>0.000024</td></tr></table>
The first two columns are copy/pasted from the table your teacher gave you. Except of course the dollar sign symbols have been erased.
The remaining 3 columns represent the absolute error when subtracting the stated y value from each regression output.


For example, when x = 0 the y value is y = 400.
If you plugged x = 0 into the linear regression function, then you should find f(0) = 379.5919047619
The error is approximately |y-f(x)| = |y-f(0)| = |400-379.5919047619| = 20.4080952381
Follow similar steps to compute the other error values. 


In a perfect world, the error would be 0. But of course nothing is ever perfect. 
The next best thing is to try to get as close to 0 as possible.
This occurs with the exponential regression function. 
Therefore, the <font color=red>exponential</font> is the best fit.



Answer: <font color=red>choice C</font>
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