Use technology to find a logistic regression curve $y = \frac { N } { 1 + A b ^ { - x } }$ approximating the given data. (Round b to three significant digits and A and N to two significant digits.) $$\begin{array} { | l | l | l | l | l | l | l | }
\hline x & 0 & 20 & 40 & 60 & 80 & 100 \
\hline y & 2.2 & 3.8 & 5.0 & 6.1 & 6.8 & 6.9 \
\hline
\end{array}$$
A) $y = \frac { 7.2 } { 1 + 2.2 \left( 1.04 ^ { - x } \right) }$
B) $y = \frac { 7.2 } { 4.4 \left( 1.04 ^ { - x } \right) }$
C) $y = \frac { 5.2 } { 1 + 2.2 \left( 1.04 ^ { - x } \right) }$
D) $y = \frac { 5.2 } { 1 + 4.4 \left( 2.08 ^ { - x } \right) }$
E) $y = \frac { 7.2 } { 1 + 2.2 \left( 2.08 ^ { - x } \right) }$

Question

Use technology to find a logistic regression curve $y = \frac { N } { 1 + A b ^ { - x } }$ approximating the given data. (Round b to three significant digits and A and N to two significant digits.) $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline x & 0 & 20 & 40 & 60 & 80 & 100 \
\hline y & 2.2 & 3.8 & 5.0 & 6.1 & 6.8 & 6.9 \
\hline
\end{array}$$  
A) $y = \frac { 7.2 } { 1 + 2.2 \left( 1.04 ^ { - x } \right) }$
B)   $y = \frac { 7.2 } { 4.4 \left( 1.04 ^ { - x } \right) }$
C)   $y = \frac { 5.2 } { 1 + 2.2 \left( 1.04 ^ { - x } \right) }$
D)   $y = \frac { 5.2 } { 1 + 4.4 \left( 2.08 ^ { - x } \right) }$
E)   $y = \frac { 7.2 } { 1 + 2.2 \left( 2.08 ^ { - x } \right) }$

Quizplus · Accepted Answer

Using technology to perform logistic regression on the given data, the curve that best fits the data is $y = \frac { 7.2 } { 1 + 2.2 \left( 1.04 ^ { - x } \right) }$, which matches option A. This involves finding the parameters N, A, and b that minimize the difference between the observed values and those predicted by the model, and rounding these parameters as specified.

Use Technology to Find a Logistic Regression Curve y=N1+Ab−xy = \frac { N } { 1 + A b ^ { - x } }y=1+Ab−xN​

Use Technology to Find a Logistic Regression Curve $y = \frac { N } { 1 + A b ^ { - x } }$