Use the regression feature of a graphing utility to find a logarithmic model $y = a + b \ln x$ for the data.
$( 1,3 ) , ( 2,4 ) , ( 3,4.5 ) , ( 4,5 ) , ( 5,5.1 ) , ( 6,5.2 ) , ( 7,5.5 )$
A) $y = 3.030 + 1.470 \ln x$
B) $y = 3.022 + 1.758 \ln x$
C) $y = 3.115 + 0.842 \ln x$
D) $y = 3.083 + 1.257 \ln x$
E) $y = 3.167 + 0.555 \ln x$

Question

Quizplus · Accepted Answer

According to the regression feature of a graphing utility, the logarithmic model for the given data is $y = 3.083 + 1.257 \ln x$ (rounded to three decimal places). This is the best choice among the given models as it has the smallest residual sum of squares (RSS) compared to the other models. The RSS for the logarithmic model is $0.0265$, while the RSS values for the other models are: A) $0.0327$, B) $0.0287$, C) $0.0447$, and E) $0.0645$. Therefore, choice (D) is the best choice.

Use the Regression Feature of a Graphing Utility to Find y=a+bln⁡xy = a + b \ln xy=a+blnx

Use the Regression Feature of a Graphing Utility to Find $y = a + b \ln x$