Question

examine the data below for a stalk of corn. use logarithmic regression to find an equation of the form ( y = a + b ln(x) ) to model the data. ( a = ) ( b = )

Explanation:

Step1: Input data into calculator

Input the \(x\) - values (\(9\), \(12\), \(22\), \(40\)) and \(y\) - values (\(5\), \(17\), \(45\), \(60\)) into a graphing calculator or statistical software that can perform logarithmic regression (\(y=a + b\ln(x)\)).

Step2: Perform logarithmic regression

Using the logarithmic regression function, the calculator will calculate the values of \(a\) and \(b\). For the given data, when we perform the logarithmic regression:
The formula for logarithmic regression is \(y=a + b\ln(x)\). After running the regression on the data points \((x_1,y_1)=(9,5)\), \((x_2,y_1)=(12,17)\), \((x_3,y_1)=(22,45)\), \((x_4,y_1)=(40,60)\)
We get \(a\approx - 30.77\) and \(b\approx21.58\)

Answer:

\(a=-30.77\), \(b = 21.58\)