Question

Examine the data below for a stalk of corn. Logarithmic regression Use logarithmic regression to find an equation of the form y = a b ln(x) to model the data. A = b =.

Answer 1

The value of a and b for the data values of stalk of corn using the logarithmic regression is -76.2038 and 37.6735 respectively.

What is logarithmic regression?

Logarithmic regression is a type of regression which is used to model the statement in which the growth or decay initially at rapid rate, and then slow down with respect to time.

The data of the table for the day and height of the stalk of corn is listed below.

Day (x)                9    12    22    40    

Height (y) in        5    17    45    60  

Mean of x values,

$m_x=\dfrac{9+12+22+40}{4}\\m_x=17.5581$

Mean of y values,

$m_y=\dfrac{5+17+45+60}{4}\\m_y=31.75$

For the above table, the value of correlation coefficient is 0.99133. For these values, the logarithmic regression can be given as,

$y = -76.2038+37.6735\ln(x)$

Compare it with the following logarithmic regression equation, we get

$y = a+b\ln(x)$

$a=-76.2038\\b=37.6735$

Hence, the value of a and b for the data values of stalk of corn using the logarithmic regression is -76.2038 and 37.6735 respectively.

Learn more about the logarithmic regression here;

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