Mathematics: slader The logarithmic equation is a nonlinear regression equation of the form ya. The accompanying data are the shoe sizes and heights (in inches) of men. Graphs of the regression line and the logarithmic equation are also provided. Which equation is a better model for the data? Explain.

One half, or 1/2.There are an equal amount of odd numbers as there are even numbers on the spinner....

slader The logarithmic equation is a nonlinear regression

tporter00

31.01.2022

The graphs and the table is missing in the question.

Step-by-step explanation:

The guidelines for interpreting correlation co-efficient r are :

1. Strong correlation 0.7<|r|≤1

2. Moderate correlation 0.4<|r|<0.7

3. Weak correlation 0.2<|r|<0.4

4. No correlation 0≤|r|<0.2

Logarithmic regression

(i). Mean : ${\overset{-}{ln}x} = \frac{\sum ln x_i}{n}, \ \ \ {\overset{-}y} = \frac{\sum y_i}{n}$

(ii) Trend line : $y = A +B \ln x, \ \ B = \frac{S_{xy}}{S_{xx}}, \ \ A={\overset{-}y-B{\overset{-}{\ln x}}}$

(iii). Correlation coefficient : $r = \frac {S_{xy}}{\sqrt{S_{xx}} \sqrt{S_{yy}}}$

$S_{xx} = \sum (\ln x_i - {\overset{-}{\ln x}})^2 = \sum (\ln x_i)^2-n. ({\overset{-}{\ln x}})^2$

$S_{yy} = \sum(y_i - {\overset{-}y})^2 = \sumy_i^2 - n. {\overset{-}y^2}$

$S_{xy} = \sum(\ln x_i - {\overset{-}{\ln x}})(y_i-{\overset{-}y}) = \sum \ln x_i y_i - n. {\overset{-}{\ln x}}{\overset{-}y}$

Now using the technology we can calculate

The equation of the regression curve is y = A + B(lnx)

we get A = 30.72 , B = 17.19

The equation of regression curve is $\hat y$ = 30.72 + 17.19(lnx)

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