Chapter 1.7, Problem 46E

Solution

The correct choice of types of regression that give most accurate model for the given scatter plot.

The correct choice is E.

Given:

The type of regression is:

A. Linear regression

B. Quadratic regression

C. .Cubic regression

D. Exponential regression

F. Sinusoidal regression

And, the scatter plot is:

  

Concept Used:

There are some basic types of plots of function called regression model that are applied accordingly to scatter plots of data to find the pattern of change by fitting accurately.

The type of regression function with their general equations and graph is as follows:

1) Linear regression, general equation is $y=ax+b$. The graph is of form:

  

2) Quadratic regression: General equation, $y=a{x}^2+bx+c$. It requires minimum three points. The graph is of form:

  

3) Cubic regression: General equation, $y=a{x}^3+b{x}^2+cx+d$, it requires minimum four points, the graph is of form:

  

4) Exponential: It is of two sub type a) exponential growth, general equation, $y=a{b}^x$ where $b>1$. The graph is of form:

  

b) Exponential decay, equation is of form, $y=a{b}^x$ where $0<b<1$. The graph is of form:

  

5) Sinusoidal: General equation is $a\sin \left(bx+c\right)+d$, the graph is of form:

  

Calculation:

The given scatter plot is:

  

The points are scattered in the pattern of sinusoidal. So the sinusoidal regression will give most accurate model.

Clearly other choice, A, B, C and D. are not possible according to position of plot of scatter points.

Hence the correct choice is E.

Conclusion

The correct choice is E.