Chapter 1.6, Problem 49E

(a)

To determine

To find:The sinusoidal regression equation that best fits the given data.

Answer to Problem 49E

The sinusoidal regression equation that best fits the given data is $y=3.0014\sin \left(0.999x+2.001\right)+2.999$ .

Explanation of Solution

Given information:The given table is:

Values of the function
$x$	$f\left(x\right)$
$1$	$3.42$
$2$	$0.73$
$3$	$0.12$
$4$	$2.16$
$5$	$4.97$
$6$	$5.97$

Calculation:

For the sinusoidal model of data follow the steps below:

First press the $\boxed{2\text{nd}}$ key and then $\boxed{\text{Y}=}$ and make sure that Plot $1$ is ON and choose the scatter plot icon in type.

Go to ${\text{Y}}_1$ and then press the key $\boxed{\text{STAT}}$ and then in edit enter the data in ${\text{L}}_1$ and ${\text{L}}_2$ .

Now enter the keystrokes $\boxed{\text{STAT}}\boxed{\to }\boxed{\text{C}}$ and press the $\boxed{\text{ENTER}}$ key for the regression.

  

Figure(1)

Therefore, the sinusoidal regression equation that best fits the given data is $y=3.0014\sin \left(0.999x+2.001\right)+2.999$ .

(b)

To determine

To find: The regression equation.

Answer to Problem 49E

The regression equation is $y=3\sin \left(x+2\right)+3$ .

Explanation of Solution

Given information:The given table is:

Values of the function
$x$	$f\left(x\right)$
$1$	$3.42$
$2$	$0.73$
$3$	$0.12$
$4$	$2.16$
$5$	$4.97$
$6$	$5.97$

Calculation:

Calculate the regression equation.

  $y=3.0014\sin \left(0.999x+2.001\right)+2.999$

Round the coefficients to the nearest integers,

  $y=3\sin \left(x+2\right)+3$

Therefore, the regression equation is $y=3\sin \left(x+2\right)+3$ .