Chapter 12.2, Problem 41E

(a)

To determine

To Calculate: and state the least regression line.

Answer to Problem 41E

  $\log y=-1.3506+2.0361\log x$

Explanation of Solution

Given:

Speed (mph)	Distance (ft)	Speed (mph)	Distance (ft)
6	1.42	32	52.08
9	4.92	40	84
19	18	48	110.33
30	44.75

Calculation:

Taking the log of the given data

Speed (mph)	Distance (ft)	log(speed)	log(distance)
6	1.42	0.7781513	0.15228834
9	4.92	0.9542425	0.6919651
19	18	1.2787536	1.25527251
30	44.75	1.4771213	1.65079304
32	52.08	1.50515	1.71667098
40	84	1.60206	1.92427929
48	110.33	1.6812412	2.04269362

Using Ti83/84 calculator

Step 1: press on STAT,

Step 2: choose 1: EDIT

Step 3: type the data of logarithmic of speed in list L1 and in L2 logarithmic of Distance in L2.

Step 4: again press on STAT, chose CALC and chose LinReg(a+bx)

Final result

  $\begin{array}{l}y=a+bx\\ a=-1.3506\\ b=2.0361\end{array}$

Putting the value in a and b

  $y=-1.3506+2.0361x$

  $x$ is representing the logarithm of speed and y is representing the logarithm of distance

  $\log y=-1.3506+2.0361\log x$

  $x$ Represents the speed and y represent the distance.

(b)

To determine

To Calculate: and explain the residual for the trial if the motorcycle speed is 48 mph.

Answer to Problem 41E

118.195 feet

Explanation of Solution

Given:

Speed (mph)	Distance (ft)	Speed (mph)	Distance (ft)
6	1.42	32	52.08
9	4.92	40	84
19	18	48	110.33
30	44.75

Calculation:

From the part (b)

  $\log y=-1.3506+2.0361\log x$

Putting the value x by 48

  $\begin{array}{l}\log y=-1.3506+2.0361\log x\\ \log y=-1.3506+2.0361\log 48\\ \log y=2.0726\end{array}$

Taking the exponential with base 10

  $\begin{array}{c}y={10}^{\log y}={10}^{2.0726}\\ =118.195\end{array}$

Therefore the expected distance is 118.195 feet.