Question

Destination	Departing Flight Numbers (list all departing flight segments)	Distance (round to nearest mile)	Amount
Miami	Delta 3899/ Delta 951	993	$328
San Diego	Delta 3899/ Delta 1909	2,321	$609
New York City	Delta 3899/ Delta 2021	555	$508
Chicago	Delta 3899/ Delta 1608	516	$205
Seattle	Delta 3899/Delta 3642	2,568	$491
Salt Lake City	Delta 2899/ Delta 2611	1,831	$475
Boston	Delta 2109/ Delta 665	744	$579
Honolulu	Delta 876/ Delta 1559	4,594	$1,168
Denver	Delta 3899/ Delta 2871	1,350	$415
*Fort Myers	Delta 3899/ Delta 462	974	$395

Plotted on the horizontal axis is distance in miles to different cities, the vertical axis is price of flight of the flight to these cities

a. looking at the scatter plot, how is the cost of the trip associated with the distance of the trip

b. use a straight edge to approximate a line of best fit to the data

c. on a scale of 0 to 1 estimate how well the line fits the data. 0= no fit 1= perfect fit. How did we choose the value of 0 or 1

d. Find the equation based on your best fit line.  HINT:  To find the estimated equation, pick two points on the line and plug into    Show your work.   Write your equation in the form,

e

.Now, let’s calculate the least-squares line based on your data.  Show your work.  You can use the following table to assist you or you may use Excel if you are more comfortable with the software. Write your equation in the form, .

x	y	x2	xy	y2

Determine the Sample Correlation Coefficient, .  

Answer 1

a. Scater Plot

(horizontal axis is distance in miles to different cities, the vertical axis is price of flight of the flight to these cities)

Drow a Scater Plot Using Excel is as below,

b. Now, straight edge to approximate a line of best fit to the data is as below,

c. Estimate how well fit the line:

Using Excel we calculate correlation to estimate how well fit the line, So Correlation is 0.85.

d. Find the equation based on your best fit line:

Using Excel we calculate regression to estimate equation is,

Y = 230.292 + 0.175 * X

e. Calculate Coreelation coefficient,

Obs.	X	Y	X^2	XY	Y^2
1	993	328	986049	325704	107584
2	2321	609	5387041	1413489	370881
3	555	508	308025	281940	258064
4	516	205	266256	105780	42025
5	2568	491	6594624	1260888	241081
6	1831	475	3352561	869725	225625
7	744	579	553536	430776	335241
8	4594	1168	21104836	5365792	1364224
9	1350	415	1822500	560250	172225
10	974	395	948676	384730	156025
Total	16446	5173	41324104	10999074	3272975

Formula for calculate Correlation of Coefficient is,

So from the above table by using formula we calculated Correlation of Coefficient is = 0.8534