Question

In: Statistics and Probability

Destination Departing Flight Numbers (list all departing flight segments) Distance (round to nearest mile) Amount Miami...

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, .  

Solutions

Expert Solution

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


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