Please find the classification of correlation type for the data and come to a conclusion

The data used is about civil aviation of Canadian air carriers.

Two data sources where used and they where matched to each other using the year.

Data source for Income:

https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=2310003401

Data source for passengers and goods

https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=2310003301

Compiled Data from two data source

(The maximum data available in the given site was from 2012 to 2020)

Year	Passengers (x1000)	Goods (x1000)	Revenue
2012	66867	747275	20343071
2013	67991	720872	20816397
2014	72236	736764	22309270
2015	76216	696491	22832738
2016	81872	758425	23230889
2017	88416	881191	25548635
2018	93337	969457	27970817
2019	94132	979161	29493379
2020	28437	936903	12223233

Thedependent variableis theRevenue.This is selected as the main dependent variable is because the final objective of any aviation company is to maximise it's revenue. Also, the revenue is depended on other factors.

TheIndependent VariablesarePassengersandGoods. It is the basic understanding that the number of passengers and goods transported by a carrier an independent factor. Even though marketing and other activities can have some influence in improving or reducing these counts, at the end it is the customer who decides the counts of this. Also, the revenue of a carrier is very highly depended on the number of passengers and goods it transport.

	Passengers (x1000)	Goods (x1000)	Revenue
Mean	74389.33	825171	22752047.67
Median	76216	758425	22832738
Variance	402329912.5	13241135863	25167463074589
Standard Deviation	20058.16	115070.13	5016718.36
Max	94132	979161	29493379
Min	28437	696491	12223233

Standard deviation gives the measure of spread of data from the mean. we can see this in a better way if we find 2*SD as a percentage of the total range.

	Passengers (x1000)	Goods (x1000)	Revenue
2*SD	40116.32	230140.26	10033436.72
2*SD/(Max-Min) (%)	61.06	81.42	58.1

Analysis on central tendency

• Passengers
  • The mean and median are similar, suggesting a higher central tendency
  • The standard deviation and the 2SD/range suggest that the spread of passengers is not too less nor too much.
  • This suggest that the passenger distribution is cantered around the mean of 74389.33 with a reasonable spread
• Goods
  • The goods have a slightly different median and mean.
  • The standard deviation is also quite high suggesting a very wide spread in the goods count.
  • From the difference in mean and median and the very high spread it can be said that the goods is almost uniformly distributed. That is the central tendency is less.
• Revenue
  • The mean and median of revenue is very similar
  • The standard deviation of the revenue a bit too high
  • The revenue tend to have a good central tendency with a high spread.

Explanation:

Correlation	Passengers	Goods
Revenue	0.981623104	0.2506799405

The correlation of Revenue with Passenger is close to positive 1. This suggest a strong positive correlation. This means the higher the number of passenger the higher the revenue will get.

The correlation of revenue with Goods is very week positive. This suggest that the change in goods wont have a significant effect in revenue. The slight effect that the goods number have is, when goods increases the revenue increases slightly.

Regression Analysis

Passenger and Revenue

Regression Statistics
Multiple R	0.981623104
R Square	0.9635839183
Adjusted R Square	0.9583816209
Standard Error	1023439.797
Observations	9

ANOVA
	df	SS	MS	F	Significance F
Regression	1	194007701464798	194007701464798	185.2227673	0.000002720850255
Residual	7	7332003131912	1047429018845
Total	8	201339704596710

	Coefficients	Standard Error
Intercept	4488548.173	1384635.247
Passengers (x1000)	245.5123426	18.03956854

This means the equation of revenue if revenue( y) and passenger( x) will be

y=245.51x+4488548.17

Here the intercept is 4488548.173. This is the revenue even when there is no passengers. The coefficient of passenger that is 245.51 is the average increase in revenue per 1000 passenger.

Goods

Regression Statistics
Multiple R	0.2506799405
R Square	0.06284043257
Adjusted R Square	-0.07103950563
Standard Error	5191853.928
Observations	9

ANOVA
	df	SS	MS	F	Significance F
Regression	1	12652274130936	12652274130936	0.4693790079	0.5153113164
Residual	7	188687430465774	26955347209396
Total	8	201339704596710

	Coefficients	Standard Error
Intercept	13733831.55	13276397.87
Goods (x1000)	10.92890579	15.95198934

This means the equation of revenue if revenue( y) and goods( x) will be

y=10.93x+13733831.55

Here the intercept is 13733831.55 .This is the revenue even when there is no goods. The coefficient of goods that is 10.93 is the average increase in revenue per 1000 goods.

Passenger
Observation	Predicted Revenue	Absolute Residual
1	20905221.99	562150.9879
2	21181177.86	364780.8611
3	22223377.76	85892.24447
4	23200516.88	367778.8792
5	24589134.69	1358245.689
6	26195767.46	647132.4593
7	27403933.7	566883.3026
8	27599116.01	1894262.99
9	11470182.66	753050.3395

Goods
Observation	Predicted Revenue	Absolute Residual
1	21900729.62	1557658.621
2	21612173.72	795776.722
3	21785855.89	523414.1073
4	21345716.07	1487021.93
5	22022586.92	1208302.079
6	23364284.97	2184350.031
7	24328935.77	3641881.233
8	24434989.87	5058389.131
9	23973156.17	11749923.17

The highest absolute residual points in Passenger regression is the 8th observation corresponding to year 2019 and in case of goods regression it is 9th observation corresponding to 2020.

let us remove both of them and perform a new regression (regression statistics for this will only be given in the link of google sheet provided as this platform cannot support too much text here)

New Regression after removing the high residual entry

Passenger

New Equation: y=230.38x+5340168.80

Goods

New Equation: y=27x+2163309.77

Both the regression improved after removing these points.

From the analysis we can conclude that the passenger count have the highest influence on the revenue with a high positive correlation value of 0.981623104 while the goods count have very little influence on revenue. with a very week correlation of 0.2506799405.

Link to the sheets with calculations

Link1: https://docs.google.com/spreadsheets/d/1NycpvIEaCE6oSU0A4y38HPwBHDZJz7UaPkqJ8vpqTXM/edit?usp=sharing

Link2: https://docs.google.com/spreadsheets/d/1J_SznEL8_vjJxGbSddktKNYYyXF8gmf9h6t3Au0oKjg/edit?usp=sharing

Link 3:

https://docs.google.com/spreadsheets/d/13W49cMwuVCfrJ4eQW_m_K7h8y5PfHUXgWi0Gk9DiBxg/edit?usp=sharing