Question 1193888: Eight (8) tourists were asked about the airfare expenses and their total
budgeted amount in their last travel/holiday.
Air fare (in $) 200 300 250 100 150 170 180 230
Total Budget (in $) 2500 2800 2100 1200 1800 1900 2000 2700
(a) Draw the scatter plot and the line of best fit. What is the expected budget
for an individual of this group if the airfare to a certain city of her choice is
$140? And what is the expected airfare if her budget is $2,200?
(b) Determine if there is a correlation between the two variables with the
assumption that all travel costs are determined by the travellers’ economic
status. Describe the correlation strength, provide your conclusion, and a
practical recommendation for the airline industry.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The use of software here is strongly recommended. Yes it could be done by hand, but it would take a while.
There are many options to pick from. The option I used is GeoGebra which is free.
The results it states are:
regression line is y = 7.4217x + 659.2081
correlation coefficient is r = 0.8746
Each decimal value mentioned is approximate.
Plug in x = 140 to find that,
y = 7.4217x + 659.2081
y = 7.4217(140) + 659.2081
y = 1,698.2461
y = 1,698.25
This says that if someone spent $140 on airfare, then we predict they would spend about $1,698.25 for their total budget.
Let's reverse the process. Plug in y = 2200 and solve for x.
y = 7.4217x + 659.2081
2200 = 7.4217x + 659.2081
7.4217x + 659.2081 = 2200
7.4217x = 2200- 659.2081
7.4217x = 1540.7919
x = 1540.7919/7.4217
x = 207.606330086099
x = 207.61
If someone had a total budget of $2,200, then we predict that they would have spent about $207.61 on airfare.
Because r = 0.8746 is fairly close to 1, this suggests a strong positive correlation.
There appears to be a strong connection between the amount spent on airfare and the total travel budget.
Intuitively this makes sense: The more someone spends on their flight, the more money they have and probably wanting to spend on other things like hotel or entertainment.
In other words, both variables increase together or decrease together. They move in the same direction.
I'll leave the scatter plot for you to do.
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