The management of JAL Airlines wants to determine if there is a
linear relationship between advertising expenditures
and the number of passengers who choose to fly JAL.
The following data is collected over the past 15 months of
performance by JAL Airlines.
Note that ADEXP represents Advertising Expenditures in $1,000s, and
Passengers is the
number of passengers in 1,000s).
ADEXP |
PASSENGERS |
100 |
15 |
120 |
17 |
80 |
13 |
170 |
23 |
100 |
16 |
150 |
21 |
100 |
14 |
140 |
20 |
190 |
24 |
100 |
17 |
110 |
16 |
130 |
18 |
160 |
23 |
100 |
15 |
120 |
16 |
a) Find the regression equation relating Passengers to ADEXP.
b) Calculate the correlation coefficient, accurate to three decimal places
c) Test the significance of the correlation coefficient with a
0.05 level of significance.
Include definition of hypotheses, test statistic, p-value or
critical value, decision about Ho, and conclusion.
d) What is the best estimate for number of passengers when $125,000 is spent on ads?
Suppose, random variables X and Y denote expenditure (in thousand dollars) in advertisements and number of passengers who choose to fly JAL Airlines respectively.
(a)
Regression equation of y on x is given by
Here,
Number of pairs of observation
(b)
Correlation coefficient is given by
(c)
We have to test for null hypothesis
against the alternative hypothesis
Our test statistic is given by
Here,
Sample size
Sample correlation coefficient is given by
Degrees of freedom
[Using R-code 'pt(-13.99492,13)+1-pt(13.99492,13)']
Level of significance
We reject our null hypothesis if
Here, we observe that
So, we reject our null hypothesis.
Hence, based on the given data we can conclude that there is significant evidence that there is a linear relationship between advertising expenditures and the number of passengers who choose to fly JAL.
(d)
For
, predicted number of passengers is given by
Hence, best estimate for number of passengers is 18.
The management of JAL Airlines wants to determine if there is a linear relationship between advertising...
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