Chapter 7, Problem 42E

(a)

To determine

To find the correlation between the flights with year.

Answer to Problem 42E

The correlation between flights with year is $0.8275$ .

Explanation of Solution

The number of flights by U.S. airlines has grown rapidly and the number of flights flown in each year from $1995\text{ to 2005}$ is given in the question as:

Year	Flights
1995	53,27,435
1996	53,51,983
1997	54,11,843
1998	53,84,721
1999	55,27,884
2000	56,83,047
2001	59,67,780
2002	52,71,359
2003	64,88,539
2004	71,29,270
2005	71,40,596

We will be calculation the correlation between the year and fights by using excel. That is,

Formula used:

The CORREL function calculates the correlation coefficient between the two data sets in the excel. The syntax is as:

CORREL(array $1$ ,array $2$ )

Calculation:

Now, we will calculate the correlation coefficient using the excel. We will use the above CORREL function for this and we will have,

  $=\text{CORREL}\left(\text{G8:G22,H8:H22}\right)$

And the answer to this will be as:

Correlation coefficient

0.8275

So, the correlation between flights with yearis $0.8275$ .

(b)

To determine

To make a scatterplot and describe the trend.

Explanation of Solution

The scatterplot between the flights and the year is as follows:

  

The number of flights is on the vertical axis and the year is on the horizontal axis. From the scatterplot on the above, we can say that the points are moving upwards and is positive. Thus, the association is positive and we can also see that the number of flights are increasing over the years or as the time increases.

(c)

To determine

To note two reasons that the correlation you found in part (a) is not suitable summary of the strength of the association and can you account for these violations of the conditions.

Answer to Problem 42E

First is in the year $2002$ , number seems to be an outlier and second is in the year $1995\text{ to 1998}$ number of flights seems to be just flat and not really growing.

Explanation of Solution

The number of flights by U.S. airlines has grown rapidly and the number of flights flown in each year from $1995\text{ to 2005}$ is given in the question. And the correlation between flights with year is $0.8275$ . The two reasons that the correlation we found in part (a) is not suitable summary of the strength of the association are first is in the year $2002$ , number seems to be an outlier and second is in the year $1995\text{ to 1998}$ number of flights seems to be just flat and not really growing. Yes, we can account for these violations of the conditions.