Question

A regional airline transfers passengers from small airports to a larger regional hub airport. The airline data analyst was assigned to estimate the revenue ( in thousands of dollars) generated by each of the 22 small airports based on two variables: the distance from each airport ( in miles) to the hub and the population ( in hundreds) of the cities in which each of the 22 airports is located. The data is given in the following table.

Airport revenue         distance         population

1          233                 233                 56

2          272                 209                 74

3          253                 206                 74

4          296                 232                 78

5          268                 125                 73

6          296                 245                 54

7          276                 213                 100

8          235                 134                 98

9          253                 140                 95       

10        233                 165                 81

11        240                 234                 52

12        267                 205                 96

13        338                 214                 96       

14        243                 183                 73

15        252                 230                 55

16        269                 238                 91

17        242                 144                 64

18        233                 220                 60

19        234                 170                 60

20        450                 170                 240    

21        340                 290                 70

22        200                 340                 75                   

1. Using PROC CORR in SAS, create a matrix of scatter plots for revenue, population, and distance. Include this graph in your LATEX document.
2. From your scatter plots in part (a), is there a data point that you think may be an “issue” for analysis?
   
3. Construct and report a multiple regression model relating :
             revenue (y)
            distance (x1)
            population (x2)
             using SAS.
   
4. Construct the 95% confidence interval for β1 by hand. (Use βˆ1 and the standard error calculated by SAS.)

Answer 1

From your scatter, plots in part (a), is there a data point that you think may be an “issue” for analysis?

Yes, there are some outliers in the data, which need to be removed. We are creating a model without removing them.

The 95% confidence interval of beta_1 is given by