Question

Suppose an article included the accompanying data on airline quality score and a ranking based on the number of passenger complaints per 100,000 passengers boarded. In the complaint ranking, a rank of 1 is best, corresponding to fewest complaints. Similarly, for the quality score, lower scores correspond to higher quality.

Airline	Passenger Complaint Rank	Airline Quality Score
Airtran	6	4
Alaska	2	3
American	8	7
Continental	7	5
Delta	12	8
Frontier	5	6
Hawaiian	3	Not rated
JetBlue	4	2
Northwest	9	Not rated
Southwest	1	1
United	11	9
US Airways	10	10

Two of the airlines did not have an airline quality score. Use the ranks for the other 10 airlines to fit a least-squares regression line. (Let x = passenger complaint rank and y = airline quality score. Round your values to three decimal places.)

ŷ =   + x

Answer 1

Let us put not rated value as 0 and compute the least-square regression line

Sum of X = 78
Sum of Y = 55
Mean X = 6.5
Mean Y = 4.5833
Sum of squares (SS_X) = 143
Sum of products (SP) = 97.5

Regression Equation = ŷ = bX + a

b = SP/SS_X = 97.5/143 = 0.682

a = M_Y - bM_X = 4.58 - (0.68*6.5) = 0.152

ŷ = 0.682X + 0.152