# Regression analysis and hypothesis testing problems

Three supplies provide the following data on defective parts.

Part Quality

Supplier / Good / Minor Defect / Major Defect

A / 90 / 3 / 7

B / 170 / 18 / 7

C / 135 / 6 / 9

Use a = .05 and test for the independence between supplier and part quality. What does the result of your analysis tell the purchasing department?

Given are five observations for two variables, x and y.

x / 2 / 3 / 5 / 1 / 8

y / 25 / 25 / 20 / 30 / 16

a. Develop a scatter diagram for these data.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Try to approximate the relationship between x and y by drawing a straight line through the data.

d. Develop the estimated regression equation by computing the values of b_0 and b_1 using (12.6) and (12.7).

e. Use the estimated regression equation to predict the value of y when x = 6.

Airline performance data for U.S. airlines were reported in The Wall Street Journal Almanac 1998. Data on the percentage of flights arriving on time and the number of complaints per 100,000 passengers follow.

Airline / Percentage on Time / Complaints

Southwest / 81.8 / 0.21

Continental / 76.6 / 0.58

Northwest / 76.6 / 0.58

US Airways / 75.7 / 0.68

United / 73.8 / 0.74

American / 72.2 / 0.93

Delta / 71.2 / 0.72

America West / 70.8 / 1.22

TWA / 68.5 / 1.25

a. Develop a scatter diagram for these data.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Develop the estimated regression equation showing how the percentage of flights arriving on time is related to the number of complaints per 100,000 passengers.

d. Provide an interpretation for the slope of the estimated regression equation.

e. What is the estimated number of complaints per 100,000 passengers if the percentage of flights arriving on time is 80%?

#### Solution Preview

Please refer to the attachment.

28. We can use Chi Square Test of Independence. The first step in computing the chi square test of independence is to compute the expected frequency for each cell under the assumption that the null hypothesis is true. To calculate the expected frequency of the first cell in the table, first calculate the proportion of each kind of quality without considering the supplier.

Good: Pg=0.888

Minor Defect: Pn=0.061

Major Defect: Pj=0.052

Supplier Good Minor Defect Major Defect Total

A 90 3 7 100

B 170 18 7 195

C 135 6 9 150

Total 395 27 23 445

Proportion 0.888 0.061 0.052

Then The general formula for expected cell frequencies is:

Eij=Ni * Nj / Nt = Ni*Pj

where Eij is the expected frequency for the cell in the ith row and the jth column, Ni is the total number of subjects in the ith row (i=A,B,C), Nj is the total number of subjects in the jth column, and N is the total ...

#### Solution Summary

The solution addresses regression analysis through hypothesis testing for each of the problems, including scatter plots and conclusions regarding the data.