Question: Statistical Concepts Exercise #4 in chapter 20 (pg. 470-471)
You are a production manager interested in the relationship between defect rate and volume at one of your plants. You've taken a random sample of 160 shifts and recorded the percentage of defective items and the volume. Attached is the plot of the two variables and the regression statistics.
a. Is there a relationship between defect rate and volume? If so, is it positive or negative?
b. Which variable is the independent variable and which is the dependent variable?
c. Write out the regression equation and sketch it on the plot.
d. What percentage of the variability in the defect rate can be explained by differences in volume?
e. What defect rate would you predict for a shift with a volume of 4000 units?
f. What defect rate would you predict for a shift with a volume of 9000 units?
g. Would you expect all shifts that produced 4000 items to have the same defect rate?
h. What would you estimate the standard deviation of the distribution of the defect rate to be for a volume of 4000 units?
i. If a particular shift produced 4000 items and had a defect rate of 10% based on the regression model, what would be the residual for the shift?