Each month, the Bureau of Labor Statistics (BLS) of the U.S. Department of Labor announces the total number of employed and unemployed persons in the United States for the previous month. At the same time, it also publishes the inflation rate, which is the rate of change in the price of goods and services from one month to the next. It seems quite plausible that there should be some relationship between these two indicators. The file titled CPI provides the monthly unemployment and inflation rates for the period 2000 through 2005.
a. Construct a scatter plot of the unemployment rate versus inflation rate for the period 2000 through 2005. Describe the relationship that appears to exist between these two variables.
b. Produce a 95% prediction interval for the unemployment rate for the maximum inflation rate in the period 2000 through 2005. Interpret the interval.
c. Produce a 95% prediction interval for the unemployment rate when the inflation rate -is 0.00.d. Which of the prediction intervals in parts b and c has the larger margin of error? Explain why this is the case.