Question

Year   Commodities%   Services%
1960 0.9 3.4
1961   0.6 1.7
1962 0.9    2.0
1963 0.9 2.0
1964 1.2 2.0
1965 1.1 2.3
1966 2.6 3.8
1967 1.9 4.3
1968 3.5 5.2
1969 4.7 6.9
1970 4.5 8.0
1971 3.6 5.7
1972 3.0 3.8
1973 7.4 4.4
1974 11.9 9.2
1975 8.8 9.6
1976 4.3 8.3
1977 5.8 7.7
1978 7.2 8.6
1979 11.3 11.0
1980 12.3 15.4
1981 8.4 13.1
1982 4.1 9.0
1983 2.9 3.5
1984 3.4 5.2
1985   2.1 5.1
1986   -0.9 5.0
1987 3.2 4.2
1988 3.5 4.6
1989 4.7 4.9
1990 5.2 5.5
1991 3.1 5.1
1992 2.0 3.9
1993 1.9 3.9
1994 1.7 3.3
1995 1.9 3.4
1996 2.6 3.2
1997 1.4 3.0
1998 0.1 2.7
1999 1.8 2.5
2000 3.3 3.4
2001 1.0 4.1
2002 -0.7 3.1
2003 1.0 3.2
2004 2.3 2.9
2005 3.6 3.3
2006 2.4 3.8

Use Data Set J, U.S. annual Percent Inflation in Prices of Commodities and Services (n=47), on page 536 of your textbook to answer the following questions. Commodities percentage (Commodities %) is the independent, variable and Services percentage (Services%) is the dependent variable. Data are year-to-year percent changes in the Consumer Price Index (CPI) in these two categories. The data file, Inflation, may be found on Canvas under Modules under Chapter 12 Textbook Data Files. Use MINITAB to obtain the simple regression equation, confidence interval, prediction interval, and required graphs. Insert tables and graphs in your report as appropriate. All interpretations should be in terms of the problem (data).

Use Minitab and produce the appropriate output to answer the following questions. Attach the output. Construct a scatter plot. Recalling what scatter plots are used for, write a couple of sentences addressing what you observed from the plot. Be sure to relate your observations to the purpose of using scatter plots in regression. (4 points)

Can we conclude that year-to-year changes in Commodities percentage (Commodities%) helps in predicting year-to year changes in Services percentage (Services%)? Follow and show the 7 steps for hypothesis testing. (12 points)

Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)

Find the coefficient of determination, and interpret its value. (3 points)

Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)

Estimate with 95% confidence the average year-to-year Services percentage for when all year-to-year Commodities change is 3.0%. Predict with 95% confidence the estimated Services percentage when an individual year’s Commodities change is 3.0%. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (8 points)

Verify that the p-value for the F is the same as the slope’s t statistic’s p-value, and show that t2 = F. (3 points)

Attach or include relevant Minitab output to support your results in parts (1, 2, 3, 4, 5, and 6). (4 points)

Answer 1