Pr1. Time Series.						Written 20%
						Test Grade
The data in the table below represent the annual revenues(in billion of dollars)
of McDonald's Corporation over the period from 1975 to 2012.
Year	Revenues
1975	1
1976	1.2
1977	1.4
1978	1.7
1979	1.9
1980	2.2
1981	2.5
1982	2.8
1983	3.1
1984	3.6
1985	3.8
1986	3.9
1987	4.9
1988	5.2
1989	5.9
1990	6.4
1991	6.7
1992	7
1993	7.4
1994	8.3
1995	9.8
1996	10.7
1997	11.4
1998	13.4
1999	14.5
2000	15.6
2001	14.9
2002	15.4
2003	17.1
2004	19
2005	20.5
2006	19.3
2007	22.4
2008	24.5
2009	23.6
2010	24.1
2011	29.5
2012	26.7
a) Calculate a five-year moving average to the data (add a column to the table)
b) Using a smoothing coefficient of W = 0.45, exponentially smooth the series
(add a column to the table, use data analysis to smooth)
c) Plot the results from a) and b) with the time series on a scatter plot.
d) Compute a quadratic trend forecasting equation and plot the predicted result with the data against the coded years.
e) Compute an exponential trend forcasting equation and plot the predicted results with the data against the coded years.
f) Compute a second -order autoregressive model, test for the significance of the second-order
autoregressive parameter, and plot the predicted results with the data against the coded years.
g) Ifnecessary, compute a first-order autoregressive model, test for the significance of the first-oder
autoregressive parameter, and plot the predicted results with the data against the coded years.
h) predict the values for years 2013 and 2014 using the best model out of d and e.
And the apropriate autoregressive model of f) or g).
Pr2 Simple Linear Regression.
The owner of a chain of ice cream store would like to study
the effect of atmosperic temperature on sales during the summer season.
A sample of 24 consecutive days is selected, with the results stored in the table below
Sales, in thousand of $	Temperature, in degrees
1.52	63
1.68	70
1.8	73
2.05	75
2.68	88
2.25	82
2.68	85
2.9	88
3.5	95
3.06	91
3.24	92
1.92	75
3.4	98
3.28	100
3.17	92
2.83	87
2.31	82
2.86	88
2.26	80
2.14	82
1.98	76
1.89	74
2.1	75
2.71	85
a) Construct a scatter diagram
b) Using Data Analysis/Regression, find the regression coefficients b0 and b1.
c) Graph the regression line on the scatter diagram
d) Interpret the meaning of b0 and b1 in this problem.
e) Predict the sales per store for a day in which the temperature is 83F.
f) determine the coefficient of determination and interpret its meaning.
(short way from the data analysy SS columns)
g) Graph the residuals in this model and determine
if the linear model is appropriate.
h) At the 0.05 level of significance, is there evidence
of a linear relationship between sales and temperature?
(based on t-test, p-value, and confidence interval for the slope)
Pr3. Anova one factor
In order to test the strength of four brands of trash bags,
one-pound weights were placed into bags, one at a time
until the bag broke.
A total of 50 bags, 10 of each brand, were used. The data in the table below
gives the weight required to break the trash bag.
KROGER	GLAD	HEFTY	TUFFSTUFF	WAND
34	32	33	38	36
30	50	34	29	29
44	40	32	20	29
38	40	40	35	28
36	32	40	20	34
31	48	34	19	29
34	39	36	31	30
42	43	36	35	36
37	38	32	29	30
38	38	37	20	25
a) Using Data analysis/Anova, test at the level of significance 0.05 for the evidence
of the difference in the mean strength of the five brands of trash bags .
(Short solution using Data Analysis only)
b) If appropriate, determine which brands differ in mean strength
Use Tukey-Kramer procedure.
c) Rank the means