Question
(a) The XYZ Election Commission maintains data showing the voting age population, the number of registered voters, and the turnout for federal elections. The following table shows the national voter turnout as a percentage of the voting age population from 1972 to 1996.
Year % Turnout Year % Turnout
1972 55 1986 36
1974 38 1988 50
1976 54 1990 37
1978 37 1992 55
1980 53 1994 39
1982 40 1996 49
1984 53
Determine a forecast of the percentage turnout in 1998 by using exponential smoothing with α = 0:1.
(b) The ABC Music Company has been in business for 5 years. During that time, the sale of electric organs has grown from 12 units in the first year to 76 units in the most recent year. The firm's owner wants to develop a forecast of organ sales for the coming year based on the historical data shown below.
Year 1 2 3 4 5
Sales 12 28 34 50 76
(1) Use the method of least squares to develop a straight-line approximation of the relationship between the two variables.
(2) What is the average increase in sales per year for the firm?