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?