Holding real income of the employed constant, an increased number of people will

Question

Holding real income of the employed constant, an increased number of people will believe future prospects to have diminished and will commit suicide." As a crude test of their hypothesis we can estimate the equation where suicide() is the number of suicides per 100,000 population in year i, unemployment(i is the unemployment rate in year i, and u(i) is the error term. suicide, = 0 + 1 unemployment, + ui Data from 1968-1978 are given: year suicide rate per 100,000unemployment rate 196810.7 97011.5 97111.7 197212.0 197312.0 197412.1 197512.7 197612.5 197713.3 197812.5 3.6 3.5 4.9 5.9 5.6 4.9 5.6 8.5 7.7 7.0 6.0 a. Compute the Ordinary Least Squares estimate of parameter B(O) and B(1) b. How would these coefficients change if suicide rates were reported per 1000 population? c. Calculate the predicted suicide rates for each year. Calculate the estimated error for each year. d. What is the average estimated error? Why? e. The unemployment rate was 5.8 in 1979. Based on your estimates, what suicide rate would you have expected that year?

Explanation / Answer

(a) To calculate the ordinary least square regression equation we need x, y, xy, x2 , y2

where x is the unemployment rate and y is the suicide rate per 100,000

THe table given below

Here n = 11

so lets say line equation is y = a +bx

and a and b = line constants.

so by formulas

a = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = (132.1 * 387.3 - 63.2 * 768.81)/ (11 * 387.3 - 63.22)

a = 2573.538/ 266.06 = 9.67

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [11 * 768.81 - 63.2 * 132.1]/ [11 * 387.3 - 63.22]

b = 108.19/ 266.06 = 0.406

so linear line equation

y^ = 9.672 + 0.406 x

(b) If suicide rate were reported per 1000 population.

Then each coefficients will be multiplied by 1000.

SO a (new) = 406 and b(new) = 9672

(c) THe predicte sucide rate for each year and its estimated error and sum of that error is given below in the table.

Estimated error for the each year is calculated above.

(d) Average estimated error = 0

It is because that the least square regression equation makes total residual error 0.

(e) Employment rate = 5.8

so y(1979) = 0.406 * 5.8 + 9.672 = 12.027 per 100,000 population.

Year Unemployment rate(x) Suicide Rate per 100,000(y) x^2 xy 1968 3.6 10.7 12.96 38.52 1969 3.5 11.1 12.25 38.85 1970 4.9 11.5 24.01 56.35 1971 5.9 11.7 34.81 69.03 1972 5.6 12 31.36 67.2 1973 4.9 12 24.01 58.8 1974 5.6 12.1 31.36 67.76 1975 8.5 12.7 72.25 107.95 1976 7.7 12.5 59.29 96.25 1977 7 13.3 49 93.1 1978 6 12.5 36 75 Sum 63.2 132.1 387.3 768.81

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