A regression of the number of cases of a particular disease per 1000 people based on the number of people vaccinated against it as children (per 1000) is performed on data collected from 34 cities. The results are summarized below:
Intercept .914
Slope -.001
a. Fill in the blanks of the ANOVA table.
b. What is the predicted number of cases per 1000 population in a city where the vaccination rate is 102 out of 1000?
c. In words, what is the meaning of the coefficient -.001? What does this mean, and
how can it be interpreted in the context of the population being studied?
d. What is the value of the correlation coefficient?
e. What is the standard deviation of the residuals?
a. The TSS is simply the sum of the two other SS values (0.622 + 0.884 = 1.506), while the df values are 1, n-2, and n-2 respectively (1, 33, 34). Dividing through by the df values, the mean squares are 0.622 and 0.884/33 = 0.027. Thus F is 0.622/0.027 = 23.037
b. The predicted solution is found by using the regression equation y = a + bx and substituting the intercept and slope so that an x of 102 is inserted as follows:
y = .914 - 0.001 * x
y = .914 - 0.001 * 102
y = 0.812
Thus we expect an incidence rate of 0.812 cases of the disease per 1000 people in the city.
c. For every vaccination per 1000 people, there will be .001 fewer reported cases. This indicates the value of vaccinating the population, and the expected return per vaccination.
d. The value of r2 is equal to the regression sum of squares divided by the total sum of squares, so that r2 = 0.622 / 1.506 = 0.413
e. The standard deviation of the residuals is equal to the square root of the residual mean square: sqrt(0.027) = 0.164
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