Question

The health department of a large city has developed an air pollution index that measures the level of several air pollutants that cause respiratory distress in humans. The following table gives the pollution index (on a scale of 1 to 10, with 10 being the worst) for 7 randomly selected summer days and the number of patients with acute respiratory problems admitted to the emergency rooms of the city’s hospitals.

Air pollution index 4.5 6.7 8.2 5.0 4.6 6.1 3.0

Emergency admissions 53 82 102 60 39 42 27

Taking the air pollution index as an independent variable x and the number of emergency admissions as a dependent variable y, we assume a probabilistic linear regression model given by y = a + bx + ε.

(a) Compute the least squares estimates ˆ a and ˆ b for a and b, respectively.

(b)Compute SSE, i.e., the minimum achieved sum of squares of errors.

Answer 1