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 accompanying 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.

a. Taking the air pollution index as an independent variable and the number of emergency admissions as a dependent variable, do you expect B to be positive or negative in the regression model y = A + Bx + E?
b. Find the least squares regression line. Is the sign of b the same as you hypothesized for B in part a?
c. Compute r and r2, and explain what they mean.
d. Compute the standard deviation of errors.
e. Construct a 90% confidence interval for B.
f. Test at a 5% significance level whether B is positive.
g. Test at a 5% significance level whether p is positive. Is your conclusion the same as in part f?

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4.6 Air pollution index Emergency admissions 53 3.0 27 4.5 8.2 5.0 82 102 60 39 42