A data related to air pollution in 10 U. S. cities. The dependent variable Y is the annual mean concentration of sulfur dioxide, in micrograms per cubic meter. The explanatory variable X records the number of manufacturing enterprises employing 20 or more workers. Below is R output of the relationship between X and Y. Coefficients:
Estimate Std. Error t value Pr(> |tl)
(Intercept) 9.4764 9.6266 0.98 0.354
x 2.0315 0.0070 4.51 0

Required:
a. Write the regression equation with parameters from the R output.
b. Suppose that the number of manufacturing enterprises employing 20 or more workers in Irvine is 250, could you predict that the annual mean concentration of sulfur dioxide in Irvine?
c. What is the residual if in Irvine the annual mean concentration of sulfur dioxide is 15 micrograms per cubic meter.
d. What is the value of the correlation coefficient?
e. Calculate a 95% confidence interval for the slope of the model.
f. Based on the confidence interval, is there a linear relationship between X and Y?