Ozone (O3) is a major component of air pollution in many cities. Atmospheric ozone levels are influenced by many factors, including weather. In one study, the mean percent relative humidity (x) and the mean ozone levels (y) were measured for 120 days in a western city. Mean ozone levels were measured in ppb. The following output (from MINITAB) describes the fit of a linear model to these data. Assume that assumptions 1 through 4 on page 540 hold The regression equation is
Ozone = 88.8 - 0.752 Humidity
Predictor Coef SE Coef T P
Constant 88.761 7.288 12.18 0.000
Humidity -0.7524 0.13024 -5.78 0.000
S = 11.43 R-Sq = 22.0% R-Sq(adj) = 21.4%
Predicted Values for New Observations
New Obs Fit SE Fit 95.0% CI 95.% PI
1 43.62 1.20 (41.23 46.00) (20.86, 66.37)
Values of Predictors for New Observations
New Obs Humidity
1 60.0
a. What are the slope and intercept of the least-squares line?
b. Is the linear model useful for predicting ozone levels from relative humidity? Explain.
c. Predict the ozone level for a day when the relative humidity is 50%.
d. What is the correlation between relative humidity and ozone level?
e. The output provides a 95% confidence interval for the mean ozone level for days where the relative humidity is 60%. There are n = 120 observations in this data set. Using the value "SE Fit," find a 90% confidence interval.
f. Upon learning that the relative humidity on a certain day is 60%, someone predicts that the ozone level that day will be 80ppb. Is this a reasonable prediction? If so, explain why. If not, give a reasonable range of predicted values.