Questions 1-3. Linear regression

An observational study evaluates the association between air pollution levels and lung function among healthy adults aged 30-70 years old. The researchers use neighborhood monitors to determine the amount of exposure to particulate matter <10 um diameter (PM10). The outcome of the study is the forced expiratory volume in 1 second (FEV1), which describes the volume of air expelled during the first second of exhalation using spirometry. Results are shown below.

	Unadjusted difference in FEV1 (ml)	Adjusted differencea in FEV1 (ml)
Age (per year older)	-30	-2
Male	+800	+820
Current Smoking	-300	-280
Height (per inch taller)	+370	+100
PM10exposure (per 10 ug/m3 greater)	-160	-90

^a Adjusted for all of the characteristics in the table

Question 19.For the linear regression equation describing the unadjusted association between age and FEV1, the value of0(the intercept) is 4400 ml. A 40-year-old person in the study has a measured FEV1 value of 3700 ml. Based on the unadjusted linear regression model, what is the residual for this person? (Show your calculations).

Question 20.Based on the unadjusted regression model relating age with FEV1, the predicted FEV1 value for a newborn (0 years old) is 4400 ml. What is the most likely reason that this predicted value is invalid?

Question 21.What is the interpretation for the adjusted effect of PM10 exposure (per 1 ug/m³greater) on the FEV1? Hint: In the table above, we only have an estimate for PM10 exposure per 10 ug/m³