Air pollution isone of the most pressing environmental and health issues across OECD countries and beyond.Fine particulate matter (PM2.5) is the air pollutant that poses the greatest risk to health globally, affecting more people than any other pollutant (WHO, 2018). Chronic exposure to PM2.5 considerably increases the risk of respiratory and cardiovascular diseases in particular (WHO, 2018). For these reasons, population exposure to (outdoor or ambient) PM2.5 has been identified as an OECD Green Growth headline indicator. We are interested in the relationship between PM2.5 exposure and economic, environmental factors and collected data from 34 countries.

Y-Mean population exposure to PM2.5

X1-CO2 emissions from fuel combustion

X2-Employment rates: total

X3-Real GDP growth

X4-Total FDI Index

X5-Gross domestic expenditure on R&D

X6-Greenhouse gas emissions

X7-Contribution of renewables to energy supply

X8-GDP per capita

X9-Unemployment rates: total

X10-Production of crude oil

Use specific statistical procedures and/or measures to answer the questions below. Throughout the questions, use significance level as .05.

A.We will fit multiple linear regression model with response variable Y (PM2.5 exposure) and explanatory variables X1-X10.

1.Obtain matrix scatter plot to check the linear relationship between Y and X1-X10 as a preliminary step. Attach the plot.

2.Fit multiple regression model with the response Y and explanatory variables X1-X10. Write the fitted model equation.

3.Is the linear model fitted above significant in explaining PM2.5 exposure? (Provide specific statistical procedure and/or measures to answer the question.)

4.Which explanatory variable(s) is (are) significant, even after accounting for all other variables in the model? (Provide specific statistical procedure and/or measures to answer the question.)

5.Does multicolinearity present within explanatory variables? If so, which variable(s) is (are) highly correlated with all other explanatory variables? (Provide specific statistical procedure and/or measures to answer the question.)

6.From the Minitab results above, Amy who is involved in this project thinks that only variables X2 and X9 should be included in the model to explain Y. Do you agree with it or not? Explain why you think that way.

7.From the Minitab results above, Alex who is involved in this project thinks that all the explanatory variables should be included in the model. Do you agree with it or not? Explain why you think that way.

8.Do you see any improvement(s) you can make in the model before choosing subset or all of (X1,..,X10) based on the scatter plots in 1? State a list of action(s) you would do to make an improvement and what you would see as a result.

B.Regardless of answers in 6-8, we will fit a new model with X2 and X9 as explanatory variables and Y and the response.

9.Is the new model significant in explaining PM 2.5? (Provide specific statistical procedure and/or measures to answer the question.)

10.List all explanatory variable(s), if there is any, that is(are) significant even after accounting for all other variables in the model. No need to explain it.

11.Now we will compare the two models, the full model in part A and the reduced model in part B.

i.Is the full model significantly better than the reduced model? (Carry out partial F-test with 5% significance level.)

ii.Compare S(=sqrt(MSE)) and adjusted R-squared of the two models.

12.Based on your answers in 9-11, what would be your next step in modeling multiple linear regression?