1. Upload the "mortality_data_ver2.csv" data set.

2. Build the plot to look at the relationship between numerical variables.

What will be the dependent variable (outcome), what will be the independent variable (predictor)?

3. Perform multiple linear regression analysis with three independent variables (predictors).

Draw the best-fit regression line between the numerical variables.

4. Check the main assumptions of the model, use the four main plots for checking:

Plot 1.Linearity of the data, independence of residuals

Plot 2.Normality of residuals using Q-Q plot

Plot 3.Constant variance of residuals

Plot 4. No influential outliers

5. The assumption "Normality of residuals" is already checked, normally distributed.

6. After checking all the assumptions, what conclusion can you make? Are they met?

Yes.

7. Obtain parameters of the regression (α, β1, β2, β3); check significance. Fill it in the check
list.

8. Obtain criteria for the model evaluation (Adjusted R-squared, RSE, the 95% confidence
intervals). Fill it in the check list.

9. Fill up the check list.

Check list

                                                                                                                   Model

                               Assumptions after Linear regression:


Plot 1: Linearity of the data, independence of residuals


                                  Plot 2: Normality of residuals

                                   +histogram + normality tests

                                                                                                                    Met

                                      Zero mean of residuals

                                                                                                                    Met

                              Plot 3: Constant variance of residuals


Plot 4: No influential outliers


Results interpretation and model evaluation:


                                   Parameters of the regression:

                                          - intercept (α)

                                           - β1, β2, β3


Significance of β1, β2, β3 and the model



Build the multiple regression formula


                                Criteria for the model evaluation:

                                     Adjusted R^2; RSE; 95% CI





Calculate mortality of a 70 y.o. smoking man.


Calculate mortality of 10 y.o. non-smoking girl.


Calculate mortality of 30 y.o. non-smoking man.


Calculate mortality of 17 y.o. smoking girl.




Check list

                                               Model

                               Assumptions after Linear regression:


                     Plot 1: Linearity of the data, independence of residuals

                                                Met

                                  Plot 2: Normality of residuals

                                   +histogram + normality tests

                                                Met

                                      Zero mean of residuals

                                                Met

                              Plot 3: Constant variance of residuals

                                                Met

                                  Plot 4: No influential outliers

                                                Met

                           Results interpretation and model evaluation:


                                   Parameters of the regression:

                                          - intercept (α)

                                           - β1, β2, β3

α= 50.21,  β1=  0.20, β2= 9.85, β3= 4.78

                             Significance of β1, β2, β3 and the model

                                        All p-values <0.001


                               Build the multiple regression formula

                        Y(mortality)=50.21+0.20*Age+9.85*Smoker+4.78*Gender

                                Criteria for the model evaluation:

                                     Adjusted R^2; RSE; 95% CI

R^2[adj.]= 0.63,  RSE=5.01,

95% CI:  β1 [0.18; 0.22], β2[9.23; 10.47], β3[4.16; 5.40]


                           Calculate mortality of a 70 y.o. smoking man.

Y(mortality)=50.21+0.20*70+9.85*1+4.78*1=78.84

                         Calculate mortality of 10 y.o. non-smoking girl.

Y(mortality)=50.21+0.20*10+9.85*0+4.78*0=52.21

                          Calculate mortality of 30 y.o. non-smoking man.

Y(mortality)=50.21+0.20*30+9.85*0+4.78*1=60.99

                           Calculate mortality of 17 y.o. smoking girl.

Y(mortality)=50.21+0.20*17+9.85*1+4.78*0=63.46