Question

How do I interpret the p-values in terms of rejecting or failing to reject H0 at a 95% confidence level? What does the intercept column mean in terms of p-value? How does the p-value of the F test compare and what does it mean? In the simple linear regression I'd conclude age isn't related to pulmonary disease (what does intercept p-value mean) but for the multiple regression I'd say age and height aren't related to pulmonary disease but smoking is related to pulmonary disease. My stats prof says I have it backwards but I don't know why.

summary(fit) Call: Im(formula = fev ~ age) Residuals: Min 1Q Median -1.57539 -0.34567 -0.04989 3Q 0.32124 Max 2.12786 Coefficients: Estimate Std. Error t value Pr( t) (Intercept) 0.431648 0.0778955.541 4.36e-08 ** age 0.222041 0.007518 29.533 < 2e-16 *** Signif. codes: (***) 0.001 (**) 0.01 (*) 0.05.' 0.1'' 1 Residual standard error: 0.5675 on 652 degrees of freedom Multiple R-squared: 0.5722, Adjusted R-squared: 0.5716 F-statistic: 872.2 on 1 and 652 DF, p-value: < 2.2e-16

Answer 1

Defination: The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect of the variable). A low p-value (< 0.05 in this case) indicates that you can reject the null hypothesis and by saying reject the null hypothesis, we mean that if we have enough evidence to reject the null hypothesis then we can say the variables are significant and can be considered in the model.

1. Now, if p-value is less than 0.05, we may reject our null hypothesis, and conclude that the variables are statistically significant.

2. The intercept (often labeled the constant) is the expected mean value of Y when all X=0. In regards to above equation:

i. For simple linear regression, the p-value is less than 0.05, which indicates that your intercept is statistically significant.

ii. For multiple linear regression, the p-value is less than 0.05, which says that your intercept is statistically significant.

3. Compare the p-value for the F-test to your significance level (0.05 in this case). If the p-value is less than the significance level, your sample data provide sufficient evidence to conclude that your regression model fits the data better than the model with no independent variables (age, height, smoke etc).

This finding is good news because it means that the independent variables in your model improve the fit!

4. In simple linear regression, we would conclude that the age variable is a significant variable as its p-value is less than the given level of significance i.e. 0.05.

5. In multiple linear regression, we would conclude that the age and height are the significant variables as its p-value is less than the given level of significance i.e. 0.05.

Note: You can also check the significance by seeing the asterisk mark. As 3 asterisk mark says the variable is significant.