Pulmonary Disease
Note: You do not actually have to run analyses to answer these questions. Just interpret the coefficients reported.
The Data Set FEV.DAT on the Companion Website contains pulmonary function measures on 654 children ages 3-19 seen in East Boston, MA as part of Childhood Respiratory Disease (CRD) Study. The dataset contains data on age, sex, height (inches), FEV=volume (liters) of air expelled in 1 second, and smoking status.
We first ran a regression of FEV on smoking shown below.
## ## Call: ## lm(formula = FEV ~ Smoke, data = fev.df) ## ## Residuals: ## Min 1Q Median 3Q Max ## -1.7751 -0.6339 -0.1021 0.4804 3.2269 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 2.56614 0.03466 74.037 < 2e-16 *** ## Smoke1 0.71072 0.10994 6.464 1.99e-10 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.8412 on 652 degrees of freedom ## Multiple R-squared: 0.06023, Adjusted R-squared: 0.05879 ## F-statistic: 41.79 on 1 and 652 DF, p-value: 1.993e-10
The regression coefficient for smoking is 0.7 ± 0.1, p-value
< 0.001.
Does this mean that smokers have higher pulmonary function than
nonsmokers? Why or why not?
Pulmonary Disease Note: You do not actually have to run analyses to answer these questions. Just...
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...
(13 points) Suppose you have a simple linear regression model such that Y; = Bo + B18: +€4 with and N(0,0%) Call: 1m (formula - y - x) Formula: F=MSR/MSE, R2 = SSR/SSTO ANOVA decomposition: SSTOSSE + SSR Residuals: Min 1Q Modian -2.16313 -0.64507 -0.06586 Max 30 0.62479 3.00517 Coefficients: Estimate Std. Error t value Pr(> It) (Intercept) 8.00967 0.36529 21.93 -0.62009 0.04245 -14.61 <2e-16 ... <2e-16 .. Signif. codes: ****' 0.001 '** 0.01 '* 0.05 0.1'' 1 Residual standard...