A data set obtained to study lung function includes the following variables. Thr
ID: 3133417 • Letter: A
Question
A data set obtained to study lung function includes the following variables.
Three additional models were also examined.
1. Are Models 3 and 4 consistent with Model 2? How, in particular, can it make sense that Model 4 has a positive slope for bmp, while Model 2 has a negatuve partial slope for bmp, as well as a much smaller p-value for that partial slope? The plot on the next page may help explain the answer.
pemax maximum expiration pressure (cm H,O) height: height in centimeters weight: weight in kilograms bmp: body mass (weight/height') as percent of median for age The goal was to model pemax in terms of the three other variables. Here is the scatterplot matrix of the data, including histograms of each variable and pairwise least squares fits.Explanation / Answer
let we take the level of significance alpha=0.05
Models 3 and 4 are consistent with model 2.
In model 2 , weight has significant regression (partial slope) where as bmp doesnot.
in model 3 , weight has the significant regression coefficient
in model 4, bmp does not have the significant regression coefficient.
so models 3,4 are consistent with model 2.
answer of second part
in the model 4 only bmp is regressed on pemax and showing positive partial slope due to positive correation with pemax.
in the model 2 weight and bmp simultanously regressed on pemax, and the partial regression coefficent became negative due to presence of wight in this model.