# Question

A physiologist wishes to investigate the relationship between the physical characteristics of preadolescent boys and their maximum oxygen uptake (measured in milliliters of oxygen per kilogram of body weight). The data below (saved in the BOYS10 file) were collected on a random sample of 10 preadolescent boys.

a. Fit the regression model

y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε

to the data, and give the least squares prediction equation.

b. It seems reasonable to assume that the greater a child’s weight, the greater should be the maximum oxygen uptake. Is β3, the estimated coefficient of weight x3, positive as expected? Give an explanation for this result.

c. It would seem that the chest depth of a child should be positively correlated with lung volume and hence to maximum oxygen uptake. Is β4 significantly different from 0, as expected? If not, explain why.

d. Calculate the correlation coefficients between all pairs of the independent variables x1-x4. Do these correlations provide an explanation for the confusing signs and small t-values associated with the estimated regression coefficients of the model?

a. Fit the regression model

y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε

to the data, and give the least squares prediction equation.

b. It seems reasonable to assume that the greater a child’s weight, the greater should be the maximum oxygen uptake. Is β3, the estimated coefficient of weight x3, positive as expected? Give an explanation for this result.

c. It would seem that the chest depth of a child should be positively correlated with lung volume and hence to maximum oxygen uptake. Is β4 significantly different from 0, as expected? If not, explain why.

d. Calculate the correlation coefficients between all pairs of the independent variables x1-x4. Do these correlations provide an explanation for the confusing signs and small t-values associated with the estimated regression coefficients of the model?

## Answer to relevant Questions

Surface albedo is defined as the ratio of solar energy directed upward from a surface over energy incident upon the surface. Surface albedo is a critical climatological parameter of sea ice. The National Snow and Ice Data ...The Journal of Natural History (May 2010) published the results of a study that investigated which of six species of slime molds are most attractive to beetles inhabiting an Atlantic rain forest. A sample of 19 beetles ...Refer to Exercise. Convert the responses to percent ages by calculating the percentage of each B class total falling into each A classification. Also, calculate the percentage of the total number of responses that constitute ...You solved the game show problem of whether or not to switch your choice of three doors, one of which hides a prize, after the host reveals what is behind a door that is not chosen. (Despite the natural inclination of many ...The National Gang Crime Research Center (NGCRC) has developed a six-level gang classification system for both adults and juveniles. The six categories are shown in the accompanying table. The classification system was ...Post your question

0