1. The basal metabolic rate (Kcal/d) and several physical condition indicators of 70 children (aged 10-15 years) were investigated, as shown in Table 15.7. The research objective is to predict the basal metabolic rate using heart rate (beats per minute), blood pressure (mmHg), height (cm), and weight (kg).

(a) Identify the independent and dependent variables.

(b) What are the assumptions for the multivariable linear regression model?

(c) What is the method for estimating the parameters in the model? What is the principle of this method?

(d) Establish a multiple linear regression model for this data.

(e) What is the difference between a simple linear regression coefficient and a partial-regression coefficient? How are they interpreted?

(f) How are the independent variables selected? How do you determine whether a certain variable is significant? Can you tell the difference between different variable selection methods?
(g) Which independent variable has the greatest impact? How do you determine this?
(h) Is the model a good fit? How can you measure and assess goodness-of-fit?
(i) Draw a plot to examine the assumptions for the model. Can you use the plot to assess goodness-of-fit?
(j) Are there any outliers in the data? How do you determine this and how are they handled?
(k) What is multicollinearity? How is multicollinearity identified and how can this issue be handled?