1. To explore the relationship between weight and transverse cardiac diameter among children, the weight (kg) and transverse cardiac diameter (cm) data were obtained from 13 healthy 7-year-old boys. The data are given in Table 13.3.

Please answer the following questions:

(a) What are the dependent variable y and independent variables x in this study?

(b) Draw a scatterplot of x and y. Determine whether a linear regression line is appropriate for depicting the relationship between x and y.

(c) Provide H0 and H1 if the researcher would like to investigate the linear dependency between the weight and transverse cardiac diameter.

(d) What is the method for estimating the parameters in the regression equation?

What is the basic rationale of this method?

(e) Perform a regression analysis, construct the regression equation, and explain the meaning of slope of the regression equation.

(f) Based on the above result, draw a regression line on the scatterplot obtained in (b).
(g) Construct the 95% CI of regression coefficient  . How do you interpret its meaning in this case?
(h) Perform hypothesis testing of the regression equation using the t-test and F-test . How are these two test statistics related? Are the conclusions the same?
(i) What is the coefficient of determination? Calculate and interpret the coefficient of determination in this case.
(j) Draw a residual plot and use it to judge whether the assumptions for the linear regression analysis are satisfied.
(k) What are Sy ,Syx , and how do they differ? Interpret the difference with reference to the plot drawn in (f).