The accompanying table gives the dry weights (Y) of 11 chick embryos ranging in age from 6 to 16 days (X). Also given in the table are the values of the common logarithms of the weights (Z).

a. Observe the following two scatter diagrams. Describe the relationships between age (X) and dry weight (Y) and between age and log10 dry weight (Z).

b. State the simple linear regression models for these two regressions: Y regressed on X and Z regressed on X.
c. Determine the least-squares estimates of each of the regression lines in part (b).
d. Sketch each estimated line on the appropriate scatter diagram. Which of the two regression lines has the better fit? Based on your answers to parts (a)-(c), is it more appropriate to run a linear regression of Y on X or of Z on X? Explain.
e. For the regression that you chose as being more appropriate in part (d), find 95% confidence intervals for the true slope and intercept. Interpret each interval with regard to the null hypothesis that the true parameter is 0.
f. For the regression that you chose as being more appropriate in part (d), find and sketch 95% confidence and prediction bands. Using your sketch, find and interpret an approximate 95% confidence interval for the mean response of an 8-day-old chick.

Transcribed Image Text:

Age (X) (days) Dry Weight (n Logio Dry Weight () 5381.284 02 0 Age 0 (days) 10 0.181 -0.903-0.742-0.583 16 0.052 0.125 0.261 12 13 14 15 0.425 0.738 1.130 Logio Dry Weight ()-.320.13 3 0.5 0.449 10 Age (x) 15 20 0.51 Age 0) 10 15 -0.5