In an experiment designed to describe the dose-response curve for vitamin K, individual rats were depleted of their vitamin K reserves and then fed dried liver for 4 days at different dosage levels. The response of each rat was measured as the concentration of a clotting agent needed to clot a sample of its blood in 3 minutes. The results of the experiment on 12 rats are given in the following table; values are expressed in common logarithms for both dose and response.
a. Determine the least-squares estimates of the slope (β1) and the intercept (β0) for the straight-line regression of Log10 concentration (Y) on Log10 dose (X).

b. Draw the estimated regression line on the accompanying scatter diagram. How well does this line fit the data?
c. Determine and sketch 95% confidence bands based on the estimated regression line.
d. Convert the fitted straight line into an equation in the original units Yʹ = 10Y and Xʹ = 10X.
e. For the converted equation obtained in part (d), determine 99% confidence intervals for the true mean responses at the maximum and minimum doses used in the experiment.
f. if the values for X and Y on each rat are converted to their original units Xʹ and Yʹ, the following fitted straight line is obtained: Yʹ = 237.16095 - 21.32117Xʹ. How would you evaluate whether using the variables Xʹ and Yʹ is better or worse than using X and Y for the regression analysis?

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Rat Logio Concentration (r) Logio Dose (A) 2.65 2.25 1.95 1.72 1.60 1.55 1.32 1.13 1.07 0.95 0.88 0.18 0.33 0.42 0.54 0.65 0.75 0.83 0.92 1.01 1.04 1.09 E 1.5 0.5 0 0 0.2 0.4 0.6 8 1.2 Logio dose (0)