13. A study was conducted to determine the relation between the (easier to measure) conductivity (S/cm) of surface water and water in the sediment at

13. A study was conducted to determine the relation between the (easier to measure) conductivity (μS/cm) of surface water and water in the sediment at the bank of a river.2 The summary statistics for 10 pairs of surface (X)

and sediment (Y) conductivity measurements are 1

Xi = 3728, 1 Yi = 5421, 1 X2 i = 1816016, 1 Y2 i = 3343359, and 1

XiYi = 2418968, with the X-values ranging from 220 to 800. Assume the regression function of Y on X is linear, and that Var(Y|X = x) is for all x.

(a) Give the LSEs for α1, β1, and σ2

ε .

(b) Construct a 95% CI for the true slope of the regression line. What additional assumptions, if any, are needed for the validity of T CIs for this data set?

(c) Construct a 95% CI for the expected sediment conductivity when the surface conductivity is 500. Repeat the same for surface conductivity of 900. Comment on the appropriateness of the two CIs.