Consider the regression model fit to the shear strength of soil in Exercise 12-5.

(a) Calculate 95% confidence intervals on each regression coefficient.

(b) Calculate a 95% confidence interval on mean strength when x₁ = 18 ft and x₂ = 43%.

(c) Calculate 95% prediction interval on strength for the same values of the regressors used in the previous part.

Exercise 12-5

A study was performed to investigate the shear strength of soil (y) as it related to depth in feet (x₁) and percent of moisture content (x₂ ). Ten observations were collected, and the following summary quantities obtained: 

n = 10, Σx_i1 = 223, Σx_i2 = 553,

Σy_i = 1,916, Σx_i1 = 5,200.9 Σx²_i2 = 31,729 Σx_i1x_i2 = 12,352

Σx_i1y_i = 43,550.8, Σx_i2y_i = 104,736.8, and Σ_yⁱ² = 371,595.6.