A study was performed to investigate the shear strength of soil (y) as it related to depth in feet (x 1 ) and moisture content (x 2 ).Ten observations were collected, and the following summary...

A study was performed to investigate the shear strength of soil (y) as it related to depth in feet (x₁) and 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,
= 5,200.9,
 = 31,729, Σx_i1x_i2
= 12,352, Σx_i1y_i
=43,550.8, Σx_i2y_i
= 104,736.8,

and
 = 371,595.6.

(a) Set up the least squares normal equations for the model

Y
= β₀+ β₁
x
₁+ β₂
x
₂+ ?.

(b) Estimate the parameters in the model in part (a).

(c) What is the predicted strength when
x
₁= 18 feet and
x
₂= 43%?