The following table lists values measured for 10 consecutive eruptions of the geyser Old Faithful in Yellowstone National Park. They are the duration, in minutes, of the eruption $\left( x _ { 1 } \right)$ , the dormant Period before the eruption $\left( x _ { 2 } \right)$ , and the dormant period after the eruption (y) .

$\begin{array} { l l l } x _ { 1 } & x _ { 2 } & y \\3.5 & 80 & 84 \\4.1 & 84 & 50 \\2.3 & 50 & 93 \\4.7 & 93 & 55 \\1.7 & 55 & 76 \\4.9 & 76 & 58 \\1.7 & 58 & 74 \\4.6 & 74 & 75 \\3.4 & 75 & 80 \\4.3 & 80 & 56\end{array}$

Construct the multiple regression equation $\hat { y}$ =b₀+b₁x₁+b₂x₂

Question

The following table lists values measured for 10 consecutive eruptions of the geyser Old Faithful in Yellowstone National Park. They are the duration, in minutes, of the eruption

\left( x _ { 1 } \right)

, the dormant Period before the eruption

\left( x _ { 2 } \right)

, and the dormant period after the eruption (y) .

\begin{array} { l l l } x _ { 1 } & x _ { 2 } & y \\3.5 & 80 & 84 \\4.1 & 84 & 50 \\2.3 & 50 & 93 \\4.7 & 93 & 55 \\1.7 & 55 & 76 \\4.9 & 76 & 58 \\1.7 & 58 & 74 \\4.6 & 74 & 75 \\3.4 & 75 & 80 \\4.3 & 80 & 56\end{array}

Construct the multiple regression equation

\hat { y}

=b₀+b₁x₁+b₂x₂

Quizplus · Accepted Answer

We need to use multiple regression to find the equation of the form: $\hat { y }=\beta _ { 0 } +\beta _ { 1 } x _ { 2 } +\beta _ { 2 } x _ { 1 }$ Using the given data, we can calculate the values of the coefficients beta0, beta1, and beta2 that minimize the sum of the squared errors. The regression equation is then: $\hat { y }$=118.78-1.7675 x₁-0.5856 x₂

The Following Table Lists Values Measured for 10 Consecutive Eruptions (x1)\left( x _ { 1 } \right)(x1​)

The Following Table Lists Values Measured for 10 Consecutive Eruptions $\left( x _ { 1 } \right)$