Answer
After removing, in this order, $x_2$, $x_4$ and $x_3$:
$ŷ=200.0- 1.624x_1$
Work Step by Step
Let's remove $x_2$ (see previous item)
In MINITAB, enter the $x_1$ values in C1, the $x_3$ values in C3, the $x_4$ values in C4 and the $y$ values in C5.
Select Stats -> Regression -> Regression -> Fit Regression Model
Enter C5 in "Responses" and C1 C3 C4 in "Continuous Predictors"
The least-squares regression line will be shown in "Regression Equation", where C5 is $ŷ$, C1 is $x_1$, C3 is $x_3$ and C4 is $x_4$
$ŷ=154.7-1.255x_1+3.43 x_3+0.105x_4$
$H_0: β_1=β_3=β_4=0$ versus $H_1: at~least~one~β_i\ne0$
$F_0=7.60$ with a P-value $=0.010\ltα$. Reject the null hypothesis.
The model is significant.
1) $H_0: β_1=0$ versus $H_1: β_1\ne0$
$t_0=-2.58$ with a P-value $=0.032\ltα$. Reject the null hypothesis.
3) $H_0: β_3=0$ versus $H_1: β_3\ne0$
$t_0=1.64$ with a P-value $=0.140\gtα$. Do not reject the null hypothesis.
4) $H_0: β_4=0$ versus $H_1: β_4\ne0$
$t_0=0.20$ with a P-value $=0.844\gtα$. Do not reject the null hypothesis.
Now, let's remove $x_4$ (the highest P-value):
Select Stats -> Regression -> Regression -> Fit Regression Model
Enter C5 in "Responses" and C1 C3 in "Continuous Predictors"
The least-squares regression line will be shown in "Regression Equation", where C5 is $ŷ$, C1 is $x_1$ and C3 is $x_3$
$ŷ=164.9-1.308 x_1+3.34x_3$
$H_0: β_1=β_3=0$ versus $H_1: at~least~one~β_i\ne0$
$F_0=12.73$ with a P-value $=0.002\ltα$. Reject the null hypothesis.
The model is significant.
1) $H_0: β_1=0$ versus $H_1: β_1\ne0$
$t_0=-3.37$ with a P-value $=0.008\ltα$. Reject the null hypothesis.
3) $H_0: β_3=0$ versus $H_1: β_3\ne0$
$t_0=1.73$ with a P-value $=0.118\gtα$. Do not reject the null hypothesis.
Now, let's remove $x_3$:
Select Stats -> Regression -> Regression -> Fit Regression Model
Enter C5 in "Responses" and C1 in "Continuous Predictors"
The least-squares regression line will be shown in "Regression Equation", where C5 is $ŷ$ and C1 is $x_1$
$ŷ=200.0- 1.624x_1$
1) $H_0: β_1=0$ versus $H_1: β_1\ne0$
$t_0=-4.33$ with a P-value $=0.001\ltα$. Reject the null hypothesis.
