Answer
$ŷ=267+11319x_1-599x_2-481.3x_3-146x_4$
Work Step by Step
In MINITAB, enter the Carat values in C1, the Color values in C2, the Clarity values in C3, the Cut values in C4 and the Price values in C5.
Select Stats -> Regression -> Regression -> Fit Regression Model
Enter C4 in "Responses" and C1 C2 C3 in "Continuous Predictors"
The least-squares regression line will be shown in "Regression Equation", where C5 is $ŷ$ (Price), C1 is $x_1$ (Carat), C2 is $x_2$ (Color), C3 is $x_3$ (Clarity) and C4 is $x_4$ (Cut).
$ŷ=267+11319x_1-599x_2-481.3x_3-146x_4$
