Answer
$ŷ=-92.28+1.2575x_1+1.0987x_2$
Work Step by Step
In MINITAB, enter the air temperature values in C1, the dew point values in C2 and the heat index values in C3.
Select Stats -> Regression -> Regression -> Fit Regression Model
Enter C3 in "Responses" and C1 C2 in "Continuous Predictors"
The least-squares regression line will be shown in "Regression Equation", where C3 is $ŷ$ (heat index), C1 is $x_1$ (air temperature) and C2 is $x_2$ (dew point).
$ŷ=-92.28+1.2575x_1+1.0987x_2$
