bobbie71G

2021-08-19

The estimated regression equation for a model ivolving two independent variables and 10 observations follows.
$\stackrel{^}{y}=33.2566+0.7625{x}_{1}+0.2507{x}_{2}$
a) Interpret ${b}_{1}$ and ${b}_{2}$ in this estimated regression equation (to 4 decimals).
b) Estimate y when ${x}_{1}=180$ and ${x}_{2}=310$ (to 3 decimals)

Mayme

Step 1
a) Interpretation of ${b}_{1}$:
The coefficient or slope of ${x}_{1}$ in the regression model is 0.7625
The interpretation is that the value of y increases by 0.7625 units for one unit increases in ${x}_{1}$ provided the effect of ${x}_{2}$ is constant.
Interpretation of ${b}_{2}$:
The coefficient or slope of ${x}_{1}$ in the regression model is 0.2507
The interpretation is that the value of y increases by 0.2507 units for one unit increases in ${x}_{2}$ provided the effect of ${x}_{1}$ is constant.
Step 2
b) Consider the equation $\stackrel{^}{y}=33.2566+0.7625{x}_{1}+0.2507{x}_{2}$
Substitute ${x}_{1}=180$ and ${x}_{2}=310$ in $\stackrel{^}{y}$
$\stackrel{^}{y}=33.2566+0.7625\left(180\right)+0.2507\left(310\right)$
$=33.2566+137.25+77.717$
$=248.2236$
Thus, the value is 248.2236.

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