bobbie71G

2021-08-19

The estimated regression equation for a model ivolving two independent variables and 10 observations follows.

$\hat{y}=33.2566+0.7625{x}_{1}+0.2507{x}_{2}$

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)

a) Interpret

b) Estimate y when

Mayme

Skilled2021-08-20Added 103 answers

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$\hat{y}=33.2566+0.7625{x}_{1}+0.2507{x}_{2}$

Substitute${x}_{1}=180$ and ${x}_{2}=310$ in $\hat{y}$

$\hat{y}=33.2566+0.7625\left(180\right)+0.2507\left(310\right)$

$=33.2566+137.25+77.717$

$=248.2236$

Thus, the value is 248.2236.

a) Interpretation of

The coefficient or slope of

The interpretation is that the value of y increases by 0.7625 units for one unit increases in

Interpretation of

The coefficient or slope of

The interpretation is that the value of y increases by 0.2507 units for one unit increases in

Step 2

b) Consider the equation

Substitute

Thus, the value is 248.2236.

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