Question

The estimate regression equation for a model involving two independent variables and 10 observations follows.
y = 29.1270 + 0.5906x1 + 0.4980x2
a. Interpret b1 and b2
b. Estimate y when x1 = 180 and x2 = 310

Answer 1

Answer:

a) $b_1 = 0.5906\\b_2 = 0.4980$

b) y = 289.815

Step-by-step explanation:

We are given the following information:

The estimate regression equation for a model involving two independent variables and 10 observations follows:

$y = 29.1270 + 0.5906x_1 + 0.4980x_2$

where $x_1, x_2$ are the two independent variable and y is the dependent variable.

a) The regression line is of the form:

$y = b_0 + b_1x_1 + b_2x_2\\\text{where } b_0 \text{ is the y-intercept and }b_1, b_2\text{ are the coefficients of} x_1, x_2\text{ respectively}$

Comparing, we get,

$b_1 = 0.5906\\b_2 = 0.4980$

These are the coefficients of $x_1, x_2$ respectively, and helps us to know the the significance of the independent variable in predicting the independent variable.

b) We have to estimate y when

$x_1 = 180 \text{ and } x_2 = 310\\y = 29.1270 + 0.5906x_1 + 0.4980x_2\\\text{Putting values}\\y = 29.1270 + 0.5906(180) + 0.4980(320)\\y = 289.815$