Question

. The estimate regression equation for a model involving two independent variables and 10 observations follows.y = 29.1270 + 0.5906x1 + 0.4980x2a. Interpret b1 and b2b. Estimate y when x1 = 180 and x2 = 310

Answer 1

b) y = 289.815 when
`x_1 = 180 \text{ and } x_2 = 310`

Explanation:

We are given the following information in the question:

`y = 29.1270 + 0.5906x_1 + 0.4980x_2`

where y is the dependent variable,

`x_1, x_2` are the independent variable.

The multiple regression equation is of the form:

`y = b_0 + b_1x_1 + b_2x_2`

where,

`b_0`: is the intercept of the equation and is the value of dependent variable when all the independent variable are zero.

`b_1`: It is the slope coefficient of the independent variable
`x_1`.

`b_2`: It is the slope coefficient of the independent variable
`x_2`.

• The regression coefficient in multiple regression is the slope of the linear relationship between the dependent and the part of a predictor variable that is independent of all other predictor variables.

Comparing the equations, we get:

`b_1 = 0.5906\\b_2 = 0.4980`

• This means holding
  `x_2` constant, a change of one in
  `x_1` is associated with a change of 0.5906 in the dependent variable.

• This means holding
  `x_1` constant, a change of 1 in
  `x_2` is associated with a change of 0.4980 in the dependent variable.

b) We have to estimate the value of y

`y = 29.1270 + 0.5906(180) + 0.4980(310) = 289.815`