Question

Finding β0 and β1 . The equation for a straight line (deterministic) is y = β0 + β1x. If the line passes through the point (0,1), then x = 0, y = 1 must satisfy the equation. That is, 1 = β0 + β1(0). Similarly, if the line passes through the point (2,3), then x = 2, y = 3 must satisfy the equation: 3 = β0 + β1(2). Use these two equations to solve for β0 and β1, and find the equation of the line that passes through the points (0,1) and (2,3).

Answer 1

`y = x + 1`

Explanation:

We are given the following in the question:

`y = \beta_0 + \beta_1x`

The line passes through (0,1).

`1= \beta_0 + \beta_1(0)\\\Rightarrow 1= \beta_0`

The line passes through (2,3)

`3= \beta_0 + \beta_1(2)\\\Rightarrow 3= 1 + \beta_1(2)\\\Rightarrow 2 = 2\beta_1\\\Rightarrow \beta_1 = 1`

Thus, the equation of the line that passes through the points (0,1) and (2,3) is given by:

Slope:

`m = \beta_1 = 1`

Intercept:

`c = \beta_0 = 1`

Equation:

`y = x + 1`

is the required equation.