Question

The equation for a straight line (deterministic model) is y = Bo + B,X.If the line passes through the point ( - 10,3), then x = - 10, y = 3 must satisfy the equation; that is, 3 = Bo + B1(-10).Similarly, if the line passes through the point (11,4), then x = 11, y = 4 must satisfy the equation; that is, 4 = Bo+B1(11).Use these two equations to solve for Bo and By; then find the equation of the line that passes through the points (-10,3) and (11,4)...Find Bo and B,B1 =Bo(Simplify your answers. Type integers or simplified fractions.)

Answer 1

To find the equation of the line we just need to find the beta constants. In order to do this we have (they provided us with) the following system of equations:

`\begin{cases}3=\beta_0+\beta_1(-10) \\ 4=\beta_0+\beta_1(11)\end{cases}`

Let us subtract the second equation to the first one:

This implies that

`\beta_1=(-1)/(-21)=(1)/(21)`

Now, let us replace this value we just got into the second equation to find beta_0:

`\begin{gathered} 4=\beta_0+(1)/(21)\cdot11, \\ 4=\beta_0+(11)/(21), \\ \beta_0=4-(11)/(21)=(4\cdot21)/(21)-(11)/(21)=(84-11)/(21)=(73)/(21) \end{gathered}`

At last,

`\beta_1=(1)/(21),\beta_0=(73)/(21)`

Then, the equation of the line is just

`y=(73)/(21)+(1)/(21)x`