I am learning multiple linear regression. I know for simple linear regression if I have the following X and Y values, then how to predict Y'. Like if I have the following datas:
X Y Y'
1 0 ?
0 1 ?
0 1 ?
0 0 ?
then I can calculate a and b and get Y' from the equation y = a + bx as shown here http://www.easycalculation.com/statistics/learn-regression.php. Now, I have multiple independent variables then what is the formula to calculate the Y' using multiple linear regression? My current datas are:
X1 X2 X3 X4 X5 Y Y'
1 0 0 1 0 1 ?
0 1 0 1 0 0 ?
0 0 0 0 1 0 ?
1 0 1 0 0 1 ?
Can anybody show me the formula to predict Y'? I have searched a lot but those shows me scatter plots and analysis and all. I just want to get the Y' values. I didn't get any tutorial like I got for linear regression (link provided above) where it is shown clearly how to calculate Y' values.
Edit:
So, according to the answers my X and Y matrix are:
X = 1 1 0 0 1 0
1 0 1 0 1 0
1 0 0 0 0 1
1 1 0 1 0 0
Y = 1
0
0
1
and then I calculate betas with help of (X'X)^-1 X'Y equation. Then put the x1, x2, x3, values to predict y1, y2, y3 and so on - right?