xi 1 2 3 4 5
yi 3 7 5 11 14
a- Develop a scatter diagram for these data
b- What does the scatter diagram developed in part (a) indicate about the relationship between the two variables ?
It indicates that those points aren't too far off a straight line.
c- Try to approximate the relationship between X and Y by drawing a straight line through the data .
d- Develop the estimated regression equation by computing the values of b0 and b1 using equation (1.46)and(1.47)
I can't see your book, but most books use this formula for
the slope b1:
Or this, when we multiply top and bottom by n:
Then from that the y-intercept, b0, is calculated:
i xi yi xiyi xi²
-----------------------------
1 1 3 3 1
2 2 7 14 4
3 3 5 15 9
4 4 11 44 16
5 5 14 70 25
-----------------------------
sums: 15 40 146 55
n = 5
Substituting in
Then we substitute into:
Therefore the equation of the regression line is
Actually the line drawn above in part c is this
regression line.
e- Use the estimated regression equation to predict the value of Y when X=4
Notice that the actual value of y in the data when x=4 is 11,
which is close.
Edwin