SOLUTION: Given are five observation for two variables,X and Y Xi 1 2 3 4 5 Yi 3 7 5 11 14 a- Develop a scatter diagram f

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Question 466807: Given are five observation for two variables,X and Y
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 ?
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) .
e- Use the estimated regression equation to predict the value of Y when X=4 .
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


 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:

b%5B0%5D=%28+sum%28y%5B1%5D%29+-b%5B1%5Dsum%28x%5Bi%5D%29%29%2Fn


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
sum%28x%5Bi%5D%29=15
sum%28y%5Bi%5D%29=40
sum%28x%5Bi%5Dy%5B1%5D%29=146
sum%28%28x%5Bi%5D%5E2%29%29=55 
Substituting in 






Then we substitute into:

b%5B0%5D=%28+sum%28y%5B1%5D%29+-b%5B1%5Dsum%28x%5Bi%5D%29%29%2Fn

b%5B0%5D=%2840+-2.6%2A15%29%2F5=%2840-39%29%2F5=1%2F5=.2

Therefore the equation of the regression line is

y=b%5B1%5Dx%2Bb%5B0%5D

y=2.6x%2B.2

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
y=2.6x%2B.2
y=2.6%284%29%2B.2
y=2.6x%2B.2
y=10.4%2B.2
y=10.6

Notice that the actual value of y in the data when x=4 is 11,
which is close.

Edwin