Question 466807
 <pre><font face = "consolas" color = "indigo"  size=2><b>

 x<sub>i</sub>     1  2  3   4    5
 y<sub>i</sub>     3  7  5  11   14
</pre></font></b>
a- Develop a scatter diagram for these data 
<pre><font face = "consolas" color = "indigo"  size=2><b>

{{{drawing(2800/17,400,-1,6,-1,16,

graph(2800/17,400,-1,6,-1,16), 

circle(1,3,.1),circle(2,7,.1),circle(3,5,.1),
circle(4,11,.1),circle(5,14,.1) )}}}
</pre></font></b>
b- What does the scatter diagram developed in part (a) indicate about the relationship between the two variables ?
  <pre><font face = "consolas" color = "indigo"  size=2><b>

It indicates that those points aren't too far off a straight line.
</pre></font></b>
c- Try to approximate the relationship between X and Y by drawing a straight line through the data .
 <pre><font face = "consolas" color = "indigo"  size=2><b>
{{{drawing(2800/17,400,-1,6,-1,16,

graph(2800/17,400,-1,6,-1,16), 
line(-6,-15.4, 12,31.4),
circle(1,3,.1),circle(2,7,.1),circle(3,5,.1),
circle(4,11,.1),circle(5,14,.1) )}}}
</pre></font></b>
d- Develop the estimated regression equation by computing the values of b0 and b1 using equation (1.46)and(1.47) 
<pre><font face = "consolas" color = "indigo"  size=2><b>

I can't see your book, but most books use this formula for
the slope b<sub>1</sub>:

{{{matrix(1,1,

b[1]=

(sum((x[i]y[i]))  -   (sum(x[i])sum(y[1]))/n) /

(   sum((x[i]^2))  -   (sum(x[i]))^2/n )   )}}}

Or this, when we multiply top and bottom by n:

{{{matrix(1,1,

b[1]=

(n*sum((x[i]y[i]))  -   sum(x[i])sum(y[1])) /

(  n*sum((x[i]^2))  -   (sum(x[i]))^2 )   )}}}

Then from that the y-intercept, b<sub>0</sub>, is calculated:

{{{b[0]=( sum(y[1]) -b[1]sum(x[i]))/n}}}


i        x<sub>i</sub>    y<sub>i</sub>   x<sub>i</sub>y<sub>i</sub>   x<sub>i</sub>²
-----------------------------
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(x[i])=15}}}
{{{sum(y[i])=40}}}
{{{sum(x[i]y[1])=146}}}
{{{sum((x[i]^2))=55}}} 
Substituting in 

{{{matrix(1,1,

b[1]=

(n*sum((x[i]y[i]))  -   sum(x[i])sum(y[1])) /

(  n*sum((x[i]^2))  -   (sum(x[i]))^2 )   )}}}


{{{matrix(1,1,

b[1]=

(5*146  -   15*40) /

(  5*55  -   15^2 )  = (730-600)/(275-225)=130/50=13/5=2.6 )}}}

Then we substitute into:

{{{b[0]=( sum(y[1]) -b[1]sum(x[i]))/n}}}

{{{b[0]=(40 -2.6*15)/5=(40-39)/5=1/5=.2}}}

Therefore the equation of the regression line is

{{{y=b[1]x+b[0]}}}

{{{y=2.6x+.2}}}

Actually the line drawn above in part c is this 
regression line. 
</pre></font></b>
e- Use the estimated regression equation to predict the value of Y when X=4 
{{{y=2.6x+.2}}}
{{{y=2.6(4)+.2}}}
{{{y=2.6x+.2}}}
{{{y=10.4+.2}}}
{{{y=10.6}}}
 <pre><font face = "consolas" color = "indigo"  size=2><b>
Notice that the actual value of y in the data when x=4 is 11,
which is close.

Edwin</pre>