Answer:
Y^= 1.767 + 0.6294X when rounded give s Y^= 1.77 +0.63X
b= 0.6294 rounded to 0.63
a= 1.77
The predicted lines are for each X and Y
3.340,3.96, 4.914, 5.228, and 5.543
Step-by-step explanation:
The data given is
Length (m) Â Â Speed (m/s) Â Â Â Â Â Â Â Predicted Line Â
2.5 Â Â Â Â Â Â Â Â Â 3 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3.340 Â
3.5 Â Â Â Â Â Â Â Â 4.5 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3.96
5 Â Â Â Â Â Â Â Â Â 4.8 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4.914
5.5 Â Â Â Â Â Â Â Â 5.2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5.228
6 Â Â Â Â Â Â Â Â Â 5.5 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5.543
The calculations are
         Xsquare   XY  Y   X
         6.25   7.5  3    2.5
         12.25 15.75 4.5    3.5
          25 24     4.8    5
         30.25 28.6 5.2    5.5
          36 33      5.5    6
Total    109.75 108.85  23     22.5
The estimated regression line of Y on X is
Y^ = a +bX
and two normal equations are
∑Y = na + b∑X
∑XY= a∑X + b∑X²
Now X`= ∑X/ n= 22.5/5=4.5
Y`= ∑Y/ n= 23/5= 4.6
b= n∑XY- (∑X)(∑Y) / n∑X²- (∑X²)
Putting the values
b= 5(108.85) - (23)(22.5)/ 5(109.75)- (22.5)²
b= 544.25-517.5/ 548.75-506.25
b= 26.75 /42.5
b= 0.6294
and
a= Y`- bX~= 4.6- 0.6294(4.5)= 4.6-2.823= 1.767
Hence the
desired estimated regression line of Y on X is
Y^= 1.767 + 0.6294X
Y^= 1.77 +0.63X
The estimated regression co efficient b= 0.6294 indicates that the values of Y increase by 0.6294 units for a unit increase in X.
