Given the following data on two variables X an independent r

Given the following data on two variables X, an independent random variable. and Y, the response, that are believed to have a liner relationship Find the fitted line that may describe the relation between X and Y Find the error at X=(20)

Solution

We will find an equation of the regression line in 4 steps.

Step 1: Find X?Y and X2 as it was done in the table below.

Step 2: Find the sum of every column:

?X=136 , ?Y=614 , ?X?Y=16948 , ?X2=3816

Step 3: Use the following equations to find a and b:

ab=?Y??X2??X??XYn??X2?(?X)2=614?3816?136?169485?3816?1362?65.233=n??XY??X??Yn??X2?(?X)2=5?16948?136?6145?3816?(136)2?2.116

Step 4: Substitute a and b in regression equation formula

y = a + b?x= 65.233 + 2.116?x

y(20) = 65.233+2.116(20)

= 65.233+42.32

= 107.553

Error = observed - Expected

= |100-107.553|=7.553

X	Y	X?Y	X?X
20	100	2000	400
24	120	2880	576
28	136	3808	784
30	128	3840	900
34	130	4420	1156