Fitting a straight line to a set of data yields the predicti

Fitting a straight line to a set of data yields the prediction line Y_i = 5 + 3X_i. The values of X used to find the prediction line range from 5 to 34. Should this model be used to predict the mean value of Y when X equals 6? Should this model be used to predict the mean value of Y when X equals - 6? Should this model be used to predict the mean value of Y when X equals 0? Should this model be used to predict the mean value of Y when X equals 33? Should this model be used to predict the mean value of Y when X equals 6?

Solution

a) YES

when x= 6, y= 5+3*6= 23 (23 is in data range 5 and 34)

b) NO

when x= -6, y= 5-3*6= -13 (-13 is not in data range 5 and 34)

c) YES

when x= 0, y= 5+3*0= -13 (5 is in data range 5 and 34)

d) NO

when x= 33, y= 5+3*33= -104 (104 is not in data range 5 and 34)