Consider the following data concerning the demand y and pric

Consider the following data concerning the demand (y) and price (x) of a consumer product. From the given plot, does it seem reasonable to use the simple liner regression model to relate y to x ? Calculate the least squares point estimates of the parameters in the simple liner regression model. Test the significance of the regression relationship between y and x. Find a point prediction of and a 95 percent prediction interval for the demand corresponding to each of the prices $2.10, $2.75 and $3.10.

Solution

a) Yes. Since there is a strong negative relation ship exists between y and x

b) Using statistiscal software, the regression output is

Predictor Coef SE Coef T P
Constant 305.38 11.68 26.13 0.000
x -26.470 4.586 -5.77 0.004

from the output the point estimates of b0= 305.38 and b1= -26.470

d) Since the P-value 0.004 is very less, we conclude that the relationship is significant.

e)The point prediction and 95% prediction intervals are

x0 point prediction prediction interval

2.1 249.79 237.491 to 262.097

2.75 232.59 221.190 to 243.987

3.1 223.32 210.090 to 236.558