Question

The general manager of a chain of pharmaceutical stores reported the results of a regression analysis, designed to predict the annual sales for all the stores in the chain (Y) – measured in millions of dollars. One independent variable used to predict annual sales of stores is the size of the store (X) – measured in thousands of square feet. Data for 14 pharmaceutical stores were used to fit a linear model. The results of the simple linear regression are provided below.

Y = 0.964 + 1.670X; S_YX =$0.9664 million; 2 – tailed p value = 0.00004 (for testing ß₁);                        

                        S_b1=0.157;    X = 2.9124; SSX=Σ( X_i –X )²=37.924;   n=14 ;

   Suppose the general manager wants to obtain a prediction interval estimate for the mean annual sales for

   pharmaceutical stores that have a size of 4000 sq. feet. Compute this prediction interval:

   

		(6.6710 , 10.9140)
		(5.4330 , 9.8540)
		(6.2130 , 9.8540)
		(5.4330 , 10.8540)

Answer 1

predcited value at X=4:		7.64
std error prediction interval=	s*√(1+1/n+(x0-x̅)2/Sxx)	=	1.0148
for 95 % CI value of t=					2.1790
margin of error E=t*std error                            =			2.21
lower prediction bound=sample mean-margin of error =		5.433
Upper prediction bound=sample mean+margin of error=		9.855

from above: correct option is :  (5.4330 , 9.8540)