Question

Question 11

1. 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 95% confidence interval estimate for the annual sales of stores based

       on the size of the stores in square feet. This confidence interval estimate is:    

      

   		(1.3332 , 2.0068)
   		(1.3902 , 1.9498)
   		(1.3935 , 1.9465)
   		(1.3279 , 2.0121)

Answer 1

Critical value, t_c = T.INV.2T(0.05, 12) = 2.1788

95% Confidence interval for slope:

Lower limit = β₁ - t_c*S_B1 = 1.67 - 2.1788*0.157 = 1.3279

Upper limit = β₁ + t_c*S_B1 = 1.67 + 2.1788*0.157 = 2.0121

(1.3279 , 2.0121)