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 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;    mean of X = 2.9124;  SSX=Σ( X_i –X )²=37.924;   n=14 ;

Referring to Table 1, interpret the estimate for σ, the standard deviation of the random error

      term (standard error of the estimate) in the model:

		For every 1.0 thousand sq. foot increase in the size of the pharmaceutical store, we expect             the annual sales to increase by 0.9664 million dollars.
		About 95% of the observed annual sales will fall within 2 x 0.9664 million dollars of the           least squares line (the line of regression).
		About 95% of the observed annual sales fall within 0.9664 million dollars of the least           squares line.
		About 95% of the observed annual sales fall within the predicted values.

Answer 1

Solution Given Q = 0.964 + 1.640x Syx = $0.9664 million Sb, = 0.157, V: 0.9124 SSy = E(*)* - 37.924 , D=14 Standard Error of the estimate is A bout 954. of the observed annual Sales will fall 2 x 0.9664 million dollars of the least squa de line within Ang! - Opton - ® ,