A review of the different retailer companies’ annual sales and annual profits by Fortune Magazine was performed to determine whether there is a correlation between the two variables. The analysis revealed the following:
Refer to the Minitab output below to answer questions A through F.
(A) Analyze the above output to determine the regression equation. Profits (billions of dollars) = 0.286133 + 0.0351855 Sales (billions of dollars)=
(B) What conclusions are possible using the meaning of b0 (intercept) and b1 (regression coefficient) in this problem? (That is, explain the meaning of the coefficients.)
(C) What conclusions are possible using the coefficient of determination (r-squared)
(D) Calculate the coefficient of correlation. Interpret this value.
(E) Does this data provide significant evidence (a=0.05) that the companies’ profits are related to the amount of sales? Find the p-value and interpret.
(F) Predict the average annual profits for annual sales of 100 billion dollars.
Regression Equation Profits (billions of dollars) = 0.286133 + 0.0351855 Sales (billions of dollars)
Coefficients Term Coef SE Coef T P 95% CI Constant Constant 0.286133 0.626256 0.45690 .0664 (-1.24626, 1.8185) Sales (billions of dollars) 0.035185 0.005166 6.81084 0.000 (0.02254, 0.04783)
Summary of Model S = 1.35441 R-Sq = 88.55% R-Sq(adj) = 86.64% PRESS = 26.6328 R-Sq(pred) = 72.29%
Analysis of Variance Source DF Seq SS Adj SS Adj MS F
Regression 1 85.0941 85.0941 85.09
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