(16 points) In an attempt to predict weekly sales at its coffee shops, Ahab Coffee Inc.

(16 points) In an attempt to predict weekly sales at its coffee shops, Ahab Coffee Inc. ran a regression analysis using as the X variable the square footage of each coffee shop and as the Y variable the shop's weekly sales in dollars. The MINITAB results are: 

 The regression equation is Weekly Sales = 1612 + 3.11 Square Feet

Predictor             Coef   SE Coef  T    P Constant             1612.5   294.3 5.48 0.003 Store Size (Sq. Ft.) 3.1109  0.3153 9.87 0.000

S = 277.116  R-Sq = 65.6%  R-Sq(adj) = 65.0%

Analysis of Variance

Source         DF     SS      MS     F     P Regression      1  7477614 7477614 97.37 0.000 Residual Error 51  3916451   76793 Total          52 11394065

a) (3 pts). Give the null and alternative hypotheses to test the significance of the slope coefficient for this equation. Use correct symbols.

b) (3 pts) At α = 0.05, do you reject the null hypothesis of part a? Answer YES or NO and fully explain why by showing and using the appropriate p-value or by comparing the appropriate test statistic value to its critical statistic value (your choice).

c) (3 pts) Explain the implication of your decision in part b:

d) (2 pts) What percent of the total variation in the weekly sales data is explained by this regression?

 ANS _____________

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e) (2 pts) What is the value of r (the Pearson correlation coefficient) for this case? 

 ANS __________

f)    (3 points) MINITAB produced the following intervals when X = 800:

       New Obs    Fit   SE Fit      95% CI           95% PI      1  4101.2   55.0  (3990.8, 4211.5) (3534.0, 4668.4)

For a group of coffee shops, each 800 square feet in size, what do you predict for average weekly sales? Pick the one correct answer and fully explain how to interpret it.