A critically important aspect of customer service in a supermarket is the waitin

Question

A critically important aspect of customer service in a supermarket is the waiting time at the checkout (defined as the time the customer enters the line until he or she is served). Data were collected during time periods where there were a constant number of checkout counters open. The total number of customers in the store and the waiting times (in minutes) were recorded. The results are displayed in the accompanying table, and the regression equation was found to be ModifyingAbove Upper Y with caret Subscript iYiequals=negative 0.1426+0.1083Xi, with Summation from i equals 1 to ni=1nYiequals=62.34, Summation from i equals 1 to ni=1nUpper Y Subscript i Superscript 2Y2iequals=158.2408, and Summation from i equals 1 to ni=1nXiYiequals=1507.13.

DATA:

b. Determine the standard error of the estimate.

SYXequals=nothing

(Round to four decimal places as needed.)

c. How useful do you think this regression model is for predicting the waiting time at the checkout line in a supermarket?

Since the value of

r2

is

and the value of

SYX

is

relatively large

relatively small

, the regression model is

not very useful

fairly useful

for predicting the waiting time at the checkout line in a supermarket.

Day Customers (X) Time (Y) 1 17 1.93 2 16 1.86 3 11 1.05 4 9 1.17 5 19 2.21 6 31 3.72 7 26 2.42 8 12 0.52 9 12 1.42 10 10 1.18 11 19 2.23 12 37 4.11 13 25 2.24 14 9 0.47 15 14 0.78 16 21 1.38 17 18 1.27 18 24 2.45 19 14 1.37 20 26 2.48 21 13 1.73 22 15 1.64 23 19 2.39 24 26 3.01 25 19 2.14 26 22 1.67 27 22 2.43 28 33 3.18 29 36 3.72 30 40 4.17

Explanation / Answer

The statistical software output for the given problem is:

Simple linear regression results:
Dependent Variable: Time (Y)
Independent Variable: Customers (X)
Time (Y) = -0.1426476 + 0.10832427 Customers (X)
Sample size: 30
R (correlation coefficient) = 0.93004586
R-sq = 0.8649853
Estimate of error standard deviation: 0.371997

Parameter estimates:

Analysis of variance table for regression model:

Hence,

b) SYX = 0.3720

c) r2 = 0.8650

Since the value of r2 is relatively large and the value of SYX is relatively small, the regression model is fairly useful for predicting the waiting time at the checkout line in a supermarket.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -0.1426476 0.17917213 0 28 -0.79614839 0.4326 Slope 0.10832427 0.008087847 0 28 13.393462 <0.0001

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