The sales department of Walmart stores has engaged in a strategy to boost the pr
ID: 1099026 • Letter: T
Question
The sales department of Walmart stores has engaged in a strategy to boost the productivity of its employees. During the last 7 years, the company collected data on the number of employees and annual gross sales shown in the following table:
Number of Employees Sales (in $'s)
1975 100
2010 110
2005 122
2020 130
2030 139
2031 152
2050 164
2100 Unknown
a) Determin the least squares trend line.
b) Determine the predicted value of sales
c) Determine the coefficient of determination
d) Determine the correlation coefficient
e) Determine the Fisher Coeficient and test the overall significance of the regression at 5% level of significance.
Explanation / Answer
a) Put the data in excel and do a regression (Data Analysis pack)
Coefficients
Intercept
-1663.0325
X Variable 1
0.8893298
Thus Y = -1663.0325 + 0.8893 X
b) Predicted value of sales
X
Y
Predicted
1975
100
93.39405
2010
110
124.5206
2005
122
120.0739
2020
130
133.4139
2030
139
142.3072
2031
152
143.1965
2050
164
160.0938
2100
204.5603
c)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.93735768
R Square
0.87863943
Adjusted R Square
0.85436732
Standard Erro
8.64346963
Observations
7
Co eff of determinagtion is R square = 87.86%
d) Correlation coefficient: 0.9373 (CORREL function in excel)
e) Fisher coeff = 0.5 - ln [ ( 1 + r ) / (1 - r ) ]
r = 0.9373
Fisher coeff = 0.5 - 3.4316 = -2.936
Overall significance at 5%
ANOVA
df
SS
MS
F
Significance F
Regression
1
2704.45216
2704.452
36.19954
0.001823439
Residual
5
373.547836
74.70957
Total
6
3078
p value is 0.001 < 0.05 hence it is significant
Coefficients
Intercept
-1663.0325
X Variable 1
0.8893298
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