Regression Analyses Using Excel:
Part 1:
BENEFITS and INTRINSIC as independent and dependent variable respectively: (equation 1)
The following is a summary of the results:
Regression Statistics
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Multiple R
0.468804
R Square
0.219778
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Adjusted R Square
0.185855
Standard Error
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0.932503
Observations
25
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ANOVA
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df
SS
MS
F
Significance F
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Regression
1
5.63369
5.63369
6.4787733
0.018084926
Residual
23
19.99991
0.869561
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Total
24
25.6336
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Coefficients
Standard Error
t Stat P-value
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Lower 95%
Upper 95%
Intercept
1.554273
1.411685
1.101006
0.2822837
-1.366019034
4.4745652
BENEFITS
0.664006
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0.260871
2.545343
0.0180849
0.124353418
1.2036581
Equation 1:
INTRINSIC = 1.554273 + 0.664 BENEFITS
T critical value at the 95% level of test is 2.06; comparing this with the t statistics value it is evident that the slope is significant while the intercept is not significant. (Ken, 2009)
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Part 2:
BENEFITS and EXTRINSIC as independent and dependent variable respectively:
(equation 2)
The following is a summary of the results:
Regression Statistics
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Multiple R
0.34268
R Square
0.11743
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Adjusted R Square
0.079057
Standard Error
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1.016694
Observations
25
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ANOVA
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df
SS
MS
F
Significance F
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Regression
1
3.163276
3.163276
3.0602491
0.093563229
Residual
23
23.77432
1.033666
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Total
24
26.9376
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Coefficients
Standard Error
t Stat P-value Lower 95%
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Upper 95%
Intercept
7.404902
1.539139
4.811069
7.457E-05
4.220951367
10.588853
BENEFITS
-0.49756
0.284424
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-1.74936
0.0935632
-1.085933127
0.0908167
Equation 2:
EXTRINSIC = 7.404902-0.49756 BENEFITS
T critical value at the 95% level of test is + or – 2.06, comparing this with the t statistics value it is evident that the slope is not significant while the intercept is significant. (Ken, 2009)
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Part 3:
BENEFITS and OVERALL as independent and dependent variable respectively:
(Equation 3)
The following is a summary of the results:
Regression Statistics
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Multiple R
0.140186
R Square
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0.019652
Adjusted R Square
-0.02297
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Standard Error
0.990779
Observations
25
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ANOVA
df
SS
MS
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F
Significance F
Regression
1
0.452594
0.452594
0.4610571
0.503906493
Residual
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23
22.57781
0.981644
Total
24
23.0304
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Coefficients
Standard Error
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t Stat P-value Lower 95% Upper 95%
Intercept
4.162472
1.499908
2.775152
0.0107666
1.059676321
7.2652673
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BENEFITS
0.188204
0.277174
0.679012
0.5039065
-0.385173504
0.7615822
Equation 3:
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OVERALL = 4.1625 + 0.1882 BENEFITS
T critical value at the 95% level of test is + or – 2.06, comparing this with the t statistics value it is evident that the slope is not significant while the intercept is significant. (Ken, 2009)
Part 4:
Graphs and Regression line equations:
Equation 1:
INTRINSIC = 1.554273 + 0.664 BENEFITS
The chart below summarizes the results for equation 1:
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From the chart there is a positive relationship between the two variables, when benefit increase then Intrinsic increases.
Slope and intercept:
The slope of the regression model is 0.664 and the Y intercept value is 1.554273. This means if benefits increase by one unit then intrinsic will increase by 0.664 units. (Bowerman, 2003)
R squared:
The R squared value for this model is 0.219778, meaning benefits explain 21.98% of changes in Intrinsic variable. (Bowerman, 2003)
Equation 2:
EXTRINSIC = 7.404902-0.49756 BENEFITS
The chart below summarizes the results for equation 2:
From the chart there is an inverse relationship between the two variables, when benefit increase then extrinsic decreases.
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Slope and intercept:
The slope of the regression model is -0.49756 and the Y intercept value is 7.4. This means if benefits increase by one unit then extrinsic will increase by –
0.49756
units. (Bowerman, 2003)
R squared:
The R squared value for this model is 0.11743, meaning benefits explain 11.74% of changes in extrinsic variable. (Bowerman, 2003)
Equation 3:
OVERALL = 4.1625 + 0.1882 BENEFITS
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The chart below summarizes the results for equation 3:
From the chart there is a positive relationship between the two variables, when benefit increase then overall increases.
Slope and intercept:
The slope of the regression model is 0.1882 and the Y intercept value is 4.1625. This means if benefits increase by one unit then overall will increase by
0.1882
units. (Bowerman, 2003)
R squared:
The R squared value for this model is 0.019652, meaning benefits explain 1.97% of changes in overall variable. (Bowerman, 2003)
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Comment:
The first equation INTRINSIC = 1.554273 + 0.664 BENEFITS produces the strongest relationship, this model has the highest slope value showing a strong relationship between the variables, the R squared value is 0.2198 which is the highest value and therefore this shows the strongest correlation coefficient. The slope of this model is statistically significant while none of the other models value are significant, the second model EXTRINSIC = 7.404902-0.49756 BENEFIT has a negative slope and from the other models benefits increases satisfaction, therefore this model will not be appropriate in estimating satisfaction values.
References:
Bruce Bowerman (2003) Business statistics in practice, New Jersey: Prentice Hall press
Ken Black (2009) Business Statistics: Contemporary Decision Making, New York: McGraw hill press
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