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Prof V Nallasivam
Regression Modeling
Technique
Dependability of
Regression Equation
Drawing Inferences
Optimising the
independent variables...
Year
R & D
Expenditure
(in Crs)
Annual
Profit
(in Crs)
x y
2002 2 20
2003 3 25
2004 5 34
2005 4 30
2006 11 40
2007 5 31
To...
Prof V Nallasivam
ˆ 20 2y x= +
ANOVA - (Test the Model)
Scatter diagram
Standard Error of Estimate
Testing the significance of Regression
Co-efficient (b...
Prof V Nallasivam
2 Explained Variation
r
Total Variation
=
Prof V Nallasivam
2 2
[ ]r Correlation=
Coefficient of Determination
x y
1 4 4 -14 196 -14 196
2 8 8 -10 100 -10 100
3 12 12 -6 36 -6 36
4 16 16 -2 4 -2 4
5 20 20 2 4 2 4
6 24 24 6 36 6 36
7 ...
Prof V Nallasivam
ˆ 4y x=
x y
1 4 4 -14 196 -14 196
2 8 8 -10 100 -10 100
3 12 12 -6 36 -6 36
4 16 16 -2 4 -2 4
5 20 20 2 4 2 4
6 24 24 6 36 6 36
7 ...
x y
1 4 4 -14 196 -14 196
2 8 8 -10 100 -10 100
3 12 12 -6 36 -6 36
4 16 16 -2 4 -2 4
5 20 20 2 4 2 4
6 24 24 6 36 6 36
7 ...
x y
1 4 4 -14 196 -14 196
2 8 8 -10 100 -10 100
3 12 12 -6 36 -6 36
4 16 16 -2 4 -2 4
5 20 20 2 4 2 4
6 24 24 6 36 6 36
7 ...
x y
1 4 4 -14 196 -14 196
2 8 8 -10 100 -10 100
3 12 12 -6 36 -6 36
4 16 16 -2 4 -2 4
5 20 20 2 4 2 4
6 24 24 6 36 6 36
7 ...
x y
1 4 4 -14 196 -14 196
2 8 8 -10 100 -10 100
3 12 12 -6 36 -6 36
4 16 16 -2 4 -2 4
5 20 20 2 4 2 4
6 24 24 6 36 6 36
7 ...
Prof V Nallasivam
2
ˆ( ) 672
1
( ) 672
y y
r
y y
−
= = =
−
∑
∑
Y = 12
ˆ 4y x=
Y
X
ˆ 12y =
Example-1
Prof V Nallasivam
x y
1 6 9 0 0 -3 9
1 12 9 0 0 3 9
3 6 9 0 0 -3 9
3 12 9 0 0 3 9
5 6 9 0 0 -3 9
5 12 9 0 0 3 9
7 6 9 0 0 -3 9
7 12 9 0 0 3 ...
Prof V Nallasivam
ˆ 9y =
x y
1 6 9 0 0 -3 9
1 12 9 0 0 3 9
3 6 9 0 0 -3 9
3 12 9 0 0 3 9
5 6 9 0 0 -3 9
5 12 9 0 0 3 9
7 6 9 0 0 -3 9
7 12 9 0 0 3 ...
Prof V Nallasivam
2
ˆ( ) 0
0
( ) 72
y y
r
y y
−
= = =
−
∑
∑
Example-2
Prof V Nallasivam
Research & Development
Expenditure - Profit
Prof V Nallasivam
x y
2 20 24 -6 36 -10 100
3 25 26 -4 16 -5 25
5 34 30 0 0 4 16
4 30 28 -2 4 0 0
11 40 42 12 144 10 100
5 31 30 0 0 1 1
30 ...
Prof V Nallasivam
2
ˆ( ) 200
0.829
( ) 241
y y
r
y y
−
= = =
−
∑
∑
y
ˆy
y
Total
Variation
Unexplained
Variation
Explained
Variation
Prof V Nallasivam
x y
2 20 24 -4 16
3 25 26 -1 1
5 34 30 4 16
4 30 28 2 4
11 40 42 -2 4
5 31 30 1 1
30 180 180 0 42
ˆy ˆy y− 2
ˆ( )y y−
ˆy ˆ...
Prof V Nallasivam
2
ˆ( ) 42
3.24
2 4
e
y y
SE
n
−
= = =
−
∑
Formulation of Hypothesis
Significance Level [
αα
Formulation of Hypothesis
Significance Level [
α
Formulation of Hyp...
-Statistic Parameter
CV
Standard Error
=
2 0
4.44
0.45r
b B
CV
SE
− −
= = =
Prof V Nallasivam
0- 2.78 2.78
4.44
Probability Curve t Distribution
Acceptance Region Rejected RegionRejected Region
Table Value
Calculated...
Acceptance Region Rejected Region
7.71
19.048
Table Value
Calculated Value
P Value 0.05
Prof V Nallasivam
ANOVA
0.012
Prof V Nallasivam
I Hypothesis Testing
II Estimation of Population Parameters
a) Point Estimate
b) Interval Estimate
Prof V Nallasivam
r
b B
t
SE
−
=
2.0 2.1
0.22
0.45
t
−
= = −
Population Growth Rate of Profit = 2.1
Prof V Nallasivam
0- 2.78 2.78
- 0.22
Probability Curve t Distribution
Acceptance Region Rejected RegionRejected Region
Table Value
Calculat...
From
Sample
statistic estimate, population Parameter
From
Sample
y estimate, population Y
From
Sample
estimate, population...
Parameter = statistic ± [Standard Error × Critical Value]
Parameter = statistic + [Standard Error × Critical Value]
Parame...
Confidence Level Significance Level
90%
(0.9)
10%
(0.1)
95%
(0.95)
5%
(0.05)
99%
(0.99)
1%
(0.01)
Prof V Nallasivam
y
ˆy
y
Upper Limit 3.25
5
Prof V Nallasivam
Lower Limit 0.75
Point Estimate 2.00
34
31
y
From Sample b confidence Interval...
y
ˆy
y
Upper Limit 38.39
5
Prof V Nallasivam
Lower Limit 21.11
Point Estimate 30
34
31
y
From Sample confidence Interval o...
y
ˆy
y
Upper Limit 27.23
5
Prof V Nallasivam
Lower Limit 12.77
Point Estimate 20
34
31
y
From Sample a confidence Interval...
y
ˆy
y
Upper Limit 39.45
5
Prof V Nallasivam
Lower Limit 20.55
Point Estimate 30
34
31
y
From Sample y confidence Interval...
Prof V Nallasivam
Prof V Nallasivam
Dependent Variable
Sales
Independent Variables
Market Potential
Number of dealers
Number of Sales People...
Prof V Nallasivam
Reg
n
SALES POTENTI DEALERS PEOPLE COMPT SERVICE CUSTOM
1 5.00 25.00 1.00 6.00 5.00 2.00 20.00
2 60.00 1...
Prof V Nallasivam
1 1 2 2 3 3 4 4 5 5 6 6y a b x b x b x b x b x b x= + + + + + +
Sales = -3.17 + 0.227Pot + 0.819Dealers ...
CORRELATION
COMPUTER OUTPUT [SPSS]
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .989 .977 .960 4.39102
Model Summary
a Predictors: (Consta...
Model Sum of Squares df Mean Square F Sig.
1 Regression 6609.485 6 1101.581 57.133 .000
Residual 154.249 8 19.281
Total 67...
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Model B Std. Error Beta
1 (Constant) -3.173 5.813 -.546 .600
...
Prof V Nallasivam
1 1 2 2y a b x b x= + +
Sales = - 10.616 + 0.234 Pot + 1.424People
Prof V Nallasivam
Men Women
Months
Employed
Base
Salary
Months
Employed
Base
Salary
6 7.50 5 6.2
10 8.60 13 8.7
12 9.10 15 9.4
18 10.30 21 9...
Ho: There is no difference in the base
Salary between Male and Female
1 2:oH x x=
Prof V Nallasivam
1
1
2
1
5
9.7
4.415
n
x
s
=
=
=
2
2
2
2
4
8.525
2.609
n
x
s
=
=
=
Men Women
( =0.01; =7)
Calculated t Value = 0.92
Table V...
Rejected Region
0- 2.365 2.356
0.92
Acceptance Region Rejected Region
0.0250.025 P - Value
Prof V Nallasivam
Prof V Nallasivam
Months
Employed
Base
Salary
6 7.50
10 8.60
12 9.10
18 10.30
30 13.00
5 6.2
13 8.7
15 9.4
21 9.8
Prof V Nallasivam
OBS ACTUAL PREDICTED
VALUE
RESIDUAL
1 7.5000 7.2085 0.2915
2 8.6000 8.1413 0.4587
3 9.1000 8.6077 0.4923
4 10.3000 10.0069...
Months
Employed
Sex
Base
Salary
M 6 0 7.50
M 10 0 8.60
M 12 0 9.10
M 18 0 10.30
M 30 0 13.00
F 5 1 6.2
F 13 1 8.7
F 15 1 9...
Ho: There is no difference in the base
Salary between Male and Female
Prof V Nallasivam
Prof V Nallasivam
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Model B Std. Error Beta
1 (Constant) 6.248 ...
Prof V Nallasivam
0.789
3.31
0.238r
b B
CV
SE
− −
= = =
Prof V Nallasivam
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Model B Std. Error Beta
1 (Constant) 6.248 ...
Rejected Region
0- 2.45 2.45
- 3.309
Acceptance Region Rejected Region
0.016 0.0250.025 P - Value
Prof V Nallasivam
7.5000 7.6109 -0.1109
8.6000 8.5192 0.0808
9.1000 8.9734 0.1266
10.3000 10.3358 -0.0358
13.0000 13.0607 -0.0607
6.2000 6.5...
Prof V Nallasivam
Modeling in regression
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Modeling in regression

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Dependability of Regression Equation
Drawing Inferences
Optimising the independent variables in a Multiple Regression
Regression Modeling Technique

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Modeling in regression

  1. 1. Prof V Nallasivam
  2. 2. Regression Modeling Technique Dependability of Regression Equation Drawing Inferences Optimising the independent variables in a Multiple Regression Prof V Nallasivam
  3. 3. Year R & D Expenditure (in Crs) Annual Profit (in Crs) x y 2002 2 20 2003 3 25 2004 5 34 2005 4 30 2006 11 40 2007 5 31 Total 30 180 Prof V Nallasivam
  4. 4. Prof V Nallasivam ˆ 20 2y x= +
  5. 5. ANOVA - (Test the Model) Scatter diagram Standard Error of Estimate Testing the significance of Regression Co-efficient (b) against Zero. Co-efficient of determination Prof V Nallasivam Dependability of a Regression Equation
  6. 6. Prof V Nallasivam
  7. 7. 2 Explained Variation r Total Variation = Prof V Nallasivam 2 2 [ ]r Correlation= Coefficient of Determination
  8. 8. x y 1 4 4 -14 196 -14 196 2 8 8 -10 100 -10 100 3 12 12 -6 36 -6 36 4 16 16 -2 4 -2 4 5 20 20 2 4 2 4 6 24 24 6 36 6 36 7 28 28 10 100 10 100 8 32 32 14 196 14 196 144 144 0 672 0 672 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam
  9. 9. Prof V Nallasivam ˆ 4y x=
  10. 10. x y 1 4 4 -14 196 -14 196 2 8 8 -10 100 -10 100 3 12 12 -6 36 -6 36 4 16 16 -2 4 -2 4 5 20 20 2 4 2 4 6 24 24 6 36 6 36 7 28 28 10 100 10 100 8 32 32 14 196 14 196 144 144 0 672 0 672 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam
  11. 11. x y 1 4 4 -14 196 -14 196 2 8 8 -10 100 -10 100 3 12 12 -6 36 -6 36 4 16 16 -2 4 -2 4 5 20 20 2 4 2 4 6 24 24 6 36 6 36 7 28 28 10 100 10 100 8 32 32 14 196 14 196 144 144 0 672 0 672 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam
  12. 12. x y 1 4 4 -14 196 -14 196 2 8 8 -10 100 -10 100 3 12 12 -6 36 -6 36 4 16 16 -2 4 -2 4 5 20 20 2 4 2 4 6 24 24 6 36 6 36 7 28 28 10 100 10 100 8 32 32 14 196 14 196 144 144 0 672 0 672 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam
  13. 13. x y 1 4 4 -14 196 -14 196 2 8 8 -10 100 -10 100 3 12 12 -6 36 -6 36 4 16 16 -2 4 -2 4 5 20 20 2 4 2 4 6 24 24 6 36 6 36 7 28 28 10 100 10 100 8 32 32 14 196 14 196 144 144 0 672 0 672 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam
  14. 14. x y 1 4 4 -14 196 -14 196 2 8 8 -10 100 -10 100 3 12 12 -6 36 -6 36 4 16 16 -2 4 -2 4 5 20 20 2 4 2 4 6 24 24 6 36 6 36 7 28 28 10 100 10 100 8 32 32 14 196 14 196 144 144 0 672 0 672 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam E V T V
  15. 15. Prof V Nallasivam 2 ˆ( ) 672 1 ( ) 672 y y r y y − = = = − ∑ ∑
  16. 16. Y = 12 ˆ 4y x= Y X ˆ 12y = Example-1 Prof V Nallasivam
  17. 17. x y 1 6 9 0 0 -3 9 1 12 9 0 0 3 9 3 6 9 0 0 -3 9 3 12 9 0 0 3 9 5 6 9 0 0 -3 9 5 12 9 0 0 3 9 7 6 9 0 0 -3 9 7 12 9 0 0 3 9 0 72 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam
  18. 18. Prof V Nallasivam ˆ 9y =
  19. 19. x y 1 6 9 0 0 -3 9 1 12 9 0 0 3 9 3 6 9 0 0 -3 9 3 12 9 0 0 3 9 5 6 9 0 0 -3 9 5 12 9 0 0 3 9 7 6 9 0 0 -3 9 7 12 9 0 0 3 9 0 72 ˆyˆy y− 2 ˆ( )y y−y y− 2 ( )y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam E V T V
  20. 20. Prof V Nallasivam 2 ˆ( ) 0 0 ( ) 72 y y r y y − = = = − ∑ ∑
  21. 21. Example-2 Prof V Nallasivam
  22. 22. Research & Development Expenditure - Profit Prof V Nallasivam
  23. 23. x y 2 20 24 -6 36 -10 100 3 25 26 -4 16 -5 25 5 34 30 0 0 4 16 4 30 28 -2 4 0 0 11 40 42 12 144 10 100 5 31 30 0 0 1 1 30 180 180 200 241 ˆyˆy y−ˆy y−y y−y y− ˆy ˆy y− 2 ˆ( )y y− y y− 2 ( )y y− Prof V Nallasivam E V T V
  24. 24. Prof V Nallasivam 2 ˆ( ) 200 0.829 ( ) 241 y y r y y − = = = − ∑ ∑
  25. 25. y ˆy y Total Variation Unexplained Variation Explained Variation Prof V Nallasivam
  26. 26. x y 2 20 24 -4 16 3 25 26 -1 1 5 34 30 4 16 4 30 28 2 4 11 40 42 -2 4 5 31 30 1 1 30 180 180 0 42 ˆy ˆy y− 2 ˆ( )y y− ˆy ˆy y− 2 ˆ( )y y− Prof V Nallasivam Standard Error of Estimate
  27. 27. Prof V Nallasivam 2 ˆ( ) 42 3.24 2 4 e y y SE n − = = = − ∑
  28. 28. Formulation of Hypothesis Significance Level [ αα Formulation of Hypothesis Significance Level [ α Formulation of Hypothesis Significance Level [ α Formation of Hypothesis Significance Level Probability Distribution Find the Table Value Find the Calculated Value Prof V Nallasivam Test Regression Coefficient ‘b’ against ZERO
  29. 29. -Statistic Parameter CV Standard Error = 2 0 4.44 0.45r b B CV SE − − = = = Prof V Nallasivam
  30. 30. 0- 2.78 2.78 4.44 Probability Curve t Distribution Acceptance Region Rejected RegionRejected Region Table Value Calculated Value P Value 0.025 0.025 Prof V Nallasivam
  31. 31. Acceptance Region Rejected Region 7.71 19.048 Table Value Calculated Value P Value 0.05 Prof V Nallasivam ANOVA 0.012
  32. 32. Prof V Nallasivam
  33. 33. I Hypothesis Testing II Estimation of Population Parameters a) Point Estimate b) Interval Estimate Prof V Nallasivam
  34. 34. r b B t SE − = 2.0 2.1 0.22 0.45 t − = = − Population Growth Rate of Profit = 2.1 Prof V Nallasivam
  35. 35. 0- 2.78 2.78 - 0.22 Probability Curve t Distribution Acceptance Region Rejected RegionRejected Region Table Value Calculated Value P Value 0.025 0.025 Prof V Nallasivam
  36. 36. From Sample statistic estimate, population Parameter From Sample y estimate, population Y From Sample estimate, population From Sample b estimate, population B From Sample a estimate, population A ˆyˆY ˆy ˆY Prof V Nallasivam
  37. 37. Parameter = statistic ± [Standard Error × Critical Value] Parameter = statistic + [Standard Error × Critical Value] Parameter = statistic - [Standard Error × Critical Value] General Formula to Calculate Interval Estimate Upper Limit Lower Limit Prof V Nallasivam
  38. 38. Confidence Level Significance Level 90% (0.9) 10% (0.1) 95% (0.95) 5% (0.05) 99% (0.99) 1% (0.01) Prof V Nallasivam
  39. 39. y ˆy y Upper Limit 3.25 5 Prof V Nallasivam Lower Limit 0.75 Point Estimate 2.00 34 31 y From Sample b confidence Interval of B b
  40. 40. y ˆy y Upper Limit 38.39 5 Prof V Nallasivam Lower Limit 21.11 Point Estimate 30 34 31 y From Sample confidence Interval ofˆy ˆY
  41. 41. y ˆy y Upper Limit 27.23 5 Prof V Nallasivam Lower Limit 12.77 Point Estimate 20 34 31 y From Sample a confidence Interval of A a
  42. 42. y ˆy y Upper Limit 39.45 5 Prof V Nallasivam Lower Limit 20.55 Point Estimate 30 34 31 y From Sample y confidence Interval of Y
  43. 43. Prof V Nallasivam
  44. 44. Prof V Nallasivam Dependent Variable Sales Independent Variables Market Potential Number of dealers Number of Sales People Competitors Activities Number of Service People Number of Existing Customers
  45. 45. Prof V Nallasivam Reg n SALES POTENTI DEALERS PEOPLE COMPT SERVICE CUSTOM 1 5.00 25.00 1.00 6.00 5.00 2.00 20.00 2 60.00 150.00 12.00 30.00 4.00 5.00 50.00 3 20.00 45.00 5.00 15.00 3.00 2.00 25.00 4 11.00 30.00 2.00 10.00 3.00 2.00 20.00 5 45.00 75.00 12.00 20.00 2.00 4.00 30.00 6 6.00 10.00 3.00 8.00 2.00 3.00 16.00 7 15.00 29.00 5.00 18.00 4.00 5.00 30.00 8 22.00 43.00 7.00 16.00 3.00 6.00 40.00 9 29.00 70.00 4.00 15.00 2.00 5.00 39.00 10 3.00 40.00 1.00 6.00 5.00 2.00 5.00 11 16.00 40.00 4.00 11.00 4.00 2.00 17.00 12 8.00 25.00 2.00 9.00 3.00 3.00 10.00 13 18.00 32.00 7.00 14.00 3.00 4.00 31.00 14 23.00 73.00 10.00 10.00 4.00 3.00 43.00 15 81.00 150.00 15.00 35.00 4.00 7.00 70.00
  46. 46. Prof V Nallasivam 1 1 2 2 3 3 4 4 5 5 6 6y a b x b x b x b x b x b x= + + + + + + Sales = -3.17 + 0.227Pot + 0.819Dealers + 1.091People -1.893Compet – 0.549Service + 0.66Cust.
  47. 47. CORRELATION
  48. 48. COMPUTER OUTPUT [SPSS]
  49. 49. Model R R Square Adjusted R Square Std. Error of the Estimate 1 .989 .977 .960 4.39102 Model Summary a Predictors: (Constant), CUSTOMER, COMPT, SERVICE, POTENTIA, DEALERS, PEOPLE
  50. 50. Model Sum of Squares df Mean Square F Sig. 1 Regression 6609.485 6 1101.581 57.133 .000 Residual 154.249 8 19.281 Total 6763.733 14 ANOVA a Predictors: (Constant), CUSTOMER, COMPT, SERVICE, POTENTIA, DEALERS, PEOPLE b Dependent Variable: SALES
  51. 51. Unstandardized Coefficients Standardized Coefficients t Sig. Model B Std. Error Beta 1 (Constant) -3.173 5.813 -.546 .600 POTENTIA .227 .075 .439 3.040 .016 DEALERS .819 .631 .164 1.298 .230 PEOPLE 1.091 .418 .414 2.609 .031 COMPT -1.893 1.340 -.085 -1.413 .195 SERVICE -.549 1.568 -.041 -.350 .735 CUSTOMER 6.594E-02 .195 .050 .338 .744 Coefficients a Dependent Variable: SALES
  52. 52. Prof V Nallasivam 1 1 2 2y a b x b x= + + Sales = - 10.616 + 0.234 Pot + 1.424People
  53. 53. Prof V Nallasivam
  54. 54. Men Women Months Employed Base Salary Months Employed Base Salary 6 7.50 5 6.2 10 8.60 13 8.7 12 9.10 15 9.4 18 10.30 21 9.8 30 13.00 Prof V Nallasivam
  55. 55. Ho: There is no difference in the base Salary between Male and Female 1 2:oH x x= Prof V Nallasivam
  56. 56. 1 1 2 1 5 9.7 4.415 n x s = = = 2 2 2 2 4 8.525 2.609 n x s = = = Men Women ( =0.01; =7) Calculated t Value = 0.92 Table Value t 2.998α γ = Prof V Nallasivam
  57. 57. Rejected Region 0- 2.365 2.356 0.92 Acceptance Region Rejected Region 0.0250.025 P - Value Prof V Nallasivam
  58. 58. Prof V Nallasivam
  59. 59. Months Employed Base Salary 6 7.50 10 8.60 12 9.10 18 10.30 30 13.00 5 6.2 13 8.7 15 9.4 21 9.8 Prof V Nallasivam
  60. 60. OBS ACTUAL PREDICTED VALUE RESIDUAL 1 7.5000 7.2085 0.2915 2 8.6000 8.1413 0.4587 3 9.1000 8.6077 0.4923 4 10.3000 10.0069 0.2913 5 13.0000 12.8054 0.1946 6 6.2000 6.9753 -0.7753 7 8.7000 8.8409 -0.1407 8 9.4000 9.3073 0.0927 9 9.8000 10.7066 -0.9066 Prof V Nallasivam
  61. 61. Months Employed Sex Base Salary M 6 0 7.50 M 10 0 8.60 M 12 0 9.10 M 18 0 10.30 M 30 0 13.00 F 5 1 6.2 F 13 1 8.7 F 15 1 9.4 F 21 1 9.8Prof V Nallasivam
  62. 62. Ho: There is no difference in the base Salary between Male and Female Prof V Nallasivam
  63. 63. Prof V Nallasivam Unstandardized Coefficients Standardized Coefficients t Sig. Model B Std. Error Beta 1 (Constant) 6.248 .291 21.439 .000 MONEM P .227 .016 .937 14.089 .000 SEX -.789 .238 -.220 -3.309 .016
  64. 64. Prof V Nallasivam 0.789 3.31 0.238r b B CV SE − − = = =
  65. 65. Prof V Nallasivam Unstandardized Coefficients Standardized Coefficients t Sig. Model B Std. Error Beta 1 (Constant) 6.248 .291 21.439 .000 MONEM P .227 .016 .937 14.089 .000 SEX -.789 .238 -.220 -3.309 .016 0.025
  66. 66. Rejected Region 0- 2.45 2.45 - 3.309 Acceptance Region Rejected Region 0.016 0.0250.025 P - Value Prof V Nallasivam
  67. 67. 7.5000 7.6109 -0.1109 8.6000 8.5192 0.0808 9.1000 8.9734 0.1266 10.3000 10.3358 -0.0358 13.0000 13.0607 -0.0607 6.2000 6.5949 -0.3949 8.7000 8.4115 0.2885 9.4000 8.8656 0.5344 9.8000 10.2281 -0.4281 Prof V Nallasivam y ˆy ˆy y−
  68. 68. Prof V Nallasivam

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