here, pal! regress this!
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Here, pal! Regress this!. Part 2. presented by. Miles Hamby , PhD Principle, Ariel Training Consultants MilesFlight.20megsfree.com [email protected]. The Equation. MODEL 3 IVB (Slope) (Constant)35.577 Age-.117 Gender-.110 Married-4.05E-02 Black.439 Native Am.719 Asian-.553 - PowerPoint PPT PresentationTRANSCRIPT
Here, pal!
Regress this!
presented by
Miles Hamby, PhD
Principle, Ariel Training ConsultantsMilesFlight.20megsfree.com
Part 2
The EquationMODEL 3
IV B (Slope)
(Constant) 35.577
Age -.117
Gender -.110
Married -4.05E-02
Black .439
Native Am .719
Asian -.553
Hispanic -.830
Unknown .531
Alien -.618
GPA -.277
Transfer Cr 4.285E-02
Undergrad -3.259
Tutoring -4.71E-07
Accounting 2.638
Business 2.651
Y = a + bAge + bGen + bMar +bBlk
+ bNA + bAsn + bHis + bUnk + bAln
+ bGPA + bXfer + bUndergrad
+ bTutor + bAcc + bBus
Y = 35.57 + (-.11)Age + (-.11)Gen
+ (-.04)Mar + (.43)Black
+ (.71)NatAm + (-.55)Asian
+ (-.83)Hisp + (-.53)Unk + (-.61)Alien
+ (.27)GPA + (.04)Xfer + (-3.25)Under
+ (-.04)Tutor + (2.63)Acc + (2.65)Bus
Let’s Predict!What is the predicted Quarters to completion for:
Age 36, Male, Single, Black, US citizen, 3.5 GPA, 35 Transfer credits, Undergraduate, no Tutoring, Business major
Y = 35.57 - (.11)Age - (.11)Gen - (.04)Mar + (.43)Black + (.71)NatAm - (.55)Asian - (.83)Hisp - (.53)Unk - (.61)Alien - (.27)GPA + (.04)Xfer – (3.25)Under - (.04)Tutor + (2.63)Acc + (2.65)Bus
Y = 35.57 - (.11)(36) - (.11)(0) - (.04)(0) + (.43)(1) + (.71)(0) - (.55)(0) - (.83)(0) - (.53)(0) - (.61)(0) - (.27)(3.5) + (.04)(35) – (3.25)(1) - (.04)(0) + (2.63)(0) + (2.65)(1)
35.86 = 35.57 – 3.96 - 0 - 0 + .43 + 0 - 0 - 0 - 0 – 0 - .94 + 1.4 – 3.25 - 0 + 0 + 2.65
What is the predicted Quarters to completion for:
Age 45, Female, Married, White, Alien, 3.0 GPA, No Transfer credits, Undergraduate, Tutored, Computer major
Y = 35.57 - (.11)Age - (.11)Gen - (.04)Mar + (.43)Black + (.71)NatAm - (.55)Asian - (.83)Hisp - (.53)Unk - (.61)Alien - (.27)GPA + (.04)Xfer – (3.25)Under - (.04)Tutor + (2.63)Acc + (2.65)Bus
Y = 35.57 - (.11)(45) - (.11)(1) - (.04)(1) + (.43)(0) + (.71)(0) - (.55)(0) - (.83)(0) - (.53)(0) - (.61)(1) - (.27)(3.0) + (.04)(0) – (3.25)(1) - (.04)(1) + (2.63)(0) + (2.65)(0)
25.8 = 35.57 – 4.95 - .11 - .04 + 0 + 0 - 0 - 0 - 0 - .61 - .81 + 0 - 3.25 - .04 + 0 + 0
Example Profiles
Excel
Variation in the DV
Each successive Model explains more of the variation (R2) in the DV (Time to Completion)
Model Summary
.179a .032 .031 6.242 .032 22.926 9 6253 .000
.343b .118 .116 5.960 .086 152.204 4 6249 .000
.392c .154 .152 5.838 .036 133.252 2 6247 .000
Model1
2
3
R R SquareAdjustedR Square
Std. Error ofthe Estimate
R SquareChange F Change df1 df2 Sig. F Change
Change Statistics
Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native Americana.
Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native American, Tutoring Sessoin Date,XFER CR, GPA , Undergrad Status
b.
Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native American, Tutoring Sessoin Date,XFER CR, GPA , Undergrad Status, Accounting, Business
c.
All three Models are significant (F < .05)
But, 84.6% or more of the variation is still unexplained
Possible factors?
Worklife, children, personal goals, financial aid, company sponsorship
Model Summary
.179a .032 .031 6.242 .032 22.926 9 6253 .000
.343b .118 .116 5.960 .086 152.204 4 6249 .000
.392c .154 .152 5.838 .036 133.252 2 6247 .000
Model1
2
3
R R SquareAdjustedR Square
Std. Error ofthe Estimate
R SquareChange F Change df1 df2 Sig. F Change
Change Statistics
Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native Americana.
Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native American, Tutoring Sessoin Date,XFER CR, GPA , Undergrad Status
b.
Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native American, Tutoring Sessoin Date,XFER CR, GPA , Undergrad Status, Accounting, Business
c.
The point is – with R2 only .154, there is some other other factor out there contributing more to Time to Completion and we need to find it!
Coefficientsa
35.577 .968 36.768 .000
-.117 .009 -.162 -13.256 .000
-.110 .157 -.009 -.701 .483
-4.05E-02 .040 -.012 -1.017 .309
.439 .176 .036 2.497 .013
.719 .641 .028 1.120 .263
-.553 .243 -.037 -2.275 .023
-.830 .351 -.041 -2.366 .018
.531 .254 .032 2.092 .036
-.618 .216 -.038 -2.867 .004
-.277 .221 -.016 -1.254 .210
4.285E-02 .002 .283 20.762 .000
-3.259 .218 -.237 -14.959 .000
-4.71E-07 .000 -.007 -.566 .571
2.638 .240 .135 10.970 .000
2.651 .181 .191 14.686 .000
(Constant)
Age
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
Accounting
Business
Model3
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Quarters to Completiona.
Variation in the Slopes
Cannot tell by the slopes – cannot compare apples to oranges
Is the slope of Age (-.117) more or less than slope of
GPA (-.277)?
Apples to apples – i.e., use Standardized ‘Beta’
Beta Age (-.162) more Beta Acc (.016);i.e., unit of Age results in greater change than unit of GPA
Drawing Conclusions
Summarize the correlations (Pearson’s R)
Summarize the effects (coefficient B)
Summarize the variation (R2)
“There is a statistically significant association between all the variables and Time to Completion.”
“Academic major and transfer credits, and Undergraduate status seem to have the greatest affects.”
“However, 86% of the variation in Time to Completion is still unexplained.”
Suggest what’s next“Data on worklife, income, finances, and company sponsorship should be collected and anlayed.”
In Summary
• Regression measures the strength of association (correlation) for all variables considered at the same time
• Regression can predict the outcome of any given profile
• Regression measures the amount of effect (slope) of each variable on the dependent variable as ameliorated by all other variables
Regress it, Pal!
It’s where it’s at!
Tests of Significance
t-test for dichotomous variable (two categories)
eg – Is there a difference in GPA between men and women?
F-test - One-way ANOVA for polychomtomous (more than two categories)
eg -- Is there a difference in GPA between African-American, Hispanic, Anglo, and Native American students?
Purpose – determine if there is a significant difference between means of the categories of the nominal variable
References
Lind, D., Marchal, R., Mason (2001); Statistical Techniques in Business & Economics, 11th ed., McGraw-Hill Companies, Inc., New York, NY. ISBN 0-07-112318-0
McClendon, J. (1994); Multiple Regression and Causal Analysis, F.E. Peacock Pulishers, Inc., Itasca, IL. ISBN 0-87581-384-4
SPSS (1999); SPSS Base 9.0 Applications Guide, SPSS, Inc., Chicago, IL. ISBN 0-13-020401-3
Shortcoming of t-test and F ~
eg -
Can we predict the GPA of a student based on gender?
Regression predicts!
Can we predict the level of satisfaction with a course based on gender?
Can we predict the likelihood of graduation of a student based on gender?
They do not predict.
Examples - Means of t-test and F
Dichotomous - Find the mean GPA of males and that of females and compare them with a t-test.
Polychotomous - Find the mean GPA for African-Americans, Hispanics, and Anglos and compare them with a one-way ANOVA
Example 1 Data
Arbitrarily Code ‘gender’ (nominal variables)
Female = 1
Male = 0
ID SAT GPA Gender
Stud 1 5 3.2 F (1)
Stud 11 3 2.7 M (0)
(a) Correlation r (SPSS ‘R’) = .846
Interpretation – GPA is strongly associated with gender type
Example 1ID SAT GPA Gender
Stud 1 5 3.2 F (1)
Stud 11 3 2.7 M (0)
Model Summary
.846a .716 .700 .76 .716 45.343 1 18 .000Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
R SquareChange F Change df1 df2 Sig. F Change
Change Statistics
Predictors: (Constant), Gendera.
Example 1
(b) Significance of difference in means of GPA by gender – ANOVA F < 0.05
Interpretation - reject Ho, i.e., there is a statistically significant difference in GPA according to gender
ID SAT GPA Gender
Stud 1 5 3.2 F (1)
Stud 11 3 2.7 M (0)
ANOVAb
26.450 1 26.450 45.343 .000a
10.500 18 .583
36.950 19
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
Predictors: (Constant), Gendera.
Dependent Variable: Satisfactionb.
(c) Regression model (y=a+bx)
Example 1
Interpretation – Male SAT is 1.9, female SAT is 1.9 + 2.3 = 4.2; i.e., mean female GPA is higher than mean male GPA
GPA = 1.9 + 2.3 (gender code)
Coefficientsa
1.900 .242 7.867 .000
2.300 .342 .846 6.734 .000
(Constant)
Gender
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Satisfactiona.
ID SAT GPA Gender
Stud 1 5 3.2 F (1)
Stud 11 3 2.7 M (0)
(a) Correlation r (SPSS ‘R’) = .837
Model Summary
.837a .701 .685 .3544Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Predictors: (Constant), Gendera.
Interpretation – GPA is strongly associated with gender type
Example 1ID SAT GPA Gender
Stud 1 5 3.2 F (1)
Stud 11 3 2.7 M (0)
Example 1
(b) Significance of difference in means of GPA by gender – ANOVA F < 0.05
ANOVAb
5.305 1 5.305 42.230 .000a
2.261 18 .126
7.566 19
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
Predictors: (Constant), Gendera.
Dependent Variable: GPAb.
Interpretation - reject Ho, i.e., there is a statistically significant difference in GPA according to gender
ID SAT GPA Gender
Stud 1 5 3.2 F (1)
Stud 11 3 2.7 M (0)
(c) Regression model (y=a+bx)
Coefficientsa
2.620 .112 23.377 .000
1.030 .158 .837 6.498 .000
(Constant)
Gender
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: GPAa.
Example 1
Interpretation – Male GPA is 2.62, female GPA 2.62 + 1.03 = 3.65; i.e., mean female GPA is higher than mean male GPA
GPA = 2.62 + 1.03 (gender code)
ID SAT GPA Gender
Stud 1 5 3.2 F (1)
Stud 11 3 2.7 M (0)
Nonsense coding – randomly assigning a random number to a nominal variable
Regardless of the number assigned to a nominal variable, the strength of association is unaffected,
ie, r (correlation), r2 (coef. of determination) and B (slope)
eg –
Male = 1, Female = 2
Male = 13, Female = 43
Male = 0, Female = 1
Hispanic = 35, African-American = 72, Anglo = 87
For dichotomous variable, coding number is not important
BUT – slopes and intercepts coded nonsense are difficult to interpret, unless coded ‘0’ or ‘1’
eg -
Male = 0, Female = 1
Mean GPA for Male (Ym) = 2.8,
Mean GPA for Female (Yf) = 3.5
Ym – YfXm - Xf
= 2.62 – 3.650 - 1
– 1.03- 1
1.03= =Slope B =
Result - the mean GPA of the category coded 0 = the Y-intercept
0 (Male)
1 (Female)
Y
X
3.65
2.62
B = 1.03
Interpretation –
Female GPAs tend to be predictably higher than Male GPAs
Ym – YfXm - Xf
= 2.62 – 3.650 - 1
– 1.03- 1
1.03= =Slope B =
0 (Female)
1 (Male)
Y
X
2.62
3.65
B = - 1.03
Interpretation – same result
Female GPAs tend to be predictably higher than Male GPAs
Recode Male = 1, Female = 0:
Ym – YfXm - Xf
= 3.65-2.620 - 1
1.03- 1
-1.03= =Slope B =
0 (Female)
1 (Male)
Y
X
2.62
3.65
Interpretation –
We can predict GPA based on male or female
Thus, regression equation is:
With one variable category = 0, (eg female) then Y intercept is the mean of that category and the slope predicts the other category
Y = 3.65 – 1.03X
Fine – but what about polychotomous variables?
Cannot use single dummy variable for more than two categories.
Why? This would assume the nominal categories were actually interval, ie, one was more of the other.
eg, if ethnic variable were coded thus:
Hispanic = 1, African-Am = 2, Anglo = 3,
the regression would assume that Anglo is 2 units greater than Hispanic, etc
Regression also interprets a dichotomous variable (eg male=0, female=1) as female being 1 unit more than male.
However, with more than two categories, this is not true.
But, with dichotomous, the mean score of code ‘0’ is the intercept, and the mean score of code ‘1’ is the intercept + the slope.
eg – Ethnic Category
Therefore, must treat each category as a unique variable –
Has it
Doesn’t have it
Hispanic
1
0
Afr-Am
1
0
Anglo
1
0
Code each category/variable as:
1 = ‘presence of characteristic’ or
0 = ‘absence of characteristic’
a ‘Dummy’ variable
(Depicts 3 students – one in each ethnic category)
For each case/subject, code each category as either ‘having it’ or ‘not’
Coding Polychotomous Nominal VariablesAs Dummy Variables
Case ID
Stud 1
Stud 2
Stud 3
Hispanic0
1
0
Afr-Am
1
0
0
Anglo
0
0
1
eg –
Student 1 is an African-American
Student 2 is an Hispanic
Student 3 is an Anglo
(Depicts 3 students – one in each ethnic category)
Regression equation would look like:
Y = a + bH + bAA + bAn
i.e., the sum of the three dummies for each case always equals ‘1’.
Stud 1 (Hispanic) ~ 0 + 1 + 0 = 1 Stud 2 (Afr-Am) ~ 1 + 0 + 0 = 1Stud 3 (Anglo) ~ 0 + 0 + 1= 1
Problem – ‘perfect multi-collinearity’
Case ID
Stud 1
Stud 2
Stud 3
Hispanic
0
1
0
Afr-Am
1
0
0
Anglo
0
0
1
The resulting regression equation would return a confusing Y-intercept (a):
Y = a + bH + bAA + bAn
Case ID
Stud 1
Stud 2
Stud 3
Hispanic
0
1
0
Afr-Am
1
0
0
Anglo
0
0
1
i.e., what is the reference point from which to determine the actual means of the other variables?
What to do -
drop one category from the regression
i.e., use only g – 1 dummies
eg, -
Y = a + bH + bAA (bAn dropped for all cases)
Reference group – the category/group chosen to be dropped
Choosing the Reference group – the group that has the most normative support
By leaving out a group, not all cases will sum to ‘1’, and therefore:
the regression equation predicts the mean Y for the group to which the case/student belongs, in reference to the Y-intercept.
Student 1 (African-AM): YAA = a + 0 (b*0H) + b (b*1AA) = a + bAA
Student 2 (Hispanic): YH = a + b (b*1H) + 0 (b*0 AA) = a + bH
Student 3 (Anglo): YAn = a + 0 (b*0H) + 0 (b*0 AA) = a
Case IDStud 1Stud 2Stud 3
Hispanic010
Afr-Am100
Anglo001
i.e., Mean Y of reference group ‘Anglo’ is the intercept ‘a’; All other groups are then compared to ‘Anglo’
Case IDStud 1Stud 2Stud 3
Satisfaction425
Hispanic010
Afr-Am100
Anglo001
Satisfaction coding:
5Very satisfied
4Satisfied
3Ambivalent
2Dissatisfie
d
1Very Dissatisfied
Example – Satisfaction with a course
Case IDStud 1Stud 2Stud 3
Satisfaction425
Hispanic010
Afr-Am100
Anglo001
Thus, predicted satisfaction level for any other Hispanic student would be ~ Y = 3.0 + 0.4*1 +0.2*0 = 3.4
Likewise, predicted satisfaction level for any other Africa-American student would be ~ = 3.0 + 0.4*0 +0.2*1 = 3.2
Assume that a multiple regression of the affect of ethnicity on satisfaction returned a Y-intercept of 3.0 with slopesH =.4, AA =.2 (An held out as reference group)
i.e., Y = 3.0 + .4H + .2AA
Predicted satisfaction level for any Anglo student is the intercept ‘a’ = 3.0
Slopes – indicate difference between a specific category/group and the reference group.
ie, the 0.4 slope for Hispanic indicates Hispanic satisfaction is 0.4 more than Anglo.
i.e., Y = 3.0 + 0.4H + 0.2AA
Likewise, African-American satisfaction is 0.2 more than Anglo.
Also, relatively, African-American satisfaction is 0.2 less than Hispanic.
Note - this does not predict the satisfaction level (or GPA, etc) of a unique individual student – only one of a particular ethnic background.
Because there is no ‘degree’ of the characteristic ‘ethnicity’
i.e., you are either Anglo, or you are not.
Coefficientsa
3.000 .588 5.106 .000
-.333 .831 -.112 -.401 .693
.375 .777 .135 .482 .636
(Constant)
African-American
Hispanic
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Satisfactiona.
Example (re Example Data)
Satisfaction and Ethnic Group – Anglo as reference group
Interpretation - Mean Anglo satisfaction level is 3.0, mean Afr-Am level is 2.667, mean Hispanic level is 3.375
Regression Model ~ Y = 3.0 -.333AA + .375H
Effect of Multi-colinearity in SPSS – If SPSS detects perfect multi-colinearity within the selected IVs, it drops one IV.
Coefficientsa
3.375 .509 6.633 .000
-.708 .777 -.239 -.911 .375
-.375 .777 -.126 -.482 .636
(Constant)
African-American
Agnlo
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Satisfactiona.
Excluded Variablesb
.a . . . .000HispanicModel1
Beta In t Sig.Partial
Correlation Tolerance
Collinearity
Statistics
Predictors in the Model: (Constant), Agnlo, African-Americana.
Dependent Variable: Satisfactionb.
To make a prediction more ‘individually unique’, add other variables
eg, gender (nominal), age (ratio), time spent on homework (ratio)
Adding Other Variables
Y = a + [b*H + b*AA] + b*Age + b*Homework
Y(GPA) = a + [b*H + b*AA] + b*Age + b*Homework
Case IDStud 1Stud 2Stud 3
GPA3.93.13.2
Hispanic010
Afr-Am100
Anglo001
Age192823
Hours on Homework
1458
Example – given above data, the regression prediction model would be:
Y(GPA) = a + [b*H + b*AA] + b*Age + b*Homework
Intercept - new ‘a’ intercept is no longer the mean score for Anglo -
it is now the individual score for someone who scored ‘0’ age and ‘0’ hours on homework
However - things now change
Slopes – now indicates difference between ethnic group and the reference group for individuals who do not differ in ‘age’ or ‘homework’.
Applications
Research Question -
Do gender, culture, or age of a student have an effect on the student’s perception of his/her learning? RETENTION????
Student Opinion Polls (RETENTION???)
at Strayer University
That is, can we predict a student’s RETNETION???perception of his/her learning based on his/her gender, culture, and age?
And if so, which variable has the greatest effect?
Applications
Collect data from a survey asking students to indicate their perception of satisfaction and instructor effectiveness and how they perceived their instructor.
Methodolgy
Survey must be designed for a regression,
i.e., must have DV and IV.
Dependent Variables:
Instructor Effectiveness - Scale data, 4 through 1
How satisfying was this course?VERY SATISFYING SATISFYING NOT SATISFYING DISAPPOINTING
How effective do you feel your instructor was?VERY EFFECTIVE EFFECTIVE SOMEWHAT NOT EFFECTIVE
Satisfaction – Scale data, 4 through 1
Independent Variables – nominal, four descriptors
FREE
DISCUSSION
LECTURE
BASED
THEORY
BASED
ACTIVITY
BASED
Which one of the following describes your instructor’s teaching technique?
STUDENT
CENTERED
LITTLE
INVOLVEMENT
GAVE TIME
TO THINK ALONE
ACTIVE
PARTICIPATION
Which one of the following describes your instructor’s involvement with students?
Which one of the following describes your instructor’s method of teaching?
Which one of the following best describes your instructor?
GOT US INVOLVED
MOSTLY INSTRUCITONS
MOSTLY
WRITTEN
MOSTLY
ACTIONS
LISTENER DIRECTOR INTERPRETER COACH
Independent Variables – nominal, four descriptors
FREE
DISCUSSION
LECTURE
BASED
THEORY
BASED
ACTIVITY
BASED
Which one of the following describes your instructor’s teaching technique?
STUDENT
CENTERED
LITTLE
INVOLVEMENT
GAVE TIME
TO THINK ALONE
ACTIVE
PARTICIPATION
Which one of the following describes your instructor’s involvement with students?
Which one of the following describes your instructor’s method of teaching?
Which one of the following best describes your instructor?
GOT US INVOLVED
MOSTLY INSTRUCITONS
MOSTLY
WRITTEN
MOSTLY
ACTIONS
LISTENER DIRECTOR INTERPRETER COACH
Model Summary
.175a .031 .019 .68 .031 2.625 4 333 .035Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
R SquareChange F Change df1 df2 Sig. F Change
Change Statistics
Predictors: (Constant), Coach, Listener, Interpretor, Directora.
SPSS Regression Output – CorrelationInstructor Descriptor on Satisfaction (all included)
Interpretation –
As all descriptors were included, the correlation (multiple R) is difficult to interpret.
Coefficientsa
3.039 .134 22.710 .000
.388 .146 .214 2.662 .008
.219 .141 .156 1.547 .123
.293 .145 .186 2.013 .045
.378 .146 .208 2.596 .010
(Constant)
Listener
Director
Interpretor
Coach
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Satisfactiona.
SPSS Regression Output – Means & SlopesInstructor Descriptor on Satisfaction (all included)
Interpretation ~
As all four descriptors were included, means and slopes are difficult to interpret. However, because it ran, perfect multi-colinearity must not exist – i.e., at least one of the records is missing a ‘1’ score for at least one descriptor.
SPSS Regression Output – Instructor Descriptor on Satisfaction
Coach as Reference
Model Summary
.105a .011 .002 .69 .011 1.233 3 334 .298Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
R SquareChange F Change df1 df2 Sig. F Change
Change Statistics
Predictors: (Constant), Interpretor, Listener, Directora.
Interpretation –
With Coach as reference, descriptors depict a modest correlation (R =.105) to Satisfaction and explain only 1.1% (R2-.101) of the variation in Satisfaction.
SPSS Regression Output – Means and SlopesInstructor Descriptor on Satisfaction (Coach as Reference)
Coefficientsa
3.313 .083 39.890 .000
.161 .118 .089 1.371 .171
-4.15E-02 .101 -.030 -.413 .680
3.835E-02 .108 .024 .354 .724
(Constant)
Listener
Director
Interpretor
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Satisfactiona.
Interpretation –
With Coach as reference, Mean score for Coach is 3.313, Listener is 3.474 (slightly higher), Director is 3.272 (slightly lower than Coach), Interpret is 3.351 (slightly higher than Coach). The relatively small slopes suggest relatively little effect the respective descriptor has on Satisfaction.
Excel OutputsExamples of same regression
analyses in MS Excel
(Refer to handouts)
In Summary
• Regression, as a primary tool for prediction, requires quantitative data.
• Qualitative variables are vastly used in social research
• Convert these qualitative variables to quantitative variables by ‘dummy’ coding them ‘1’ – presence of quality, or ‘0’ – absence of quality.
• By so doing, the correlations, means, and slopes become meaningful.
Applications
Research Question -
Do gender, culture, or age of a student have an effect on the student’s perception of his/her learning? RETENTION????
Student Opinion Polls (RETENTION???)
at Strayer University
That is, can we predict a student’s RETNETION???perception of his/her learning based on his/her gender, culture, and age?
And if so, which variable has the greatest effect?