Statistical Inference, Regression SPSS Report

7/28/2019 Statistical Inference, Regression SPSS Report

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Transform Data into KnowledgeSPSS

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Context:

The objective of the assignment is to study the regression analysis of the

validity co-efficient which we get in the correlation analysis of our sample.

For the analysis and learning purpose we had taken data from the BBA-16 (A &

B) of Graduate School of business at International Islamic University,

Islamabad. We recorded there CGPA, Intermediate percentage, medium of

instruction in Matric , intermediate institution, accounting1, accounting 2, cost

accounting, English1, English 2 and oral communication.

In the previous assignment we studied we the correlation and in this we will

study the regression of these variables.

We have made a comparison, of theirCGPA, Inter-Percentage, MOIM,

Public or Private Institution, Accounting Grades and Functional English

Grades in the Variable View by giving them appropriate values.

We study the following variables in our analysis:-

1) CGPA of the students, ( Dependent Variable)2) Intermediate Percentage, ( Independent Variable)3) Medium of Instruction up to Matric, ( Independent Variable)4) Grades of Accounting 1, 2 and 3, ( Independent Variable)5) Grades of Functional English 1 and 2, ( Independent Variable)6) Public or Private Sector, (Independent Variable).


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Regression Models:-

As we have 6 variables but 1 is dependent variable. So we has five validity co-

efficient; which are as given below

The above given validity co-efficient we get from Correlation Matrix.


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Question: Which is the Predictor we should study first?

The answer is that the validity co-efficient with highest value ofsignificance

will study first. The reason is because this has highest impact on the dependent

variable. So we should study these independent variable on there importance.

So we study Quantitative first as it has .526** level of significance.

After it we study Verbal which has .488** level of significance.

In the same we study MOIM, Inter-Percentage and Public orPrivate as they

have .261, .081 and .020 level of significance respectively.

So we have to study five Regression models.

Model # 1: =a+b1x1 (Quantitative)

Model # 2: =a+b2x2 (Verbal)

Model # 3: =a+b3x3 (MOIM)

Model # 4: =a+b4x4 (Inter-Percentage)

Model # 5: =a+b5x5 (Public or Private)


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DVs

IVs

CGPA

QUNT

Verbal

MOIM

Inter-pet

Istit

Dependent

Variable

Independent

Variables


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This is the simple model which we will study in this assignment.

At first;

When we open the data source file than this view will open, it has two views the

Data view and variable view these are explained in the previous assignment


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Model 1

(CGPA and QNT)

Scatter Dot

We want to calculate the regression, for this purpose we shall go in Graphs

then Legacy Dialogues and click on Scatter Dot. As shown in following

dialogue box

Theses are the steps for finding out the Scatter Dot Matrix;1. First go to Graphs2. Click on Legacy Dialogue3.Now click on Scatter Dot4. Select Simple Scatter5. Click Define6. Select CGPA on Y-axis.7. Select Quant on x-axis.8. Click Ok9. Simple Scatter is formed10.Double click on it.11.Click on Add to fit lines at Total.12.Click on Linear and now click on apply.13.A Linear curve is formed14.Click on Add to Fit Line.15.Click on Loess and then click on Apply.16.Loess Curve is formed.

These are the general steps that would be used to find out the regression of all

the variables.

In order to draw a Simple Scatter we have to follow following steps shown in

the fig.

These entire steps are those which are mention earlier


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When we click on scatter Dot, the following Dialogue box will appear.


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This is the close dialogue box of Scatter/ Dot; where we select the Simple

scatter

CGPA: is the dependent variable which we a studying


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Qunat: is the independent variable which relation on CGPA we are trying to

find out

Select the independent variables as well as dependent variable. In this case

independent variable is QNT and Dependent variable is CGPA.


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In this dialogue box, we shall click on Simple scatter Plot and then press OK.

Now the following dialogue box will appear.

Now we shall press OK. Now the graph will appear in the SPSS statistics

viewer as shown in the following diagram.


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The scatter plot appears in the out put view of the SPSS

Shown in the following diagram,


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We shall double click on the graph; the following dialogue box will appear.


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To ad fit lineinthe graph this is the procedure

This is the linear line which does not truly represent the data i.e. is does not

passes through maximum no of values. So is not the best method.

We can improve this by applying a much better method because our data does

not lies in linear symmetry.


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We go into the add fit line and select the LOESS curve this time,


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The Loess curve is shown in the graph;

It passes through the more data rather the linear curve

The loess curve suggests that instead of fitting a linear curve, we should fit a

quadratic curve.

So we will put the quadratic curve; procedure is explained in the figure.


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This graph shows the three curves .i.e. linear, loess and quadratic curve


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Now we will estimate that how quadratic curve is better from linear curve in

this situation.

Here we shall put the CGPA and QNT.

T


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heses are the steps

I. Go to analyzeII. Select the regression

III. Select linear regressionIV. Put the DV and IVV. Select the linear and quadratic

VI. Select Display ANOVAVII. Press OkThis is the procedure of finding out the estimation curve and in the next steps on

curves are shown rather the complete procedures

We also mark the option of Quadric and then mark display the anova table


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Now we shall press OK. Now the graph will appear in the SPSS statistics

viewer as shown in the following diagram.

Now we shall press OK. The graph will appear in the SPSS statistics viewer as

shown in the following diagram.


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Model 1

Model Description Table:

This table summarizes all the results of the model

Case Processing Company:

It tells us about total cases, excluded cases, forecasted cases, newly created

cases.

Variable Processing Summary:

It tells us about number of positive values, number of zeroes, number of

negative values, number of missing values of Dependent and Independent

Variables.


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Linear Tables:

CGPA of the student

Linear

Reporting Results

= a+ b1x1

=2.726+.150x1Interpretation

When the QNT is0 then CGPA is 2.726. per unit increase in QNT, CGPA

increase by .150

Intercept:

This is the predicted value of the response variable i.e. CGPA performance

when the predictor variables i.e. QNT is 0. In this case exam CGPA is 2.726,

when the QNT is 0.

The slope or the regression coefficient b1:

b1 is equal to .150 which is the change in the response variable i.e. CGPA when

the predictor variable i.QNT increases by one unit.

To simplify our interpretation, we can say that with an increase in QNT by 1

unit, the performance would increase by 0.150.

Model Summary


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CGPA

of the

student

R

Square

Adjusted R

Square

Std. Error of

the Estimate.283 .265 .304

It tells us R, R square, Adjusted R Square and standard error of the estimates. If

standard error of the estimates is less than the standard error of estimates of

Quadratic tables than we dont apply the quadratic eq and vice versa.

R square tells us how much variation in the dependent variable can be

accounted for by the independent variable.

Ris the sample correlation coefficient between the dependent variable (sales

during the year) and the independent variable.

Standard erroris measured in units of the response variable i.e. the sales

during the year and it tells us the standard distance of the data values from the

regression line or it tells us how far the values lie away from the regression line.

For different model comparisons, we always look at the standard error. The

model with smaller standard error will be a better model.

The standard error in the modern summary suggests that we should fit a

quadratic model instead of a linear model.

For model comparison we can look at R2

only when both models have equal

number of predictors.

But in the current situation, in the linear model we have one predictor i.e QNT,

and in the second model we have two predictors QNT and QNT square. So in

this case instead of looking at the R square we shall be looking for model

comparison standard error is the best fit model.

The discussion of the quadratic model is beyond our syllabus.

ANOVA:

ANOVA


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Sum of

Squares df

Mean

Square F Sig.

Regressio

n

1.499 1 1.499 16.173 .000

Residual 3.800 41 .093

Total 5.299 42

The independent variable is QNT.

The ANOVA table shows us the overall impact of the model. It depicts the

amount of variation in the response data explained by the predictor and the

amount of variation left unexplained.

We have the p-value which is the observed level of significance.

If p< , then we reject Ho (significant)

If p>, then we do not reject Ho (non-significant)

Coefficient:

Coefficients

Unstandardized

Coefficients

Standardize

d

Coefficients

t Sig.B Std. Error Beta

QNT .150 .037 .532 4.022 .000

(Constant

)

2.726 .156 17.467 .000

It tells us whether the predictor variables have a significant effect on model or

not. If any predictor variable is not having significant impact then we exclude

that variable which has not significant impact on our linear eq.

Quadratic Tables:


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Quadratic

= a+ b1x1+b2x12

=3.310-1.86 x1+ .043x12

Model Summary:

Model Summary

R

R

Square

Adjusted R

Square

Std. Error of

the Estimate

.574 .330 .296 .298









Standard erroris measured in units of the response variable i.e. the salesduring the year and it tells us the standard distance of the data values from the




ANOVA:

ANOVA

Sum ofSquares df

MeanSquare F Sig.

Regressio

n

1.748 2 .874 9.846 .000

Residual 3.551 40 .089

Total 5.299 42



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Coefficients:

Coefficients

Unstandardized

Coefficients

Standardize

d

Coefficients


QNT -.186 .204 -.661 -.914 .366

QNT **

2

.043 .026 1.213 1.675 .102

(Constant

)

3.310 .381 8.697 .000





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Here we have graph in which observed, linear and quadratic values are shown.


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Model 2


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Again the previous procedures are carried

This is the simple graph having linear curve


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This is final shape of the graph after having done the complete procedure to

apply the curves.


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Now the following dialogue box will appear and we shall interpret each

dialogue box.


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Model 2

(CGPA and Verbal)



Model Description

Model Name MOD_1

Dependent

Variable

1 CGPA of the student

Equation 1 Linear

2 QuadraticIndependent Variable Verbal

Constant Included

Variable Whose Values Label

Observations in Plots

Unspecified

Tolerance for Entering Terms in

Equations

.0001



cases

Case Processing

Summary

N

Total Cases 43

Excluded Casesa 1

Forecasted Cases 0

Newly Created

Cases

0

a. Cases with a missing

value in any variable are

excluded from the analysis.


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Variables.

Variable Processing Summary

Variables

Dependent

Independe

nt

CGPA of

the student Verbal

Number of Positive Values 43 42

Number of Zeros 0 0

Number of Negative Values 0 0

Number of Missing

Values

User-Missing 0 0

System-Missing 0 1

Linear Tables:

CGPA of the student

Linear

Reporting Results

= a+ b2x2

=2.366+.206x2Interpretation

When the Verbal is0 then CGPA is 2.366. Per unit increase in Verbal, CGPA

increase by .206

Intercept:

This is the predicted value of the response variable i.e. CGPA when the

predictor variables i.e. Verbal is 0. In this case CGPA is 2.366, when the

Verbal is 0.


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B2 is equal to .206 which is the change in the response variable i.e. CGPA when

the predictor variable i.Verbal increases by one unit.

To simplify our interpretation, we can say that with an increase in Verbal by 1

unit, the performance would increase by 0.206.

Model Summary

R

R

Square

Adjusted R

Square

Std. Error of

the Estimate

.440 .194 .174 .316

The independent variable is Verbal.














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ANOVA

Sum of

Squares df

Mean

Square F Sig.Regressio

n

.962 1 .962 9.625 .004

Residual 3.998 40 .100

Total 4.960 41

The independent variable is Verbal.

The ANOVA table shows us the overall impact of the model. It depicts theamount of variation in the response data explained by the predictor and the





Coefficient:

Coefficients

Unstandardized

Coefficients

Standardize

d

Coefficients


Verbal .206 .066 .440 3.102 .004

(Constant

)

2.366 .318 7.451 .000




There is no need to apply the quadratic eq to this model because standard error

is greater than the standard error of linear


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Model 3

If we carry out the previous procedures than this again will be the result of

model 3 where the variables are CGPA and Medium of instruction up to matric.

(CGPA and MOIM)

Curve Fit

[DataSet1] F:\Ijaz Bajwa. Data.sav

Warnings

The Quadratic model could not be fitted due to near-collinearity

among model terms.


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Model Description

Model Name MOD_4

Dependent

Variable


Equation 1 Linear

Independent Variable Medium of Institution

upto Matric

Constant IncludedVariable Whose Values Label


Unspecified



cases

Case Processing

Summary

N

Total Cases 43

Excluded Casesa

0

Forecasted Cases 0Newly Created

Cases

0





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Variables.


Variables

Dependent Independent

CGPA of

the student

Medium of

Institution

upto Matric


Number of Zeros 0 16


Number of Missing

Values

User-Missing 0 0

System-Missing 0 0

CGPA of the student

Linear

Reporting Results

= a+ b3x3

=3.218+.178x3

Interpretation

When the MOIM is 0 then CGPA is 3.218. Per unit increase in MOIM, CGPA

increase by .178

Intercept:


predictor variables i.e. MOIM is 0. In this case CGPA is 3.218, when the

MOIM is 0.


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the predictor variable i.e MOIM increases by one unit.

To simplify our interpretation, we can say that with an increase in MOIM by 1

unit, the CGPA would increase by 0.178.

Model Summary

Model Summary

R

R

Square

Adjusted R

Square

Std. Error of

the Estimate

.237 .056 .033 .349

The independent variable is Medium of

Institution upto Matric.


standard error of the estimates is less than the standard error of estimates ofQuadratic tables than we dont apply the quadratic eq and vice versa.







regression line or it tells us how far the values lie away from the regression line.For different model comparisons, we always look at the standard error. The



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ANOVA

ANOVA

Sum ofSquares df

MeanSquare F Sig.

Regressio

n

.298 1 .298 2.440 .126

Residual 5.002 41 .122

Total 5.299 42

The independent variable is Medium of Institution upto Matric.







Coefficient

Coefficients

Unstandardized

Coefficients

Standardize

d

Coefficients


Medium ofInstitution upto

Matric

.172 .110 .237 1.562 .126

(Constant) 3.218 .087 36.847 .000





is greater than the standard error of linear.


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When we calculate quadratic the Sebecomes same so we dont need to apply the

quadratic eq.


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Model 4

(CGPA and Inter pct)


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(CGPA and Inter pct)

Model Description

Model Name MOD_6

Dependent

Variable


Equation 1 Linear

2 Quadratic

Independent Variable Intermediate

Percentage of the

student

Constant Included



Unspecified


Equations

.0001



cases

Case Processing

Summary

N

Total Cases 43

Excluded Casesa 0

Forecasted Cases 0

Newly Created

Cases

0





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Variables.


Variables


CGPA of

the student

Intermediat

e

Percentage

of the

student


Number of Zeros 0 0


Number of MissingValues

User-Missing 0 0System-Missing 0 0

CGPA of the student

Linear

= a+ b4x4

=3.052+.004x4

Interpretation

When the inter pct is 0 then CGPA is 3.052. Per unit increase in inter pct,

CGPA increase by .178

Intercept:


predictor variables i.e. Inter pct is 0. In this case CGPA is 3.0525, when the

inter pct is 0.


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the predictor variable i.e inter pct increases by one unit.

To simplify our interpretation, we can say that with an increase in inter pct by 1

unit, the CGPA would increase by 0.004

Model Summary

Model Summary

R

R

Square

Adjusted R

Square

Std. Error of

the Estimate.086 .007 -.017 .358

The independent variable is Intermediate

Percentage of the student.














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ANOVA

Sum of

Squares df

Mean

Square F Sig.Regressio

n

.040 1 .040 .309 .581

Residual 5.260 41 .128

Total 5.299 42

The independent variable is Intermediate Percentage of the

student.







Coefficient

Coefficients

Unstandardized

Coefficients

Standardize

d

Coefficients


Intermediate

Percentage of the

student

.004 .007 .086 .556 .581

(Constant) 3.052 .496 6.151 .000







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Model 5

(CGPA and Institution from which inter done)


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(CGPA and Institution from which inter done)

Model Description

Model Name MOD_8

Dependent

Variable


Equation 1 Linear

2 QuadraticIndependent Variable Institution from which

interdone

Constant Included



Unspecified


Equations

.0001



cases

Case Processing

Summary

N

Total Cases 43

Excluded Casesa 0

Forecasted Cases 0

Newly Created

Cases

0


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Variables.


Variables


CGPA of

the student

Institution

from which

interdone


Number of Zeros 0 1


Number of Missing

Values

User-Missing 0 0

System-Missing 0 0

CGPA of the student

Linear

= a+ b5x5

=3.379-.38x4

Interpretation

When the institution from which inter done is 0 then CGPA is 3.379. Per unit

increase in institution from which inter done, CGPA decrease by .38

Intercept:


predictor variables i.e. institution from which inter done is 0. In this case

CGPA is 3.379, when the institution from which inter done is 0.


B5 is equal to - .38 which is the change in the response variable i.e. CGPA when

the predictor variable i.e institution from which inter done increases by one unit.

To simplify our interpretation, we can say that with an increase in institution

from which inter done by 1 unit, the CGPA would decrease by 0.38


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Model Summary

Model Summary

RR

SquareAdjusted R

SquareStd. Error ofthe Estimate

.058 .003 -.021 .359

The independent variable is Institution from

which interdone.













ANOVA

ANOVA

Sum of

Squares df

Mean

Square F Sig.

Regressio

n

.018 1 .018 .138 .712

Residual 5.282 41 .129

Total 5.299 42

The independent variable is Institution from which interdone.


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Coefficient

Coefficients

Unstandardized

Coefficients

Standardize

d

Coefficients


Institution from

which interdone

-.038 .102 -.058 -.371 .712

(Constant) 3.379 .154 21.907 .000




There is no need to apply the quadratic e.g. to this model because standard error


There is no need to apply the quadratic e.g. to this model because standard error



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Regression with more than one independent Variables

(= b0+ b1x1+b2x2+b3x3+b4 x4+b5 x5)

We shall go in analyze, click on regression then click on linear. When we click

on linear then following dialogue box will appear.

Now we shall select the dependent variable which is CGPA and independent

variable which are QNT, inter pct, Institution from which inter done, verbal,

MOIM.


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Now we shall click on statistics and check the following icons.


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When we click ok than following tables appear in out put file.


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Descriptive Statistics:

Regression

[DataSet1] E:\Education\IjazData\Statistical inference\IjazData.sav

Descriptive Statistics

Mean

Std.

Deviation N

CGPA of the student 3.3393 .34783 42

QNT 4.0119 1.27642 42

Medium of Institution

upto Matric

.64 .485 42

Intermediate

Percentage of the

student

67.02 7.592 42

Institution from which

interdone

1.43 .547 42

Verbal 4.7302 .74440 42

In this we find the mean and SD.


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Variables Entered/Removed:

Variables Entered/Removed

Model Variables Entered Variables Removed Method

1 Verbal, QNT,

Institution from

which interdone,

Intermediate

Percentage of the

student, Medium ofInstitution upto

Matrica

. Enter

a. All requested variables entered.

In this we can see which variables are entered and which are removed.

Model:We can input more than one model in a same regression command in SPSS.And in this column the numbers of models are shown.

Variables Entered:This column tells us about all the independent variable that we have specified

but did not blocked as SPSS allows us to enter variables in block for stepwise

regression.

Variables removed:Usually, this column is empty and only lists the removed variables when we do

stepwise regression.

Methods:The method used by SPSS to run regression is mentioned in this column.

Enter means that every independent variable was entered in usual manner.

But when stepwise regression is done, the entry tells us about that.


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Model Summary:

Model:This column tells us the number of models reported. As in SPSS we can input

more than one model in a same regression command.

R:

The correlation between the observed and predicted values of dependentvariable is called R and is the square root of R-Squared.

R-Square:R-Square is the proportion of variance in the dependent variable (CGPA) which

can be predicted from the independent variables (VER, QNT, Institution of

Inter, Inter-percentage and MOIM). This value indicates that 50.3% of the

variance in CGPA can be predicted from the variables VER, QNT, Institution

of Inter, Inter-percentage and MOIM. Note that this is an overall measure ofthe strength of association, and does not reflect the extent to which any

particular independent variable is associated with the dependent variable. R-

Square is also called the coefficient of determination.

Adjusted R-square:As predictors are added to the model, each predictor will explain some of the

variance in the dependent variable simply due to chance. One could continue to

add predictors to the model which would continue to improve the ability of the

Model Summary

Mod

el R

R

Square

Adjusted

R Square

Std. Error

of the

Estimate

Change Statistics

R Square

Change

F

Chang

e df1 df2

Sig. F

Change

1 .709a

.503 .434 .26171 .503 7.284 5 36 .000

a. Predictors: (Constant), Verbal, QNT, Institution from which interdone,

Intermediate Percentage of the student, Medium of Institution upto Matric


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predictors to explain the dependent variable, although some of this increase in

R-square would be simply due to chance variation in that particular sample. The

adjusted R-square attempts to yield a more honest value to estimate the R-

squared for the population. The value ofR-square was .503, while the value of

Adjusted R-square was .434, Adjusted R-squared is computed using the

formula 1 - ((1 - Rsq)(N - 1 )/ (N - k - 1)). From this formula, you can see that

when the number of observations is small and the number of predictors is large,

there will be a much greater difference between R-square and adjusted R-square

(because the ratio of (N - 1) / (N - k - 1) will be much greater than 1). By

contrast, when the number of observations is very large compared to the number

of predictors, the value of R-square and adjusted R-square will be much closer

because the ratio of (N - 1)/(N - k - 1) will approach 1.

Std. Error of the Estimate:The standard error of the estimate, also called the root mean square error, is the

standard deviation of the error term, and is the square root of the Mean Square

Residual (or Error).

ANOVA

ANOVA

Model

Sum of

Squares df

Mean

Square F Sig.

1 Regressio

n

2.495 5 .499 7.284 .000a

Residual 2.466 36 .068

Total 4.960 41

a. Predictors: (Constant), Verbal, QNT, Institution from which

interdone, Intermediate Percentage of the student, Medium of

Institution upto Matric

b. Dependent Variable: CGPA of the student


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This is the source of variance, Regression, Residual and Total. The Total

variance is partitioned into the variance which can be explained by theindependent variables (Regression) and the variance which is not explained by

the independent variables (Residual, sometimes called Error). Note that the

Sums of Squares for the Regression and Residual add up to the Total, reflecting

the fact that the Total is partitioned into Regression and Residual variance.

Sum of Squares:These are the Sum of Squares associated with the three sources of variance,

Total, Model and Residual. These can be computed in many ways.

Conceptually, these formulas can be expressed as:

SSTotal The total variability around the mean. S(Y - Ybar)2.

SSResidual The sum of squared errors in prediction. S(Y - Ypredicted)2.

SSRegression The improvement in prediction by using the predicted value

of Y over just using the mean of Y. Hence, this would be the squared

differences between the predicted value of Y and the mean of Y, S(Ypredicted -

Ybar)2. Another way to think of this is the SSRegression is SSTotal -

SSResidual. Note that the SSTotal = SSRegression + SSResidual.

Note that SSRegression / SSTotal is equal to 4.960, the value of R-Square.

This is because R-Square is the proportion of the variance explained by the

independent variables, hence can be computed by SSRegression / SSTotal.

Df:

These are the degrees of freedom associated with the sources of variance. Thetotal variance has N-1 degrees of freedom. In this case, there were N=43


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students, so the DF for total is 42. The model degrees of freedom corresponds

to the number of predictors minus 1 (K-1). You may think this would be 5-1

(since there were 5 independent variables in the model, VER, QNT, Institution

of Inter, Inter-percentage and MOIM). But, the intercept is automatically

included in the model (unless you explicitly omit the intercept). Including the

intercept, there are 6 predictors, so the model has 6-1=5 degrees of freedom.

The Residual degrees of freedom is the DF total minus the DF model, 42 - 5 is

37.

Mean Square:These are the Mean Squares; the Sum of Squares divided by their respective

DF. For the Regression, 2.495/ 5 = .499 . For the Residual, 2.466/ 36= .068 .These are computed so you can compute the F ratio, dividing the Mean Square

Regression by the Mean Square Residual to test the significance of the

predictors in the model.

F and Sig.:

The F-value is the Mean Square Regression (.499) divided by the Mean Square

Residual (0.068), yielding F=7.284. The p-value associated with this F valueis very small (0.000). These values are used to answer the question "Do the

independent variables reliably predict the dependent variable?". The p-value is

compared to your alpha level (typically 0.05) and, if smaller, you can conclude

"Yes, the independent variables reliably predict the dependent variable". You

could say that the group of variables VER, QNT, Institution of Inter, Inter-

percentage and MOIM can be used to reliably predict CGPA (the dependent

variable). If the p-value were greater than 0.05, you would say that the group of

independent variables does not show a statistically significant relationship withthe dependent variable, or that the group of independent variables does not

reliably predict the dependent variable. Note that this is an overall significance

test assessing whether the group of independent variables when used together

reliably predict the dependent variable, and does not address the ability of any

of the particular independent variables to predict the dependent variable. The

ability of each individual independent variable to predict the dependent variable

is addressed in the table below where each of the individual variables are listed.


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Coefficients:






This column shows the predictor variables (constant, VER, QNT, Institution

of Inter, Inter-percentage and MOIM). The first variable (constant)

represents the constant, also referred to in textbooks as the Y intercept, the

Coefficients

a

Model

Unstandardized

Coefficients

Standardi

zed

Coefficie

nts

t Sig.

95.0% Confidence

Interval for B

B

Std.

Error Beta

Lower

Bound

Upper

Bound

1 (Constant) 1.623 .500 3.249 .003 .610 2.637

QNT .155 .036 .567 4.349 .000 .082 .227

Medium of

Institution upto

Matric

.094 .101 .131 .931 .358 -.111 .299

Intermediate

Percentage of the

student

.002 .006 .046 .348 .730 -.010 .014

Institution from

which interdone

.025 .080 .040 .312 .757 -.138 .188

Verbal .182 .063 .389 2.902 .006 .055 .309

a. Dependent Variable: CGPA of the student


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height of the regression line when it crosses the Y axis. In other words, this is

the predicted value ofCGPA when all other variables are 0.

B:These are the values for the regression equation for predicting the dependent

variable from the independent variable. These are called unstandardized

coefficients because they are measured in their natural units. As such, the

coefficients cannot be compared with one another to determine which one is

more influential in the model, because they can be measured on different

scales. For example, how can you compare the inter-percentage with the CGPA

scores? The regression equation can be presented in many different ways, for

example:

Y -Predicted = b0 + b1*x1 + b2*x2 + b3*x3 + b3*x3 +

b4*x4+b5*x5

The column of estimates (coefficients or parameter estimates, from here on

labeled coefficients) provides the values for b0, b1, b2, b3 and b4 for this

equation. Expressed in terms of the variables used in this example, the

regression equation is

CGPA = 1.623+ .155*QNT +.182*VER +.094*MOIM+.002*inter-

percent+.025* inter-institution

These estimates tell you about the relationship between the independent

variables and the dependent variable. These estimates tell the amount of

increase in science scores that would be predicted by a 1 unit increase in the

predictor. Note: For the independent variables which are not significant, the

coefficients are not significantly different from 0, which should be taken into

account when interpreting the coefficients. (See the columns with the t-value

and p-value about testing whether the coefficients are significant).

Std. Error:These are the standard errors associated with the coefficients. The standard

error is used for testing whether the parameter is significantly different from 0by dividing the parameter estimate by the standard error to obtain a t-value (see


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the column with t-values and p-values). The standard errors can also be used to

form a confidence interval for the parameter, as shown in the last two columns

of this table.

Beta:These are the standardized coefficients. These are the coefficients that youwould obtain if you standardized all of the variables in the regression, including

the dependent and all of the independent variables, and ran the regression. By

standardizing the variables before running the regression, you have put all of the

variables on the same scale, and you can compare the magnitude of the

coefficients to see which one has more of an effect. You will also notice that

the larger betas are associated with the larger t-values.

T and Sig.:These columns provide the t-value and 2 tailed p-value used in testing the null

hypothesis that the coefficient/parameter is 0. If you use a 2 tailed test, then

you would compare each p-value to your preselected value of alpha.

Coefficients having p-values less than alpha are statistically significant. For

example, if you chose alpha to be 0.05, coefficients having a p-value of 0.05 or

less would be statistically significant (i.e., you can reject the null hypothesis and

say that the coefficient is significantly different from 0). If you use a 1 tailedtest (i.e., you predict that the parameter will go in a particular direction), then

you can divide the p-value by 2 before comparing it to your preselected alpha

level. However, if you used a 2-tailed test and alpha of 0.01, the p-value of

.0255 is greater than 0.01 and the coefficient for variable would not be

significant at the 0.01 level. Had you predicted that this coefficient would be

positive (i.e., a one tail test), you would be able to divide the p-value by 2

before comparing it to alpha. This would yield a one-tailed p-value of 0.00945,

which is less than 0.01 and then you could conclude that this coefficient isgreater than 0 with a one tailed alpha of 0.01.

The constant is significantly different from 0 at the 0.05 alpha levels.

However, having a significant intercept is seldom interesting.


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The coefficient forQNT (.155) is statistically significantly different from 0

using alpha of 0.05 because its p-value is 0.000, which is smaller than 0.05.

The coefficient forMOIM(.094) is not statistically significantly different

from 0 because its p-value is definitely larger than 0.05.The coefficient forVER(.182) is statistically significant because its p-value

of 0.008 is less than .05.

The coefficient forINTER.Inst (.025) is not significantly different form 0

because its p-value is greatly larger than 0.05.

The coefficient forINTER-Percent (.002) is not significantly different from

0 because its value is definitely larger than 0.05.

Reporting Results (Combine)= b0+ b1x1+b2x2+b3x3+b4 x4+b5 x5

=1.623+.155 x1+ .182x2+.094x3+ .002x4+ .025x5

Interpretation:

When all the independent variables are 0 then the CGPA is 1.623. Per unitincrease in QNT, the value of CGPA increase by .155; Per unit increase in

verbal, CGPA increase by .182; Per unit increase in MOIM, CGPA increase by

.094; Per unit increase in inter pct, CGPA increase by .002; Per unit increase in

institute from which inter done, CGPA increase by .025.

Intercept:


predictor variables is 0. In this case CGPA is 1.623, when the all the predictorsare 0.

The slope or the regression coefficient:

When all the independent variables are 0 then the CGPA is 1.623. Per unit

increase in QNT, the value of CGPA increase by .155; Per unit increase in

verbal, CGPA increase by .182; Per unit increase in MOIM, CGPA increase by

.094; Per unit increase in inter pct, CGPA increase by .002; Per unit increase in

institute from which inter done, CGPA increase by .025.


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Documents

Statistical Inference, Regression SPSS Report