Practical Statistics

Regression

There are six statistics that willanswer 90% of all questions!1. Descriptive2. Chi-square3. Z-tests4. Comparison of Means5. Correlation6. Regression

Regression tests the degree of association between interval and ratio measures,

AND

gives the best fit to the data.

Regression

Does three things:

1. Association2. Best fit

3. Prediction

Regression

Regression creates an equation:

A simple linear equation would be:

Y = bX + a

Correlations

1 .787** .306** .138**

.000 .000 .002

556 548 556 517

.787** 1 .248** .139**

.000 .000 .002

548 550 550 511

.306** .248** 1 .672**

.000 .000 .000

556 550 560 520

.138** .139** .672** 1

.002 .002 .000

517 511 520 616

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Evaluation

Personality

ExpGrdW16

FinalGrd

Evaluation Personality ExpGrdW16 FinalGrd

Correlation is significant at the 0.01 level (2-tailed).**.

An example from the classroom….

Can we use the correlations to create equationsto estimate one variable from another?

For example:

Evaluations = b(Personality) + a

Y = bx + a

Model Summary

.787a .619 .619 .54491Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), Personalitya.

ANOVAb

263.738 1 263.738 888.235 .000a

162.120 546 .297

425.858 547

Regression

Residual

Total

Model1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), Personalitya.

Dependent Variable: Evaluationb. Coefficientsa

-.530 .118 -4.511 .000

.637 .021 .787 29.803 .000

(Constant)

Personality

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: Evaluationa.

So… Evaluation = 0.637(Personality) - 0.530

An example can be found here:

http://en.wikipedia.org/wiki/Linear_regression

The equations do not have to be linear?

Regression can use more than one variable topredict. This is called multiple regression.

An example……

Caring = Evaluations

But what is “Caring”??

Correlations

1 .613** .702** -.397* .510** .577** .843**

.000 .000 .015 .001 .000 .000

37 37 37 37 37 37 37

.613** 1 .864** -.243 .668** .356* .808**

.000 .000 .147 .000 .030 .000

37 37 37 37 37 37 37

.702** .864** 1 -.365* .654** .460** .864**

.000 .000 .026 .000 .004 .000

37 37 37 37 37 37 37

-.397* -.243 -.365* 1 -.294 -.420** -.437**

.015 .147 .026 .077 .010 .007

37 37 37 37 37 37 37

.510** .668** .654** -.294 1 .311 .657**

.001 .000 .000 .077 .061 .000

37 37 37 37 37 37 37

.577** .356* .460** -.420** .311 1 .606**

.000 .030 .004 .010 .061 .000

37 37 37 37 37 37 37

.843** .808** .864** -.437** .657** .606** 1

.000 .000 .000 .007 .000 .000

37 37 37 37 37 37 37

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Eval

EC

PT

PD

Lenient

Rigor

Care

Eval EC PT PD Lenient Rigor Care

Correlation is significant at the 0.01 level (2-tailed).**.

Correlation is significant at the 0.05 level (2-tailed).*.

Model Summary

.914a .835 .808 .83178Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), Rigor, Lenient, PD, EC, PTa.

Coefficientsa

.685 .730 .939 .355

.387 .226 .263 1.712 .097

.569 .213 .426 2.670 .012

-.236 .240 -.082 -.980 .335

.131 .130 .101 1.003 .323

.365 .126 .251 2.898 .007

(Constant)

EC

PT

PD

Lenient

Rigor

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: Carea.

But I know that this is not true!

Coefficientsa

2.536 .300 8.464 .000

1.157 .114 .864 10.165 .000

.735 .644 1.142 .261

.994 .115 .743 8.646 .000

.385 .125 .265 3.080 .004

(Constant)

PT

(Constant)

PT

Rigor

Model1

2

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: Carea.

Forced entry by significance….

Path Diagram

Correlations

1 .787** .138** .289** .071 .306** .074

.000 .002 .000 .096 .000 .080

556 548 517 556 556 556 556

.787** 1 .139** .243** .046 .248** .036

.000 .002 .000 .280 .000 .401

548 550 511 550 550 550 550

.138** .139** 1 .711** .636** .672** .594**

.002 .002 .000 .000 .000 .000

517 511 616 520 520 520 520

.289** .243** .711** 1 .735** .824** .648**

.000 .000 .000 .000 .000 .000

556 550 520 560 560 560 560

.071 .046 .636** .735** 1 .664** .890**

.096 .280 .000 .000 .000 .000

556 550 520 560 560 560 560

.306** .248** .672** .824** .664** 1 .731**

.000 .000 .000 .000 .000 .000

556 550 520 560 560 560 560

.074 .036 .594** .648** .890** .731** 1

.080 .401 .000 .000 .000 .000

556 550 520 560 560 560 560

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

evtot

per4

FinalGrd

GrdNowW16

GradDesNW16

ExpGrdW16

DesGRdW16

evtot per4 FinalGrd GrdNowW16GradDes

NW16 ExpGrdW16 DesGRdW16

Correlation is significant at the 0.01 level (2-tailed).**.

Coefficientsa

2.306 .189 12.199 .000

-.145 .073 -.119 -1.974 .049

.385 .115 .312 3.364 .001

-.256 .155 -.187 -1.658 .098

.493 .115 .382 4.298 .000

-.240 .150 -.176 -1.600 .110

(Constant)

FinalGrd

GrdNowW16

GradDesNW16

ExpGrdW16

DesGRdW16

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: evtota.

Coefficientsa

1.713 .165 10.364 .000

.400 .054 .310 7.397 .000

2.258 .186 12.115 .000

.714 .076 .553 9.419 .000

-.460 .080 -.337 -5.741 .000

2.215 .187 11.875 .000

.548 .105 .424 5.230 .000

-.481 .080 -.353 -5.990 .000

.208 .091 .168 2.291 .022

2.255 .187 12.070 .000

.571 .105 .442 5.439 .000

-.449 .082 -.329 -5.503 .000

.284 .097 .230 2.926 .004

-.157 .073 -.129 -2.144 .032

(Constant)

ExpGrdW16

(Constant)

ExpGrdW16

DesGRdW16

(Constant)

ExpGrdW16

DesGRdW16

GrdNowW16

(Constant)

ExpGrdW16

DesGRdW16

GrdNowW16

FinalGrd

Model1

2

3

4

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: evtota.

Service Encounter

Are demographics related to satisfactionwith a service encounter?

Service Encounter

Are respondents’ personality traits related to satisfactionwith a service encounter?

Service Encounter

Are service providers’ personality traits related to satisfactionwith a service encounter?