MULTIPLE REGRESSIONS

Multiple Regressions

Multiple Regressions

Introduction

Here we are going to make a regression equation with the help of given data of sales and different other variables. The case involves the decision to locate a new store at one of two candidate sites. The decision will be based on estimates of sales potential, and for this purpose, you will need to develop a multiple regression model to predict sales.

Data

Data given to us in excel file is showing that there are different variables. In the first column we can see the data variables as stores which are showing the serial numbers of different observations. There are 32 other variables in the dataset including the variable sales. And each variable has 250 observations.

We have to analyze firstly the correlation between the sales and the comp type variable. And there is a scatter plot showing correlation between the variables. After that is a brief summary of regression analysis of data to which we are familiar. We have to make a regression equation which will help us in prediction of the future values of variables. Actually regression gives us the dependency relationship of two variables.

Results and discussion

Sales in the middle categories 3 - 6 are in similar ranges on the vertical axis, but 1 and 2 have somewhat higher sales, and category 7 appears to have somewhat lower sales. This implies that, when you create dummy variables for comtype, dummy variables for categories 1, 2, 7 are likely to be statistically significant in the multiple regression models (and dummy variables for categories 3 - 6 are likely to be not significant.

Given below are the tables showing a continuation of correlation between the sales and other variables in the sense that it different values for correlation between the variables. We have not included the stores due to the reason that the values in stores column is showing that the serial numbers for the variables. Correlation variables are being shown in bold.

 

%black

%spanishsp

%inc0-10

%inc10-14

%inc14-20

%inc20-30

%inc30-50

%inc50-100

%inc100+

%black

1

%spanishsp

0.357427

1

%inc0-10

0.362107

0.726546

1

%inc10-14

0.457146

0.691285

0.77167

1

%inc14-20

0.258855

0.307898

0.467917

0.445675

1

%inc20-30

-0.09728

-0.2023

-0.19229

-0.12769

0.100411

1

%inc30-50

-0.26088

-0.46347

-0.53141

-0.58086

-0.47484

-0.10451

1

%inc50-100

-0.15994

-0.27106

-0.43594

-0.37013

-0.53457

-0.49964

0.190495

1

%inc100+

-0.09349

-0.05814

-0.2058

-0.18094

-0.30687

-0.47028

-0.28237

0.393417

1

medianinc

-0.24338

-0.4433

-0.50953

-0.47957

-0.3511

0.023333

0.337775

0.367527

0.104077

medianrent

-0.25587

-0.47718

-0.57385

-0.56233

-0.3611

0.139653

0.447805

0.25987

0.014864

medianhome

-0.16203

-0.16396

-0.21734

-0.27103

-0.34112

-0.26177

0.210398

0.45391

0.189482

%owners

-0.23069

-0.49081

-0.6785

-0.67266

-0.35936

0.295064

0.486771

0.159258

-0.00133

%nocars

0.345944

0.614018

0.775739

0.748319

0.400051

-0.27983

-0.51292

-0.28128

-0.02377

%1car

0.123581

-0.18832

-0.03531

0.001752

0.078698

-0.04701

-0.08659

0.07361

0.078594

%tvs

0.093697

0.018538

-0.07821

-0.02379

0.042768

0.011531

-0.04748

0.003554

0.086017

%washers

-0.20157

-0.41246

-0.55679

-0.51408

-0.30793

0.191278

0.378661

0.196096

0.022294

%dryers

-0.42793

-0.45287

-0.65238

-0.6672

-0.43538

0.265067

0.471975

0.247908

0.007152

%dishw

-0.37281

-0.42938

-0.63281

-0.65789

-0.47741

0.027258

0.535406

0.406822

0.081965

%aircond

-0.12488

-0.4069

-0.38638

-0.42986

-0.17775

-0.122

0.357187

0.344613

0.036188

%freezer

-0.30988

-0.41081

-0.65183

-0.63883

-0.44748

0.156002

0.530266

0.285889

0.02411

%sechome

-0.09138

-0.27526

-0.32441

-0.3254

-0.25463

-0.15453

0.392878

0.324265

-0.00091

%sch0-8

0.322587

0.533597

0.664647

0.625479

0.369669

-0.16176

-0.51621

-0.28566

0.009884

%sch9-11

0.193613

0.275794

0.25788

0.243109

0.201412

0.172021

-0.27617

-0.32679

-0.03781

%sch12

-0.08104

-0.23518

-0.31339

-0.31211

-0.0885

0.143911

0.239439

0.001755

-0.01949

%sch12+

-0.27392

-0.36596

-0.407

-0.37146

-0.30854

-0.04272

0.349707

0.353606

0.021023

population

0.459857

0.394565

0.515098

0.521082

0.322593

-0.20415

-0.30771

-0.22

-0.05598

familysize

-0.14715

-0.11384

-0.21871

-0.27426

-0.13895

0.174816

0.15144

0.025405

-0.0234

selling_sqrft (in 1000s)

0.215144

0.14474

0.217351

0.261532

0.2191

-0.14756

-0.15275

-0.01554

-0.05674

sales (in $1000s)

0.274686

0.547427

0.615054

0.61405

0.265031

-0.31003

-0.40371

-0.10666

0.010405

medianinc

medianrent

medianhome

%owners

%nocars

%1car

%tvs

%washers

%dryers

%dishw

%aircond

1

0.338675

1

0.28343

0.233588

1

0.296713

0.502462

0.10303

1

-0.43326

-0.5452

-0.17962

-0.84667

1

0.094887

-0.02583

-0.01319

-0.04599

0.012165

1

-0.03998

0.010248

-0.07697

0.065414

-0.01908

-0.14887

1

0.231024

0.334522

0.091914

0.61592

-0.64096

-0.03349

0.030832

1

0.3847

0.454108

0.177265

0.758404

-0.79981

-0.15638

0.084337

0.663177

1

0.456397

0.466217

0.313716

0.635515

-0.66661

-0.158

0.081797

0.485032

0.690043

1

0.308554

0.239947

0.23632

0.238798

-0.32381

-0.03254

0.00852

0.243451

0.187352

0.332953

1

0.327953

0.481519

0.160979

0.75627

-0.76103

-0.20303

0.064363

0.632635

0.792721

0.697435

0.213012

0.272736

0.223736

0.228777

0.31387

-0.29784

-0.12657

0.092936

0.305367

0.356459

0.464875

0.523516

-0.38713

-0.51689

-0.21895

-0.61511

0.681949

0.074723

-0.09917

-0.48054

-0.62474

-0.611

-0.31198

-0.27948

-0.2489

-0.19581

-0.11733

0.197764

-0.01349

0.038365

-0.07224

-0.17752

-0.29309

-0.21112

0.194872

0.303938

-0.08422

0.353458

-0.32615

0.012231

0.084403

0.178108

0.274093

0.239167

0.114437

0.281288

0.295108

0.30717

0.28397

-0.38724

-0.06085

0.003744

0.280838

0.370123

0.430365

0.250019

-0.31629

-0.29829

-0.15946

-0.579

0.641109

0.183335

-0.01078

-0.47076

-0.64801

-0.50905

-0.12824

0.029826

0.123929

-0.03479

0.321108

-0.29133

-0.03909

-0.04211

0.273843

0.326702

0.251451

-0.06656

-0.14107

-0.24716

-0.05195

-0.2832

0.299593

0.084676

-0.06612

-0.19569

-0.33736

-0.23141

0.073247

-0.32539

-0.39391

0.029872

-0.68985

0.700939

0.009904

-0.0584

-0.56226

-0.65733

-0.49124

-0.29024

%freezer

%sechome

%sch0-8

%sch9-11

%sch12

%sch12+

population

familysize

selling_sqrft (in 1000s)

sales (in $1000s)

1

0.353215

1

-0.64322

-0.29341

1

-0.1416

-0.23188

0.238672

1

0.265051

0.014981

-0.36328

-0.00024

1

0.37601

0.311942

-0.62543

-0.59231

-0.40048

1

-0.57667

-0.1102

0.488521

0.133415

-0.14483

-0.33466

1

0.321659

0.089155

-0.18507

-0.02167

0.066079

0.107372

-0.21113

1

-0.33474

0.004429

0.306365

-0.08974

-0.15165

-0.09774

0.306989

-0.18811

1

-0.63945

-0.28745

0.486217

0.007783

-0.23765

-0.21836

0.599957

-0.27955

0.349022

1

Variables having higher correlation are %inc14-20, %inc20-30, %inc30-50, %inc50-100, %inc100+, medianinc, medianrent, medianhome, %owners, %nocars.

Regression between sales and other 10 variables

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.758935

R Square

0.575982

Adjusted R Square

0.558241

Standard Error

3623.869

Observations

250

ANOVA

df

SS

MS

F

Significance F

Regression

10

4.26E+09

4.26E+08

32.46557

3.09E-39

Residual

239

3.14E+09

13132430

Total

249

7.4E+09

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

29992.26

5634.274

5.323181

2.35E-07

18893.08

41091.44

18893.08

41091.44

%inc14-20

-218.377

101.365

-2.15436

0.032212

-418.06

-18.6937

-418.06

-18.6937

%inc20-30

-247.175

71.69977

-3.44737

0.000669

-388.42

-105.931

-388.42

-105.931

%inc30-50

-226.18

67.52907

-3.34937

0.000941

-359.208

-93.1517

-359.208

-93.1517

%inc50-100

-154.335

85.79453

-1.79889

0.073297

-323.345

14.67481

-323.345

14.67481

%inc100+

-209.654

68.48379

-3.06137

0.002455

-344.563

-74.7453

-344.563

-74.7453

medianinc

-0.04507

0.046098

-0.97776

0.329181

-0.13588

0.045738

-0.13588

0.045738

medianrent

2.951005

4.161783

0.709072

0.478971

-5.24745

11.14946

-5.24745

11.14946

medianhome

0.050972

0.016838

3.027244

0.002738

0.017803

0.084142

0.017803

0.084142

%owners

-54.7744

16.54521

-3.31059

0.001075

-87.3675

-22.1813

-87.3675

-22.1813

%nocars

91.90787

34.95944

2.628985

0.009119

23.03988

160.7758

23.03988

160.7758

We can predict the values of y with the help of x variables. As our variables are showing the regression equation as: Sales= 29992+ (-218.377 x1)+(-247.175 x2)+ … + 91.90787 ...