Pizza Corner

MARKETING RESEARCH

Assignment No : 3

Submitted by

K.NARESH KUMAR (172)

Section-C

PGDM-General

Question : The owner of Pizza Corner (a chain of Pizza outlets), Gurgaon would like to

build a regression model consisting of six factors to predict the sales of pizzas. Data for

the past fifteen months on sales and six different factors were collected for the purpose.

Now send me the correlation and regression output with your interpretation and

recommendations (Hard Copy Only).

Solution :

In statistics, regression analysis is a statistical process for estimating the relationships among

variables. It includes many techniques for modeling and analyzing several variables, when

the focus is on the relationship between a dependent variable and one or more independent

variables. Multi-collinearity must be avoided in regression.

Two methods of regression :

1. Enter Regression Method.

2. Stepwise Regression Method.

2a) Forward Regression Method

2b) Backward Regression Method.

i) For Pizza Corner case, dependability by Enter Regression Method is given below :

REGRESSION

/MISSING LISTWISE

/STATISTICS COEFF OUTS R ANOVA CHANGE

/CRITERIA=PIN(.05) POUT(.10)

/NOORIGIN

/DEPENDENT Sales

/METHOD=ENTER DelBoys Adcost Outlets Variants Comp.Int NoofExtCustomer.

Regression [DataSet1]

Variables Entered/Removeda

Model Variables Entered Variables Removed Method

1

No of Ext Customer, Comp. Int,

Variants, Del Boys, Outlets, Ad

costb

. Enter

a. Dependent Variable: Sales

b. All requested variables entered.

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

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

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

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

Model Summary

Model R R

Square

Adjusted R

Square

Std. Error of

the

Estimate

Change Statistics

R Square

Change

F

Change

df1 df2 Sig. F

Change

1 .976a .953 .918 6.260 .953 27.254 6 8 .000

a. Predictors: (Constant), No of Ext Customer, Comp. Int, Variants, Del Boys, Outlets, Ad cost

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1

Regression 6408.864 6 1068.144 27.254 .000b

Residual 313.536 8 39.192

Total 6722.400 14


b. Predictors: (Constant), No of Ext Customer, Comp. Int, Variants, Del Boys, Outlets, Ad cost

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1

(Constant) 6.372 32.586 .196 .850

Del Boys .919 .910 .189 1.010 .342

Ad cost .699 1.303 .152 .537 .606

Outlets 1.620 .618 .617 2.621 .031

Variants -1.978 2.310 -.147 -.856 .417

Comp. Int .067 2.211 .003 .030 .977

No of Ext Customer .242 .299 .182 .808 .442


Interpretation : By Enter Regression Method, significance of “Outlets” is less than 0.05

and hence it is the most significant factor of sales in Pizza Corner.

ii) Now, let us see the stepwise regression methods.

Forward Regression Method for Pizza Corner sales dependency :

REGRESSION

/MISSING LISTWISE



/NOORIGIN

/DEPENDENT Sales

/METHOD=FORWARD DelBoys Adcost Outlets Variants Comp.Int NoofExtCustomer.

Regression

[DataSet1]



1 Outlets .

Forward (Criterion:

Probability-of-F-to-enter <=

.050)

2 Del Boys .

Forward (Criterion:

Probability-of-F-to-enter <=

.050)


Model Summary

Model R R

Square

Adjusted R

Square

Std. Error of

the

Estimate

Change Statistics

R Square

Change

F

Change

df1 df2 Sig. F

Change

1 .953a .908 .900 6.913 .908 127.676 1 13 .000

2 .970b .940 .930 5.789 .033 6.535 1 12 .025

a. Predictors: (Constant), Outlets

b. Predictors: (Constant), Outlets, Del Boys

ANOVAa


1

Regression 6101.176 1 6101.176 127.676 .000b

Residual 621.224 13 47.786

Total 6722.400 14

2

Regression 6320.215 2 3160.108 94.288 .000c

Residual 402.185 12 33.515

Total 6722.400 14


b. Predictors: (Constant), Outlets

c. Predictors: (Constant), Outlets, Del Boys

Coefficientsa


Coefficients

t Sig.

B Std. Error Beta

1 (Constant) -13.013 3.746 -3.474 .004

Outlets 2.503 .222 .953 11.299 .000

2

(Constant) -11.817 3.172 -3.726 .003

Outlets 1.753 .347 .667 5.053 .000

Del Boys 1.640 .641 .338 2.556 .025


Excluded Variablesa

Model Beta In t Sig. Partial

Correlation

Collinearity

Statistics

Tolerance

1

Del Boys .338b 2.556 .025 .594 .286

Ad cost .400b 2.361 .036 .563 .183

Variants -.085b -.600 .560 -.171 .370

Comp. Int -.006b -.064 .950 -.018 .999

No of Ext Customer .241b 1.560 .145 .411 .267

2

Ad cost .226c 1.085 .301 .311 .113

Variants -.087c -.732 .480 -.215 .370

Comp. Int .019c .257 .802 .077 .981

No of Ext Customer .113c .736 .477 .217 .219


b. Predictors in the Model: (Constant), Outlets

c. Predictors in the Model: (Constant), Outlets, Del Boys

Interpretation : In Forward Regression Method, we can find the predictors of sales in

steps. First step, only outlets factor was taken along with constant, the significance value

was well below considered significance value ie 0.05.

So we took delivery boys factor along with outlets and constant. Even then the

significance value was less than considered significance value ie 0.05.

Variants, Comp. int., No of ext customer, Ad Cost are excluded factors in this method.

Hence, outlets and delivery boys are the two factors which predict the sales much more

than other factors.

iii) Backward Regression Method :

The best regression method of the three methods.

REGRESSION

/MISSING LISTWISE



/NOORIGIN

/DEPENDENT Sales

/METHOD=BACKWARD DelBoys Adcost Outlets Variants Comp.Int

NoofExtCustomer.

Regression [DataSet1]



1

No of Ext Customer, Comp.

Int, Variants, Del Boys,

Outlets, Ad costb

. Enter

2 . Comp. Int

Backward (criterion:

Probability of F-to-remove >=

.100).

3 . Ad cost



.100).

4 . Variants



.100).

5 . No of Ext Customer



.100).


b. All requested variables entered.

Model Summary

Model R R

Square

Adjusted R

Square

Std. Error of

the

Estimate

Change Statistics

R Square

Change

F

Change

df1 df2 Sig. F

Change

1 .976a .953 .918 6.260 .953 27.254 6 8 .000

2 .976b .953 .927 5.903 .000 .001 1 8 .977

3 .975c .951 .932 5.732 -.002 .429 1 9 .529

4 .971d .943 .927 5.903 -.008 1.668 1 10 .226

5 .970e .940 .930 5.789 -.003 .542 1 11 .477

a. Predictors: (Constant), No of Ext Customer, Comp. Int, Variants, Del Boys, Outlets, Ad cost

b. Predictors: (Constant), No of Ext Customer, Variants, Del Boys, Outlets, Ad cost

c. Predictors: (Constant), No of Ext Customer, Variants, Del Boys, Outlets

d. Predictors: (Constant), No of Ext Customer, Del Boys, Outlets

e. Predictors: (Constant), Del Boys, Outlets

ANOVAa


1

Regression 6408.864 6 1068.144 27.254 .000b

Residual 313.536 8 39.192

Total 6722.400 14

2

Regression 6408.828 5 1281.766 36.789 .000c

Residual 313.572 9 34.841

Total 6722.400 14

3

Regression 6393.881 4 1598.470 48.657 .000d

Residual 328.519 10 32.852

Total 6722.400 14

4

Regression 6339.099 3 2113.033 60.640 .000e

Residual 383.301 11 34.846

Total 6722.400 14

5

Regression 6320.215 2 3160.108 94.288 .000f

Residual 402.185 12 33.515

Total 6722.400 14


b. Predictors: (Constant), No of Ext Customer, Comp. Int, Variants, Del Boys, Outlets, Ad cost

c. Predictors: (Constant), No of Ext Customer, Variants, Del Boys, Outlets, Ad cost

d. Predictors: (Constant), No of Ext Customer, Variants, Del Boys, Outlets

e. Predictors: (Constant), No of Ext Customer, Del Boys, Outlets

f. Predictors: (Constant), Del Boys, Outlets

Coefficientsa


Coefficients

t Sig.

B Std. Error Beta

1

(Constant) 6.372 32.586 .196 .850

Del Boys .919 .910 .189 1.010 .342

Ad cost .699 1.303 .152 .537 .606

Outlets 1.620 .618 .617 2.621 .031

Variants -1.978 2.310 -.147 -.856 .417

Comp. Int .067 2.211 .003 .030 .977


2

(Constant) 7.061 21.908 .322 .755

Del Boys .920 .858 .189 1.072 .311

Ad cost .678 1.035 .147 .655 .529

Outlets 1.629 .522 .620 3.123 .012

Variants -2.014 1.868 -.150 -1.078 .309

No of Ext Customer .246 .245 .186 1.003 .342

3

(Constant) 12.422 19.733 .630 .543

Del Boys 1.200 .721 .247 1.665 .127

Outlets 1.811 .429 .689 4.223 .002

Variants -2.285 1.769 -.170 -1.291 .226

No of Ext Customer .294 .227 .222 1.294 .225

4

(Constant) -12.690 3.445 -3.684 .004

Del Boys 1.413 .723 .291 1.955 .076

Outlets 1.602 .409 .610 3.917 .002


5

(Constant) -11.817 3.172 -3.726 .003

Del Boys 1.640 .641 .338 2.556 .025

Outlets 1.753 .347 .667 5.053 .000


Excluded Variablesa

Model Beta In t Sig. Partial

Correlation

Collinearity

Statistics

Tolerance

2 Comp. Int .003b .030 .977 .011 .589

3 Comp. Int -.026

c -.320 .756 -.106 .830

Ad cost .147c .655 .529 .213 .103

4

Comp. Int .012d .151 .883 .048 .960

Ad cost .201d .909 .385 .276 .108

Variants -.170d -1.291 .226 -.378 .281

5

Comp. Int .019e .257 .802 .077 .981

Ad cost .226e 1.085 .301 .311 .113

Variants -.087e -.732 .480 -.215 .370

No of Ext Customer .113e .736 .477 .217 .219


b. Predictors in the Model: (Constant), No of Ext Customer, Variants, Del Boys, Outlets, Ad cost

c. Predictors in the Model: (Constant), No of Ext Customer, Variants, Del Boys, Outlets

d. Predictors in the Model: (Constant), No of Ext Customer, Del Boys, Outlets

e. Predictors in the Model: (Constant), Del Boys, Outlets

Interpretation : In Backward Regression Method, we exclude the factors one by one.

Here in the fifth step, we are getting desired significance level below 0.05. So the

predicting factors of sale are Outlets and Del Boys.

Discriminant Analysis :

From co-efficients table of backward regression,

Sales Dependance equation is

Y = 6.372 + (0.919)(Del Boys) + (0.699)(Ad Cost) + (1.620)(Outlets) – (1.978)(Variants) +

(0.067)(Comp Int) + (0.242)(No of Ext Customers)

Correlartion : In statistics, dependence is any statistical relationship between two random

variables or two sets of data. Correlation refers to any of a broad class of statistical

relationships involving dependence.

CORRELATIONS

/VARIABLES=Sales DelBoys Adcost Outlets Variants Comp.Int NoofExtCustomer

/PRINT=TWOTAIL NOSIG

/STATISTICS DESCRIPTIVES XPROD

/MISSING=PAIRWISE.

Correlations [DataSet1]

Descriptive Statistics

Mean Std. Deviation N

Sales 24.20 21.913 15

Del Boys 6.07 4.511 15

Ad cost 11.07 4.758 15

Outlets 14.87 8.340 15

Variants 13.67 1.633 15

Comp. Int 3.40 .986 15

No of Ext Customer 29.93 16.529 15

Correlations

Sales Del Boys Ad cost Outlets Variants Comp.

Int

No of Ext

Customer

Sales

Pearson

Correlation 1 .902

** .934

** .953

** .725

** -.040 .880

**

Sig. (2-tailed) .000 .000 .000 .002 .886 .000

Sum of Squares

and Cross-

products

6722.400 1247.800 1363.800 2437.400 363.000 -

12.200 4462.200

Covariance 480.171 89.129 97.414 174.100 25.929 -.871 318.729

N 15 15 15 15 15 15 15

Del Boys

Pearson

Correlation .902

** 1 .905

** .845

** .672

** -.103 .841

**

Sig. (2-tailed) .000 .000 .000 .006 .715 .000

Sum of Squares

and Cross-

products

1247.800 284.933 271.933 445.133 69.333 -6.400 878.067

Covariance 89.129 20.352 19.424 31.795 4.952 -.457 62.719

N 15 15 15 15 15 15 15

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

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

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

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

Ad cost

Pearson

Correlation .934

** .905

** 1 .904

** .702

** -.189 .867

**

Sig. (2-tailed) .000 .000 .000 .004 .500 .000

Sum of Squares

and Cross-

products

1363.800 271.933 316.933 502.133 76.333 -

12.400 954.067

Covariance 97.414 19.424 22.638 35.867 5.452 -.886 68.148

N 15 15 15 15 15 15 15

Outlets

Pearson

Correlation .953

** .845

** .904

** 1 .794

** -.036 .856

**

Sig. (2-tailed) .000 .000 .000 .000 .897 .000

Sum of Squares

and Cross-

products

2437.400 445.133 502.133 973.733 151.333 -4.200 1651.867

Covariance 174.100 31.795 35.867 69.552 10.810 -.300 117.990

N 15 15 15 15 15 15 15

Variants

Pearson

Correlation .725

** .672

** .702

** .794

** 1 -.178 .819

**

Sig. (2-tailed) .002 .006 .004 .000 .527 .000

Sum of Squares

and Cross-

products

363.000 69.333 76.333 151.333 37.333 -4.000 309.667

Covariance 25.929 4.952 5.452 10.810 2.667 -.286 22.119

N 15 15 15 15 15 15 15

Comp. Int

Pearson

Correlation -.040 -.103 -.189 -.036 -.178 1 .006

Sig. (2-tailed) .886 .715 .500 .897 .527 .983

Sum of Squares

and Cross-

products

-12.200 -6.400 -12.400 -4.200 -4.000 13.600 1.400

Covariance -.871 -.457 -.886 -.300 -.286 .971 .100

N 15 15 15 15 15 15 15

No of Ext

Customer

Pearson

Correlation .880

** .841

** .867

** .856

** .819

** .006 1

Sig. (2-tailed) .000 .000 .000 .000 .000 .983

Sum of Squares

and Cross-

products

4462.200 878.067 954.067 1651.867 309.667 1.400 3824.933

Covariance 318.729 62.719 68.148 117.990 22.119 .100 273.210

N 15 15 15 15 15 15 15

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

Interpretation : According to Correlation coefficients table, Sales have a positive

relationship with Outlets, Del boys , Ad cost, No of ext customers and variants. While

sales have negative relationship (dependence) with Comp Int.

Controlling other variables constant, if Number of delivery boys is increased by 1 then Sales

will increase by 0.919

Controlling other variables constant, if of ad cost is increased by 1 then

Sales will increase by 0.699

Controlling other variables constant, if Number of outlets is increased by 1 then Sales will

increase by 1.620

Controlling other variables constant, if variants of pizza is increased by 1 then Sales will

decrease by 1.978

Controlling other variables constant, if Competitors’ index is increased by 1 then sales will

increase by 0.067

Controlling other variables constant, if Number of existing customers is increased by 1 then

sales will increase by 0.242

RECOMMENDATIONS :

1. Increase the no. of delivery boys.

2. Increase the pizza outlets.

3. Reduce the expense on competitors’ index.

4. Variants don’t have any significant effect on sales, so don’t spend much on variants.

Documents

Pizza Corner