Velu Pandian RavichandranSPSS Lab 4 : Analysis on the Last pageQuestion 1 : Describe and interpret the ZscoreDescriptive analysis of the variablesDescriptive Statistics

NMinimumMaximumMeanStd. Deviation

Presentation365.68.97.437.9182

Cleanliness362.94.63.762.4413

Taste364.06.85.553.6322

Balance36.02.2.969.5701

Valid N (listwise)36

Descriptive analysis of the standardized variables For interpretation purposes Only

Descriptive Statistics

NMinimumMaximumMeanStd. Deviation

Zscore(Presentation)36-2.031241.54720.00000001.00000000

Zscore(Cleanliness)36-2.050191.99623.00000001.00000000

Zscore(Taste)36-2.456061.97276.00000001.00000000

Zscore(Balance)36-1.700412.15841.00000001.00000000

Valid N (listwise)36

Normal distribution, 95% of the distribution is between -2 and 2.Zscore values > 2 or < -2 Extreme Values

Question 2 : Analyse the correlation matrix R and explain why you can run a factorial analysis.

Correlations

Zscore(Presentation)Zscore(Cleanliness)Zscore(Taste)Zscore(Balance)

Zscore(Presentation)Pearson Correlation1.712**.513**-.398*

Sig. (2-tailed).000.001.016

Sum of Squares and Cross-products35.00024.92217.963-13.928

Covariance1.000.712.513-.398

N36363636

Zscore(Cleanliness)Pearson Correlation.712**1.377*-.402*

Sig. (2-tailed).000.023.015

Sum of Squares and Cross-products24.92235.00013.193-14.072

Covariance.7121.000.377-.402

N36363636

Zscore(Taste)Pearson Correlation.513**.377*1-.668**

Sig. (2-tailed).001.023.000

Sum of Squares and Cross-products17.96313.19335.000-23.365

Covariance.513.3771.000-.668

N36363636

Zscore(Balance)Pearson Correlation-.398*-.402*-.668**1

Sig. (2-tailed).016.015.000

Sum of Squares and Cross-products-13.928-14.072-23.36535.000

Covariance-.398-.402-.6681.000

N36363636

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

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

+/- 2/n =>2/36=+/-0.333Matrix is Symmetric and correlations are outside (-0.33,0.33)

Question 3 , 4, 5 & 6 (Explanations and Interpretation Given Below)

Factor AnalysisTotal Variance Explained

ComponentInitial EigenvaluesExtraction Sums of Squared Loadings

Total% of VarianceCumulative %Total% of VarianceCumulative %

12.53763.41763.4172.53763.41763.417

2.85021.24384.660.85021.24384.660

3.3829.56294.222

4.2315.778100.000

Extraction Method: Principal Component Analysis.

Component Matrixa

Component

12

Zscore(Presentation).830.403

Zscore(Cleanliness).783.504

Zscore(Taste).803-.432

Zscore(Balance)-.769.497

Extraction Method: Principal Component Analysis.a

a. 2 components extracted.

Component Score Coefficient Matrix

Component

12

Zscore(Presentation).327.474

Zscore(Cleanliness).309.593

Zscore(Taste).317-.508

Zscore(Balance)-.303.585

Extraction Method: Principal Component Analysis. Component Scores.

Component Score Covariance Matrix

Component12

11.000.000

2.0001.000

SchoolCase Processing Summary

SchoolCases

ValidMissingTotal

NPercentNPercentNPercent

REGR factor score 1 for analysis 1Cambronn12100.0%00.0%12100.0%

Garibald12100.0%00.0%12100.0%

Sko12100.0%00.0%12100.0%

Descriptives

SchoolStatisticStd. Error

REGR factor score 1 for analysis 1CambronnMean-.1948437.31335442

95% Confidence Interval for MeanLower Bound-.8845321

Upper Bound.4948448

5% Trimmed Mean-.1478043

Median.0827993

Variance1.178

Std. Deviation1.08549156

Minimum-2.42191

Maximum1.18552

Range3.60743

Interquartile Range1.91646

Skewness-.715.637

Kurtosis-.1731.232

GaribaldMean-.0479483.25052979

95% Confidence Interval for MeanLower Bound-.5993607

Upper Bound.5034640

5% Trimmed Mean-.0368293

Median.2853231

Variance.753

Std. Deviation.86786066

Minimum-1.33781

Maximum1.04177

Range2.37958

Interquartile Range1.59741

Skewness-.318.637

Kurtosis-1.7221.232

SkoMean.2427920.30850633

95% Confidence Interval for MeanLower Bound-.4362258

Upper Bound.9218099

5% Trimmed Mean.3009525

Median.5931711

Variance1.142

Std. Deviation1.06869727

Minimum-2.07194

Maximum1.51064

Range3.58258

Interquartile Range1.54036

Skewness-1.052.637

Kurtosis.5731.232

Question 3, 4, 5 & 6: Quality of F1=1/p=2.537/4 = 63.417%F1= Zscore(Presentation)*0.327+ Zscore(Cleanliness)*0.309+ Zscore(Taste)*0.317- Zscore(Balance)*(0.303)F1 is maximum when Cleanliness and balance are high and when balance is low.

Sko seems to have higher scores followed by Garibaldi and finally Cambronne. Garibaldi seems to have more evenly distributed scores with grade more concentrated.

We believe that there exists a relation between the school and F1.

Quality of F2=2/p=0,850/4=21.243%F2= Zscore(Presentation)*0. 474+ Zscore(Cleanliness)*0. 593+ Zscore(Balance)*(0.585) - Zscore(Taste)*(0. 508)F2 is maximum when Cleanliness and presentation are high and when taste and balance are low.

Quality of the projection of F1 & F2 is: (1+2)/4=(2.537+0,850)/4=84.660%Projection will have ~ 85% of the information.Sko School: top right Quadrant. This school trains cooks for high quality restaurants and fast food places

Garibaldi school: bottom of the graph. They have a lower standard than other schools

Cambronne School: Majority close to 0 on the F2 axis but spread on the F1 axis. This school trains high presentation and cleanliness.