Statistics and business analytics

Assignment 4

Oleksiy NIKIFOROV

Statistics and Business analytics Page 1-8

Question 1 Describe and interpret the Zscore Action SPSS : « Analyse », « Descriptive statistics », « Descriptives » save standardized values as variables

Descriptive Statistics

N Range Minimum Maximum Mean Std. Deviation Variance

Zscore(Presentation) 36 3.57845 -2.03124 1.54720 .0000000 1.00000000 1.000

Zscore(Cleanliness) 36 4.04642 -2.05019 1.99623 .0000000 1.00000000 1.000

Zscore(Balance) 36 3.85882 -1.70041 2.15841 .0000000 1.00000000 1.000

Zscore(Taste) 36 4.42881 -2.45606 1.97276 .0000000 1.00000000 1.000

Valid N (listwise) 36

Question 2 Analyse the correlation matrix R and explain why you can run a factorial analysis. Action SPSS : « Analyse », Correlate, bivariate

Correlations

Presentation Cleanliness Taste Zscore(Balance) Zscore(Taste)

Presentation Pearson Correlation 1 .712** .513** -.398*

Sig. (2-tailed) .000 .001 .016

N 36 36 36 36

Cleanliness Pearson Correlation .712** 1 .377* -.402*

Sig. (2-tailed) .000 .023 .015

N 36 36 36 36

Taste Pearson Correlation .513** .377* 1 -.668**

Sig. (2-tailed) .001 .023 .000

N 36 36 36 36

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

Sig. (2-tailed) .016 .015 .000

N 36 36 36 36

Zscore(Taste) Pearson Correlation .513** .377* 1.000** -.668**

Sig. (2-tailed) .001 .023 .000 .000

N 36 36 36 36

Zscore(Cleanliness) Pearson Correlation .712** 1.000** .377* -.402*

Sig. (2-tailed) .000 .000 .023 .015

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N 36 36 36 36

Zscore(Presentation) Pearson Correlation 1.000** .712** .513** -.398*

Sig. (2-tailed) .000 .000 .001 .016

N 36 36 36 36

Balance Pearson Correlation -.398* -.402* -.668** 1.000**

Sig. (2-tailed) .016 .015 .000 .000

N 36 36 36 36

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

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

We can proceed with the multi-factor analysis because all correlation coefficients are significant with at least 0.05 level that is there is a correlation between each pair of the variables involved in the analysis.

Question 3 We run now a factorial analysis on the variables X1, X2, X3 and X4.. The School variable just bears an illustrative role. Interpret the first factor F1. Action SPSS in the course slide

Correlation Matrixa

Zscore(Presenta

tion)

Zscore(Cleanlin

ess) Zscore(Taste) Zscore(Balance)

Correlation Zscore(Presentation) 1.000 .712 .513 -.398

Zscore(Cleanliness) .712 1.000 .377 -.402

Zscore(Taste) .513 .377 1.000 -.668

Zscore(Balance) -.398 -.402 -.668 1.000

Sig. (1-tailed) Zscore(Presentation) .000 .001 .008

Zscore(Cleanliness) .000 .012 .008

Zscore(Taste) .001 .012 .000

Zscore(Balance) .008 .008 .000

a. Determinant = .191

Communalities

Initial Extraction

Zscore(Presentation) 1.000 .851

Zscore(Cleanliness) 1.000 .866

Zscore(Taste) 1.000 .831

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Zscore(Balance) 1.000 .838

Extraction Method: Principal Component Analysis.

Total Variance Explained

Component

Initial Eigenvalues Extraction Sums of Squared Loadings

Total % of Variance Cumulative % Total % of Variance Cumulative %

1 2.537 63.417 63.417 2.537 63.417 63.417

2 .850 21.243 84.660 .850 21.243 84.660

3 .382 9.562 94.222

4 .231 5.778 100.000

Extraction Method: Principal Component Analysis.

Component Matrixa

Component

1 2

Zscore(Presentation) .830 .403

Zscore(Taste) .803 -.432

Zscore(Cleanliness) .783 .504

Zscore(Balance) -.769 .497

Extraction Method: Principal Component Analysis.

a. 2 components extracted.

Component Score Coefficient Matrix

Component

1 2

Zscore(Presentation) .327 .474

Zscore(Cleanliness) .309 .593

Zscore(Taste) .317 -.508

Zscore(Balance) -.303 .585

Extraction Method: Principal Component Analysis.

Component Scores.

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Component Score Covariance Matrix

Component 1 2

1 1.000 .000

2 .000 1.000

Extraction Method: Principal

Component Analysis.

Component Scores.

F1 factor is maximized when the following variables are maximized - presentation, taste, balance and when the balance is minimized.

Descriptives

School Statistic Std. Error

REGR factor score 1 for

analysis 1

Cambronn Mean -.1948437 .31335442

95% Confidence Interval for

Mean

Lower Bound -.8845321

Upper Bound .4948448

5% Trimmed Mean -.1478043

Median .0827993

Variance 1.178

Std. Deviation 1.08549156

Minimum -2.42191

Maximum 1.18552

Range 3.60743

Interquartile Range 1.91646

Skewness -.715 .637

Kurtosis -.173 1.232

Garibald Mean -.0479483 .25052979

95% Confidence Interval for

Mean

Lower Bound -.5993607

Upper Bound .5034640

5% Trimmed Mean -.0368293

Median .2853231

Variance .753

Std. Deviation .86786066

Minimum -1.33781

Maximum 1.04177

Range 2.37958

Interquartile Range 1.59741

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Skewness -.318 .637

Kurtosis -1.722 1.232

Sko Mean .2427920 .30850633

95% Confidence Interval for

Mean

Lower Bound -.4362258

Upper Bound .9218099

5% Trimmed Mean .3009525

Median .5931711

Variance 1.142

Std. Deviation 1.06869727

Minimum -2.07194

Maximum 1.51064

Range 3.58258

Interquartile Range 1.54036

Skewness -1.052 .637

Kurtosis .573 1.232

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Question 5

Interpret F2F2 factor is maximized when cleanness, balance, and presentation are maximized and taste is minimized - this corresponds

Question 6

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