4) Verify the sales agent's claim using canonical discriminant analysis (use the stepwise method, in case there is correlation between any two independent variables) in SPSS (or any other software) and report your findings by answering the following questions:

(i) List the attributes that are significantly different per vehicle type. Justify your answer

(ii) Are covariance matrices homogeneous? Justify your answer.

(iii) Does the discriminant model significantly differentiate the vehicles? Justify your answer.

(iv) Are all variables significant in the model?

Make use of the following outputs in order to answer the questions above:

Analysis 1

Analysis Case Processing Summary Unweighted Cases N Percent Valid 117 74.5 Excluded Missing or out-of-range .0 group codes At least one missing 40 25.5 discriminating variable Both missing or out-of- .0 range group codes and at least one missing discriminating variable Total 40 25.5 Total 157 100.0Group Statistics Valid N (listwise) Vehicle type Mean Std. Deviation Unweighted Weighted Car Log-transformed sales 3.1986457 1.36253758 88 88.000 Zscore: 4-year resale 0494824 1.13955229 88 88.000 value Zscore: Price in thousands -.0560305 1.09004744 88 88.000 Zscore: Engine size -.1170351 1.04685498 88 88.000 Zscore: Horsepower -.0552120 1.13924831 88 88.000 Zscore: Wheelbase -.2529194 77179170 88 88.000 Zscore: Width -.1175252 89303697 88 88.000 Zscore: Length -.0368326 95837892 88 88.000 Zscore: Curb weight -.3396515 80662966 88 88.000 Zscore: Fuel capacity -.3632147 67280234 88 88.000 Zscore: Fuel efficiency 3809480 91575391 88 88.000 Lorry Log-transformed sales 4.0158513 1.06124383 29 29.000 Zscore: 4-year resale -.1647496 .42790852 29 29.000 value Zscore: Price in thousands -.2295179 55831748 29 29.000 Zscore: Engine size .3081034 82507800 29 29.000 Zscore: Horsepower -.1645146 61793543 29 29.000 Zscore: Wheelbase 6826413 1.43732319 29 29.000 Zscore: Width 4030797 1.28209184 29 29.000 Zscore: Length .2242137 1.22387390 29 29.000 Zscore: Curb weight 6852919 93620546 29 29.000 Zscore: Fuel capacity 9578226 1.08647674 29 29.000 Zscore: Fuel efficiency -.8974452 70877953 29 29.000 Total Log-transformed sales 3.4012009 1.33783635 117 117.000 Zscore: 4-year resale -.0036179 1.01329285 117 117.000 value Zscore: Price in thousands -.0990316 98592818 117 117.000 Zscore: Engine size -.0116589 1.01006668 117 117.000 Zscore: Horsepower -.0823041 1.03335898 117 117.000 Zscore: Wheelbase -.0210283 1.05356217 117 117.000 Zscore: Width 0115136 1.02267717 117 117.000 Zscore: Length 0278712 1.03113307 117 117.000 Zscore: Curb weight -.0856057 94714541 117 117.000 Zscore: Fuel capacity -.0357781 97599948 117 117.000 Zscore: Fuel efficiency 0640813 1.02835670 117 117.000Tests of Equality of Group Means Wilks' Lambda F df1 df2 Sig. Log-transformed sales .930 8.677 115 004 Zscore: 4-year resale 992 975 115 326 value Zscore: Price in thousands .994 673 115 414 Zscore: Engine size .967 3.963 115 049 Zscore: Horsepower 998 .242 115 623 Zscore: Wheelbase .852 20.020 115 <.001 zscore: width .951 length curb weight .780 fuel capacity efficiency within-groups matrices log- transformed price sales resale value in thousands engine size horsepower wheelbase covariance log-transformed .625 .225 .955 .812 .207 .378 ..484 .873 ..656 .267 .020 .101 .515 .665 .889 .196 .510 ..225 .506 ..533 .656 correlation .288 .435 .556 ..216 .757 .005 .520 .219 .773 .204 .853 .327 .559 .529 .756 .262 .738 .338 .742 .734 .687 .585 .168 .721 .309 a. the matrix has degrees of freedom. ..585 determinants log vehicle type rank determinant car lorry pooled ranks and natural logarithms printed are those group matrices.test results box m f approx. df1 df2 sig. tests null hypothesis equal population matrices.variables entered wilks lambda exact step removed statistic df3 .516 .302 .307 at each variable that minimizes overall is entered. maximum number steps b. minimum partial to enter c. remove d. level tolerance or vin insufficient for further computation.variables analysis .607 .500 .437 .343 .334 .424 .326 .175 .184 .319 .407 .324 .173 .177 .353 .351 .330 .374 .299 .157 .339 .337 .176 .328 .316 .174 .395 .372variables not min. .992 .994 .603 .001 .617 .359 .504 .313 .239 .649 .200 .335 .341 .614 .269 .282 .212 .386 .384 .280 .320 .783 .135 .161 .055 .294 variables co comparisons a d freedom e. f. g. h. i. canonical function eigenvalue variance cumulative .833 first discriminant functions were used analysis. coefficients .632structure .426 .075 .051 correlations between discriminating standardized ordered by absolute within function. this analysis.canonical unstandardized coefficientsfunctions centroids evaluated meansclassification processing summary processed excluded missing out-of-range codes least one output probabilities groups cases prior unweighted weighted .752 .248 total .433 .131 fisher linear functionsclassification : predicted membership original count .9 cross-validated grouped correctly classified. cross validation done only case classified derived from all other than case.>