→ States.jmp contains the following variables (variables names are listed in the first row).
stateState abbreviation
agrEmployment in agriculture (percent), 1990
manEmployment in manufacturing (percent), 1990
incPer capita income, 1990
unempUnemployment rate, 1993
unionUnion members (percent of workers), 1995
eduBachelor or advanced degree, 1990
avpayAverage annual pay, 1993
medyMedian income, 1993
povPoverty rate, 1993
exemplExport related employment (percent of total), 1991
serEmployment in services and government (percent), 1990
a.Run a multiple regression with the unemployment rateunempas the dependentYvariable and the following as explanatoryXvariables (10 total):
agravpay
manmedy
incpov
unionexempl
eduser
Which variables are statistically significant (95% level or higher)?Generate theVIFcolumn in the ‘Parameter Estimates’ area.What variables have aVIFover 5?Save your regressions results to a Data Table.
b.Return to the Model Dialog box and run a ‘Stepwise’ regression with the same variables (you can leave all of the default options for your stepwise parameters).Were the same variables selected; the ones that were statistically significant from part (a)?Are there any issues with the VIF values now?Write out your regression equation with the parameter estimates.Hint: you can double-check your equation with the ‘Prediction Expression’ feature.
c.In the model selected via stepwise regression, put in the ‘Prediction Profiler’ feature.What is your estimated unemployment rate when the following parameters are specified (round to 2 decimals)?
agr = 7.43pov = 15
man = 15exempl = 15
union = 15
d.In the model selected via stepwise regression,what is the direction of the relationship between each retained X variable andunemp(+ or -)?In other words, when each of the following increase, does the unemployment rate increase or decrease?
agrmanunionpovexempl
Save your stepwise regression results to a Data Table.
e.Check for ‘outliers’ in the variables retained in the stepwise regression.There is one big outlier.What Row is the clear outlier?Go back to the data table.What State is the outlier?
Select Analyze > Multivariate Methods > Multivariate
Select the five variables from part (d) and then click Y, Columns
Click OK
Click the red triangle next to Multivariate > Outlier Analysis > Mahalanobis Distances
Click the red triangle next to Multivariate > Outlier Analysis > Jackknife Distances
Save your Outlier Analysis to a Data Table.
f.Check for ‘influential observations.’Open up your stepwise regression results that you saved to a data table.What is the clear influential observation from Cook’s D Influence unemp?Is it the same Row and State you diagnosed from part (e)?
Click the red triangle next to Response unemp > Save Columns > Cook’s D Influence
Select Analyze > Distribution
Select Cook’s D Influence Oxy, and then click Y, Columns
Click OK
Save your Cook’s D analysis to a Data Table.
3.[33.3 points]Wine
DATA:Wine.jmp
→ The dataset contains the results of a chemical analysis of wines grown in a specific area of Italy.Three types of wine are represented in the 178 samples, with the results of 13 chemical analyses recorded for each sample.The Type variable has been transformed into a categoric variable, with a three-class target variable for classification.The chemical records are of:
Wine Type:
type 1 (59)type 2 (71)type 3 (48)
Chemicals:
AlcoholMalic acidAshAlcalinity of ash
MagnesiumTotal phenolsFlavanoidsNonflavanoid phenols
ProanthocyaninsColor intensityHueDilutionProline
a.Test the null hypothesis thatfor the type 1, type 2, and type 3 wines…there is no difference across all of the Chemicals.In other words, can you conclude that the chemical measures are different across the 3 groups?Run a MANOVA by selecting all 13 Chemicals into the Y box andTypeinto Construct Model Effects.Can you reject the null hypothesis at the 99% level for each of the 4 tests?What is your conclusion?Save your MANOVA regression to a data table.
b.Run an ANOVA forMagnesium (Y)versusType (X).Test the null hypothesis thatthe Magnesium level is not different across the 3 Types.Can you reject the null hypothesis at the 99% level (Prob > F)?What is your conclusion?Save your ANOVA-Magnesium to a data table.
c.Run an ANOVA forProline (Y)versusType (X).Test the null hypothesis thatthe Proline level is not different across the 3 Types.Can you reject the null hypothesis at the 99% level (Prob > F)?What is your conclusion?Save your ANOVA for Proline to a data table.
d.Perform a principal components analysis on all 13 Chemical variables, Alcohol-Proline.Retain 2 principal components.Save you Principal Components analysis to a data table.
e.
What is the equation for Prin1?
f.
What is the equation for Prin2?