how many factors will be needed if the criterion is to explain 80% of the total variance

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

QUESTION 1

 In this question you are using the data set HATCO. Use SPSS to answer the following questions.

 (a) Is the data appropriate for factor analysis? Substantiate your answer.

(b) Which variables will be appropriate for factor analysis?

(c) Do a factor analysis using the principal component analysis with a promax rotation. Ensure that you include the scree plot, and under options sort the factors by size and use items with factor loadings .5 and above. Produce the output.

(d) How many factors will be needed if the criterion is to explain 80% of the total variance?

(e) What do you notice about the item "Price flexibility"?

(f) Create a new variable "Price flexibility2" by computing the necessary transformation of "10 - Price flexibility" and redo a factor analysis using the principal component analysis with a promax rotation using "Price flexibility2" instead of "Price flexibility". Produce the output and do not suppress small coefficients in your output.

(g) Interpret the results of the factor analysis (including appropriateness of the factor analysis, grouping the variables according to the factor loadings and suggesting, with justification, possible labels for the factors).

(h) Show numerically that the communality estimate for Price flexibility2 is :714. Interpret this estimate.

(i) Do reliability analysis of the factors obtained in (f) and give the reliability coefficient for each construct and the overall reliability analysis of the instrument, and interpret it using Jain and Angural (2017) guidelines.

(j) Three new variables were created, using the factor analysis. (i) Explain how these new variables for each respondent may be obtained. (ii) Suggest one possible way that these new variables can be used.

(k) Discuss the rotation method used, paying specific attention to: (i) the method used, its implications and appropriateness, (ii) the necessity of the rotation method, and (iii) the success of the rotation method.

(l) Calculate the composite variables of each factor (by taking the average), and give the descriptive statistics for the composite variables and interpret them

(m) Use the distribution command in SAS JMP to test for normality of the three composite variables created. (Hint: Use histograms, boxplots, normal quantile plots and Shapiro Wilk’s test). Ensure that on the summary statistics output you add skewness and kurtosis on the analysis results.

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