A sample of 30 respondents was interviewed using mall intercept interviewing. The respondents were asked to indicate their degree of agreement with the following statements using a seven-point scale (1 = strongly disagree, 7 = strongly agree).

V1 = It is important to buy a toothpaste that prevents cavities

V2 = I like a toothpaste that gives a shiny teeth

V3 = A toothpaste should strengthen your gums teeth

V4 = I prefer a toothpaste that freshens breath

V5 = Prevention of tooth decay is not an important benefit offered by a toothpaste

V6 = The most important consideration in buying a toothpaste is attractive teeth

By using the variables,

(1) How many factors is extracted from data for principal component analysis?

(2) What is the total percentage of variance explained by these principal components?

(3) Which variables are included in the same factors ? How can you name these factors?

You can find the data set below

 V1, V2, V3, V4, V5, V6 7.00 , 3.00 , 6.00 , 4.00 , 2.00 , 4.00 1.00 , 3.00 , 2.00 , 4.00 , 5.00 , 4.00 6.00 , 2.00 , 7.00 , 4.00 , 1.00 , 3.00 4.00 , 5.00 , 4.00 , 6.00 , 6.00 , 5.00 1.00 , 2.00 , 2.00 , 3.00 , 2.00 , 2.00 6.00 , 3.00 , 6.00 , 4.00 , 4.00 , 4.00 5.00 , 3.00 , 6.00 , 3.00 , 1.00 , 3.00 6.00 , 4.00 , 7.00 , 4.00 , 6.00 , 4.00 3.00 , 4.00 , 2.00 , 3.00 , 7.00 , 3.00 2.00 , 6.00 , 2.00 , 6.00 , 2.00 , 6.00 6.00 , 4.00 , 7.00 , 3.00 , 5.00 , 3.00 2.00 , 3.00 , 1.00 , 4.00 , 1.00 , 4.00 7.00 , 2.00 , 6.00 , 4.00 , 3.00 , 3.00 4.00 , 6.00 , 4.00 , 5.00 , 6.00 , 6.00 1.00 , 3.00 , 2.00 , 2.00 , 3.00 , 4.00 6.00 , 4.00 , 6.00 , 3.00 , 3.00 , 4.00 5.00 , 3.00 , 6.00 , 3.00 , 1.00 , 4.00 7.00 , 3.00 , 7.00 , 4.00 , 6.00 , 4.00 2.00 , 4.00 , 3.00 , 3.00 , 6.00 , 3.00 3.00 , 5.00 , 3.00 , 6.00 , 4.00 , 6.00 1.00 , 3.00 , 2.00 , 3.00 , 5.00 , 3.00 5.00 , 4.00 , 5.00 , 4.00 , 2.00 , 4.00 2.00 , 2.00 , 1.00 , 5.00 , 4.00 , 4.00 4.00 , 6.00 , 4.00 , 6.00 , 4.00 , 7.00 6.00 , 5.00 , 4.00 , 2.00 , 1.00 , 4.00 3.00 , 5.00 , 4.00 , 6.00 , 4.00 , 7.00 4.00 , 4.00 , 7.00 , 2.00 , 2.00 , 5.00 3.00 , 7.00 , 2.00 , 6.00 , 4.00 , 3.00 4.00 , 6.00 , 3.00 , 7.00 , 2.00 , 7.00 2.00 , 3.00 , 2.00 , 4.00 , 7.00 , 2.00