Questions: After you calculate the value of r, you find it's -0.76 for orange flowers, but -0.05 for blue ones. Which type of flower could you use a principal component approach for to reduce the data complexity? (A) Blue (B) Orange (C) Both (D) Neither

Solution Steps

To determine which type of flower could benefit from a principal component approach to reduce data complexity, we need to consider the correlation coefficient \( r \). A higher absolute value of \( r \) indicates a stronger linear relationship, which means the data can be more effectively reduced using principal component analysis (PCA).

Given:

• \( r = -0.76 \) for orange flowers
• \( r = -0.05 \) for blue flowers

Since \( r \) for orange flowers is closer to -1, it indicates a stronger linear relationship compared to blue flowers. Therefore, PCA would be more effective for orange flowers.

We are given the correlation coefficients for two types of flowers:

• For orange flowers, \( r = -0.76 \)
• For blue flowers, \( r = -0.05 \)

To determine which type of flower could benefit more from a principal component approach, we compare the absolute values of the correlation coefficients:

• \( |r_{\text{orange}}| = |-0.76| = 0.76 \)
• \( |r_{\text{blue}}| = |-0.05| = 0.05 \)

Since \( 0.76 > 0.05 \), the orange flowers have a stronger linear relationship compared to the blue flowers. A stronger linear relationship indicates that the data can be more effectively reduced using principal component analysis (PCA).

Final Answer