Question

In Exercise 23, add data for a child who is 6 years old and has a vocabulary of 900 words. Describe how this affects the correlation coefficient r.

Accepted Answer

Step 1: Understand the correlation coefficient (r). The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values close to 1 or -1 indicate strong relationships, and values near 0 indicate weak or no linear relationship. Step 2: Identify the existing dataset and the variables involved. In this case, the variables are the age of the child and their vocabulary size. The new data point to be added is (6 years, 900 words). Step 3: Consider how the new data point fits into the existing trend. If the new data point aligns well with the existing linear relationship, it will strengthen the correlation coefficient. If it deviates significantly from the trend, it may weaken the correlation coefficient. Step 4: Recalculate the correlation coefficient after adding the new data point. Use the formula for the correlation coefficient: r=&#x2211;(x-x_{mean})(y-y_{mean})&#x2211;(x-x_{mean})2&#x2211;(y-y_{mean})2. This involves recalculating the mean and standard deviation for both variables and determining the covariance. Step 5: Analyze the impact of the new data point on the correlation coefficient. Compare the recalculated value of r with the original value. If the new data point is consistent with the existing trend, r will likely increase or remain stable. If it deviates, r may decrease.

In Exercise 23, add data for a child who is 6 years old and has a vocabulary of 900 words. Describe how this affects the correlation coefficient r.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Correlation Coefficient (r)

Impact of Outliers

Linear Relationship