QuestionWhy is the correlation coefficient called linear? Choose the correct answer: A, B, C, or D.
Studdy Solution
STEP 1
Assumptions1. The linear correlation coefficient is denoted by .
. We need to understand why this correlation coefficient is referred to as being linear.
3. We have four possible answers to choose from.
STEP 2
Let's analyze each of the options given.
Option A The term linear refers to a straight line that passes through the average values of the paired data, and measures how well a scatterplot fits a straight-line pattern.
Option B The term linear refers to the straight line that passes through the greatest number of points, and measures the fraction of the points the line passes through.
Option C The term linear refers to a straight line, and measures how well a scatterplot fits a straight-line pattern.
Option D The term linear refers to a straight line, and measures the fraction of the points the best line passes through.
STEP 3
We need to understand what a linear correlation coefficient is. The linear correlation coefficient, or Pearson's correlation coefficient, is a measure that determines the strength and direction of the linear relationship between two variables. This coefficient is represented by the symbol .
STEP 4
The term linear in the linear correlation coefficient refers to the fact that measures how well the data fits a straight-line pattern. This is because the correlation coefficient is used in linear regression, which is a statistical method for predicting the value of one variable based on the value of another, assuming a linear relationship.
STEP 5
The correlation coefficient does not measure the fraction of points that a line passes through, but rather how well the data points fit a straight line. Therefore, options B and D can be eliminated.
STEP 6
Between options A and C, option A adds that the straight line passes through the average values of the paired data. However, this is not necessarily true for the line of best fit in a scatterplot, which is determined by minimizing the sum of the squares of the vertical distances of the points from the line, not by passing through the average values of the paired data.
STEP 7
Therefore, the correct answer is option C The term linear refers to a straight line, and measures how well a scatterplot fits a straight-line pattern.
The correct answer is C.
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