Suppose You Will Perform a Test to Determine Whether There $r$

question 42

Multiple Choice

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of $r$ given the number of pairs of data $n$ and the significance level $\alpha$ . $n = 14 , \alpha = 0.01$

• A) \(r = 0.661\)
• B) \(r = 0.684\)
• C) \(r = \pm 0.532\)
• D) \(r = \pm 0.661\)

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Definitions:

Coefficient of Correlation

A rephrased definition of the correlation coefficient, highlighting its role in measuring the degree of correlation between two variables.

Sum of Squares

A statistical measure that quantifies the total deviation of each data point from the mean, squared and summed up.

Regression Analysis

A statistical technique for estimating the relationships among variables, often used to predict the value of a dependent variable based on the value of one or more independent variables.

Error Variable

An error variable represents the difference between observed and predicted values in a model, reflecting the amount of inaccuracy in predictions.