Math Problem Statement
Solution
The provided text translates to:
"The sample regression equation of the straight line on is given as:
Then the sample correlation coefficient may be equal to..."
This problem relates to the interpretation of the regression equation and the calculation of the correlation coefficient.
The regression equation here is for predicting based on , where the slope of the line is . However, correlation coefficients also depend on the standard deviations of and , and the slope alone cannot directly determine the correlation coefficient unless additional information (like variances of and ) is provided.
If you need help calculating or reasoning further, please provide options for the correlation coefficient or additional data, such as the standard deviations of and .
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Math Problem Analysis
Mathematical Concepts
Regression Analysis
Correlation Coefficient
Linear Regression
Formulas
Regression equation: x = a + by
Correlation coefficient formula: r = b * (σ_y / σ_x)
Theorems
Properties of Linear Regression
Relationship Between Slope and Correlation
Suitable Grade Level
Undergraduate Level (Statistics)
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