Math Problem Statement

Выборочное уравнение прямой линии регрессии X на Y имеет вид x = -4,72 + 2,36y. Тогда выборочный коэффициент корреляции может быть равен...

Solution

The provided text translates to:

"The sample regression equation of the straight line XX on YY is given as:
x=4.72+2.36yx = -4.72 + 2.36y
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 xx based on yy, where the slope of the line is 2.362.36. However, correlation coefficients also depend on the standard deviations of xx and yy, and the slope alone cannot directly determine the correlation coefficient unless additional information (like variances of xx and yy) 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 xx and yy.

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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)