Math Problem Statement

If the linear correlation coefficient between the explanatory variable (x) and response variable (y) is r = 0.35, the slope of the regression line is 

negative

positive

not enough information to answer

Solution

The slope of the regression line has the same sign as the correlation coefficient rr. Since r=0.35r = 0.35 is a positive number, the slope of the regression line is positive.

Would you like further details on this topic or have any other questions?

Here are some related questions:

  1. What is the formula for calculating the slope of a regression line?
  2. How do we interpret the value of the correlation coefficient?
  3. Can a correlation coefficient of 0 imply a non-linear relationship?
  4. What is the significance of a positive or negative correlation?
  5. How is the coefficient of determination r2r^2 related to rr?

Tip: The closer the correlation coefficient rr is to 1 or -1, the stronger the linear relationship between xx and yy.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Linear Regression

Formulas

Slope of the regression line is b = r * (sy/sx)
Correlation coefficient (r) formula

Theorems

Linear regression model

Suitable Grade Level

Grades 10-12