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The coefficient of determination of a set of data points is 0.93 and the slope of the regression line is -5.26. Determine the linear correlation coefficient of the data.

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Answer:

- 0.964

Step-by-step explanation:

Given that Coefficient of determination (R^2) = 0.93

Slope of regression line = - 5.26

The linear correlation Coefficient =?

The Coefficient of determination (R^2) is used to obtain the proportion of explained variance of the regression line. It is the square of the linear correlation Coefficient (R).

Hence. To obtain the linear correlation Coefficient (R) from the Coefficient of determination (R^2); we take the square root of R^2

Therefore,

R = √R^2

R = √0.93

R = 0.9643650

R = 0.964

However, since the value of the slope is negative, this depicts a negative relationship between the variables, hence R will also be negative ;

Therefore, R = - 0.964

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The linear correlation coefficient of the data is: -0.96

Recall:

  • Coefficient of determination = R²
  • R represents the linear correlation coefficient.
  • A negative slope of regression line suggests relationship between variables will be negative, hence linear correlation coefficient will be negative.

Thus, given:

Coefficient of determination of a set of data points = 0.93

Slope of the regression line = -5.26

Therefore:

R² = 0.93

R = √0.93

R = 0.96

Since the slope the regression line is negative, R will be negative in this case.

  • Therefore, the linear correlation coefficient of the data is: -0.96

Learn more about linear correlation coefficient on:

https://brainly.com/question/9436626

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