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Find the correlation coefficient of the following linear equation using technology (such as GeoGebra). For your r-value, use the first two decimal places.

y=43x−4

(1 point)
Responses

0.90
0.90

−0.99
negative 0.99

2.66
2.66

1.00

1 answer

To find the correlation coefficient \( r \) for the linear equation \( y = 43x - 4 \), we can analyze the characteristics of the equation.

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. For a linear equation of the form \( y = mx + b \), where \( m \) is the slope, the correlation coefficient \( r \) can be interpreted as follows:

  1. If the slope \( m \) is positive (which it is, since 43 is positive), \( r \) will be close to 1.
  2. If the slope \( m \) is negative, \( r \) will be close to -1.
  3. A slope of 0 indicates no correlation, hence \( r \) would be 0.

In the equation you provided:

  • Slope \( m = 43 \) (positive), which indicates a strong positive linear relationship.

Therefore, the correlation coefficient \( r \) would be 1, representing a perfect positive correlation.

Based on your options, the correct response would be:

1.00