Question

A botanist created a linear model to predict plant height from soil acidity (pH level) for a certain type of plant. The slope of the model was 2.5 centimeters per pH level, the standard deviation of the sample of plant heights was 4 centimeters, and the standard deviation of the soil acidity was 1 pH level. What is the value of the correlation coefficient?

Answer 1

Answer:

  0.625

Explanation:

The slope (m) of a linear regression line is ...

  $m=r_{xy}\cdot\dfrac{s_y}{s_x}$

Then we have ...

  $2.5=r_{xy}\cdot\dfrac{4}{1}\\\\\dfrac{2.5}{4}=r_{xy}=0.625$

The value of the correlation coefficient is 0.625.

Answer 2

Here, we are required to find the value of the correlation coefficient given the slope of the regression model and the standard deviation of the dependent and independent variables.

The value of the correlation coefficient is 0.625

and it is dimensionless.

The relationship between the slope of a regression model and the correlation coefficient is given by;

m = r (Sy/Sx)

where

• m= slope of the regression model = 2.5cm/pH.

• r = the correlation coefficient = ?

• Sy = The standard deviation of the dependent variable i.e Plant height = 4cm

• Sx = The standard deviation of the independent variable i.e soil acidity(pH level) = 1pH

Therefore;

2.5 = r × (4/1)

r = 2.5/4

r = 0.625

P.S: It is important to know that the correlation coefficient is a dimensionless parameter.

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