Questions: QUESTION 14 - 1 POINT Norville collected the data below about the length of the femur and their height both in centimeters for 10 different adults. Use this information to determine the correlation coefficient, round to 4 decimals. femur length: 47.18, 47.88, 35.56, 35.99, 37.75, 43.03, 41.45, 44.95, 38.19, 37.61 height: 160, 186, 190, 165, 163, 157, 161, 154, 185, 163 Provide your answer below: r=

Solution Steps

To determine the correlation coefficient between the femur length and height, we will use the Pearson correlation formula. This involves calculating the covariance of the two variables and dividing it by the product of their standard deviations. The correlation coefficient will give us an indication of the strength and direction of the linear relationship between the two variables.

To find the correlation coefficient, we first calculate the mean of the femur lengths and the heights. The mean is given by:

\[ \bar{x} = \frac{\sum x_i}{n} \]

where \( x_i \) are the individual data points and \( n \) is the number of data points.

The covariance between the femur length and height is calculated using:

\[ \text{Cov}(X, Y) = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n} \]

where \( x_i \) and \( y_i \) are the individual data points for femur length and height, respectively.

The standard deviation for each dataset is calculated as:

\[ \sigma_x = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}} \]

\[ \sigma_y = \sqrt{\frac{\sum (y_i - \bar{y})^2}{n}} \]

The correlation coefficient \( r \) is calculated using the formula:

\[ r = \frac{\text{Cov}(X, Y)}{\sigma_x \sigma_y} \]

Final Answer