# Calculation problem: Regression lines. Mens faces have higher width-to-height ratios than womens, on average. This turns out

## Question:

Calculation problem: Regression lines. Men’s faces have higher width-to-height ratios than women’s, on average. This turns out to reflect a difference in testosterone expression during puberty. Testosterone is also known to predict aggressive behavior. Does face shape predict aggression? To test this, Carré and McCormick (2008) compared the face width-to-height ratio of 21 university hockey players with the average number of penalty minutes awarded per game for aggressive infractions like fighting or cross-checking. Their data are below along with some partial calculations. We will calculate the equation for the line that best predicts penalty minutes from face width-to-height ratio.

**a. **Plot the data in a scatter plot.

**b. **Examine the graph. Based on this graph, do the assumptions of linear regression appear to be met?

**c. **Calculate the means of the two variables. (While you’re doing so, record the sum of all X-values and the sud. Calculate the sum of X^{2}, the sum of Y^{2}, and the sum of the product X Y .m of all Y-values.

**e. **Calculate the sum of products (Σ_{i}(X_{i}−x̄) (Y_{i}−Y̅)) and the sum of squares (Σ_{i}(X_{i}−x̄)^{2}) of the explanatory variable, face ratio.

**f. **How steeply does the number of penalty minutes increase per unit increase in face ratio? From the sum of products and sum of squares for face ratio, calculate the estimate b of the slope. Doublecheck that the sign of the slope matches your impression from the scatter plot.

**g. **Calculate the estimate of the intercept, a from the variable means and b.

**h. **Write the result in the form of an equation for the line. Add your line to the graph in (a).

## Step by Step Answer:

**Related Book For**

## The Analysis Of Biological Data

**ISBN:** 9781319226237

3rd Edition

**Authors:** Michael C. Whitlock, Dolph Schluter