Cola Consumption vs. Bone Density Example 5 in Section 4.1 discussed the effect of cola consumption on bone mineral density in the femoral neck of women.
b. Explain the meaning of the slope.

Verified step by step guidance

1. Identify the variables involved: the independent variable is cola consumption, and the dependent variable is bone mineral density in the femoral neck of women.
2. Recall that in a linear regression model, the slope represents the average change in the dependent variable for each one-unit increase in the independent variable.
3. Express the slope interpretation in context: it tells us how much the bone mineral density is expected to increase or decrease when cola consumption increases by one unit (e.g., one serving or one can).
4. Note the sign of the slope: if the slope is negative, it indicates that higher cola consumption is associated with lower bone density; if positive, it indicates the opposite.
5. Summarize the meaning of the slope as the estimated change in bone mineral density per unit increase in cola consumption, holding other factors constant.

Key Concepts

Slope in Linear Regression

The slope represents the rate of change in the dependent variable for each one-unit increase in the independent variable. In this context, it shows how bone mineral density changes with each additional unit of cola consumption.

Interpretation of Regression Coefficients

Regression coefficients quantify the relationship between variables. The slope coefficient specifically indicates the direction (positive or negative) and strength of the association between cola consumption and bone density.

Contextual Meaning of Variables

Understanding the real-world meaning of variables is crucial. Here, cola consumption is the predictor, and bone mineral density is the outcome; interpreting the slope requires linking statistical results to biological or health implications.