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The image provided shows a regression analysis relating cola consumption per week and bone density in women, with some questions about interpreting the slope and intercept of the regression line.

### Key Equation
The regression equation provided in the image is:

\[
\hat{y} = -0.0244x + 0.9003
\]

Where:
- \( \hat{y} \) is the predicted bone mineral density (in g/cm³),
- \( x \) is the number of colas consumed per week.

### (b) Interpreting the Slope
The slope of the equation is \(-0.0244\). This means that for every additional cola consumed per week, the bone mineral density decreases by \( 0.0244 \, \text{g/cm}^3 \), on average.

In the image, option A is selected, and it correctly interprets the slope.

### (e) Interpreting the Intercept
The intercept of the equation is \(0.9003\). This represents the predicted bone mineral density when 0 colas are consumed per week. It means that if a woman consumes 0 colas in a week, the model predicts her bone density to be \(0.9003 \, \text{g/cm}^3\).

In this case, option C seems to be the correct choice, stating: "For 0 colas consumed in a week, the bone density is predicted to be **0.9003 g/cm³**."

Would you like further details or help on interpreting the results? Here are some questions that can expand on this content:

1. How does the slope impact predictions for higher levels of cola consumption?
2. What does it mean if the slope was positive instead of negative?
3. How would predictions change if the intercept was lower than 0.9003?
4. How could you interpret the goodness-of-fit of this regression model?
5. How could you explain this data in terms of health recommendations?

### Tip:
Interpreting the slope in linear regression models gives insight into the direction and magnitude of the relationship between the two variables.

Researchers wanted to know whether cola consumption is associated with lower bone mineral density in women. The accompanying data lists the typical number of cans of cola consumed in a week and the femoral neck bone mineral density for a sample of 15 women. Interpret the slope and intercept of the regression equation.

Learn how cola consumption impacts bone mineral density in women using linear regression analysis. This problem involves interpreting the slope (-0.0244) and intercept (0.9003) of the regression equation: ŷ = -0.0244x + 0.9003. Suitable for college-level statistics students.

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