In this table, we have the residuals from a regression of Price on Capacity for hard drive data. Here's how we can approach each part of the question:

a) Which drive capacity contributes the most to the sum of squared residuals?

To find this, we need to square the residuals for each capacity and see which has the largest value.

1. Square each residual:
   • $3.28^2 = 10.7584$
   • $3.74^2 = 13.9876$
   • $4.58^2 = 20.9764$
   • $14.26^2 = 203.5076$
   • $(-15.67)^2 = 245.7489$
   • $(-15.86)^2 = 251.5396$
   • $5.67^2 = 32.1489$

The largest squared residual is 251.5396, which corresponds to a capacity of 4.0 TB.

b) What does it mean that two of the residuals are negative?

Residuals represent the difference between the observed and predicted values. A negative residual means that the observed price for that drive was lower than the predicted price by the regression model.

Specifically:

• For the drive with a capacity of 2.0 TB, the price was $15.67 less than predicted.
• For the drive with a capacity of 4.0 TB, the price was $15.86 less than predicted.

This suggests that the model overestimated the price for these drives, as their actual prices were lower than expected.

Let me know if you need more details or have any further questions!

5 Questions to expand your understanding:

1. What is the importance of minimizing the sum of squared residuals in regression analysis?
2. How do positive and negative residuals affect the interpretation of a regression model's predictions?
3. What are some potential causes of high residuals in a regression analysis?
4. Why is squaring residuals a common practice in regression analysis?
5. How can outliers (like large residuals) impact the overall accuracy of a regression model?

Tip:

Always check for outliers when analyzing residuals. Large residuals may indicate that the regression model isn't a good fit for certain data points.