The Sum of Squares of Residuals (SSR), also known as the residual sum of squares (RSS), is a statistical measure used in regression analysis. Let's evaluate each statement:

1. Will increase if you increase the number of observations: True. Generally, as you add more data points, the SSR is likely to increase because there are more residuals (differences between observed and predicted values) contributing to the total sum.

2. Is a measure of the variation in $Y$ that our model fails to explain: True. SSR quantifies the unexplained variation in the dependent variable $Y$ after fitting the model.

3. Is our preferred measure of goodness of fit: False. The preferred measure of goodness of fit is typically the coefficient of determination, $R^2$, which represents the proportion of the variance in the dependent variable that is predictable from the independent variables.

Given these evaluations, the correct answer is:

(a) and (b) are true, but (c) is false.

This is because both statements (a) and (b) correctly describe the properties of SSR, whereas (c) is incorrect since SSR is not the preferred measure of goodness of fit.

Would you like more details on any of these points or have any additional questions? Here are some related questions that might interest you:

1. What is the relationship between SSR and $R^2$ in regression analysis?
2. How is the SSR calculated in a regression model?
3. What are other common measures of goodness of fit besides $R^2$?
4. How does the addition of variables to a model affect SSR?
5. Can SSR ever decrease with the addition of more observations?
6. How does SSR relate to the Total Sum of Squares (TSS) and the Explained Sum of Squares (ESS)?
7. What are the implications of a high SSR in a regression model?
8. How can you interpret the residuals in a regression model?

Tip: Always plot the residuals after fitting a regression model to visually assess the fit and identify any potential patterns that might indicate model inadequacies.