Question: MULTIPLE CHOICE QUESTIONS

1. Circle all that apply. In class we discussed the implications of multicollinearity. If multicollinearity is present, then we can typically conclude that

1. the fitted regression model is not useful at predicting the response.
2. the fitted regression model may result in estimated slopes very different from what we should expect based on the relationship seen in the scatterplot. Thus the correct interpretation of the effect on the response becomes more difficult.
3. the fitted regression model contains redundant information.
4. the fitted regression model will have a very low $R^{2}$ value.
5. the fitted regression model will have a significant interaction term between the variables that are related.
6. None of the above. Provide at least two implications of multicollinearity in the space given below.

(b) Circle all that apply. In a study of the relationship between intelligence and achievement, scores on the Dorge- Thorndike Intelligence Test and the Stanford Achievement Test are collected from a large group of students. A score on each test is obtained for all students. An appropriate statistical analysis is:

1. correlation coefficient
2. a matched pairs t-test
3. simple linear regression
4. descriptive analysis
5. a two-sample independent t-test
6. Analysis of Variance
7. None of the above, a more sophisticated statistical analysis is needed.

(c) Circle one. Which of the following statements is not an assumption for ANOVA and Regression Analysis?

1. Across all values of \(x\), the residuals have the same variance.
2. The residuals are independent.
3. The residuals follow a Normal distribution.
4. The residuals alternate between positive and negative values as a function of the explanatory variable.
5. None of the above, all are necessary assumptions.

(d) Circle all that apply. As a combination, the two best plots to assess the assumptions of an ANOVA model or a simple linear regression model are:

1. A Normal Quantile Plot of the residuals and a histogram of the residuals.
2. A Normal Quantile Plot of the response values and a scatterplot of the response values against the explanatory variable \(x\).
3. A Normal Quantile Plot of the residuals and a scatterplot of the response values against the explanatory variable \(x\).
4. A Normal Quantile Plot of the residuals and a scatterplot of the response values against the fitted values.
5. None of the above. The two best plots are

(e) Match. Match the measures of variability with the correct sum squares.

1. Groups Sum of Squares
2. Error Sum of Squares
3. Total Sum of Squares

1. Variability of observations about the overall/grand mean:
2. Variability of group means about the overall/grand mean:
3. Variability of the observations about the group means:

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