3. Suppose you are hired to serve as a statistical consultant. In each of the following cases, what advice (if any) would you give to your client concerning the procedures and/or conclusions he or she has drawn, or about the kind of statistical techniques most suitable? Be sure to briefly explain the reasoning underlying your advice.

(a) A researcher studies the effects of education (High School or less, Some College, 4 Year College Degree, Graduate/Professional Degree) on income by randomly calling 5,000 participants in the United States. At a presentation of his results, several colleagues suggest that effects of education on income may not be robust when considering other predictors such as work experience, time with their current employer, age, and personal investments. What sort of analysis did the researcher conduct, and how can the researcher address these criticisms of his research?

The researcher might have conducted the multiple linear regression model in which he have included education, work experience, time with their current employer, age, and personal investments as the predictors. The researcher can address these criticisms of his research by checking the multicollinearity, if education is not correlated with any other predictor and there is a significant p-value of education in the model then we can say that there is an significant impact of education.
The researcher can also proceed with the ANOVA (analysis of variance) to access if there is a difference or not in High School or less, Some College, 4 Year College Degree and Graduate/Professional Degree for income.

(b) A researcher is interested in predicting the mental health of college students based on their reported level of stress. What kind of sample should she collect and what statistical technique should she use to achieve this goal?

Since the researcher is interested in predicting the mental health of college students, she should collect the sample which should be not biased. So she should conduct a survey in which she should prepare the valid questionnaire and enroll the subject randomly and then assess their level of stress and mental health based on the questions being asked in the questionnaires. She can select different colleges in different regions to avoid the biasedness in data.
If the variable â€œmental healthâ€ is being captured on binary scale (i.e. Stable=1 or Unstable=0) then logistic regression approach can be followed to achieve this goal and if the variable is being captured on continuous scale then we will proceed with linear regression.

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