Explanation of Unsuitability: Sweet treat and linear regression question

Question 1

Nominal Predictor Variable: Unsuitability

Answer 1

Sweet treat choice is a categorical variable with unordered categories (chocolate, mints, dried fruits, chewing gum). Linear regression assumes that the predictor variable is continuous or ordinal. Treating categorical variables as continuous can lead to misinterpretation of results.

Question 2

Limited Predictive Power: Unsuitability

Answer 2

Sweet treat choice alone may not sufficiently capture the variability in agreeableness. Personality traits are complex constructs influenced by various factors beyond simple preferences for sweet treats. Linear regression may not adequately account for these nuanced relationships

Question 3

Violation of Linearity Assumption: Unsuitability

Answer 3

Linear regression assumes a linear relationship between the predictor and outcome variables. However, the relationship between sweet treat choice and agreeableness may not be linear. For example, the effect of switching from one sweet treat to another may not be consistent across all levels of agreeableness.

Question 4

Measurement of Sweet Treat Preference: Redesign

Answer 4

Instead of categorical choices (e.g., chocolate, mints), participants could rate their preference for each sweet treat on a continuous scale (e.g., Likert scale from 1 to 5).v

Question 5

Multiple Predictor Variables: Redesign

Answer 5

Include additional predictor variables that may influence agreeableness, such as age, gender, socioeconomic status, or dietary habits. These variables should be continuous or ordinal to meet the assumptions of linear regression.

Question 6

Large Sample Size: Redesign

Answer 6

Ensure a sufficiently large sample size to improve the robustness of the linear regression analysis and increase statistical power.

Question 7

Assumption Checking: Redesign

Answer 7

Assess the assumptions of linear regression, including linearity, independence of errors, homoscedasticity, and normality of residuals, to ensure the validity of the analysis.

Question 8

Linearity: Assumption

Answer 8

Assumption: The relationship between the predictor variables and the outcome variable is linear. This means that the change in the outcome variable associated with a one-unit change in the predictor variable is constant.

Example: In a study examining the relationship between study hours and exam scores, linearity assumes that for every additional hour of study, the increase in exam score remains consistent. A scatterplot of study hours (predictor) against exam scores (outcome) should show a linear pattern, where the points roughly form a straight line.

Question 9

Independence of Errors: Assumption

Answer 9

Assumption: The errors (residuals) of the regression model are independent of each other. This means that the error in predicting one observation does not depend on the error in predicting another observation.

Example: In a longitudinal study tracking individuals’ income over time, the errors in predicting income at one time point should not be correlated with errors at another time point. Autocorrelation in residuals indicates a violation of this assumption, suggesting that the model does not adequately capture temporal dependencies.

Question 10

Homoscedasticity: Assumption

Answer 10

Assumption: The variance of the errors (residuals) is constant across all levels of the predictor variables. In other words, the spread of residuals should be consistent across the range of predicted values.

Example: Consider a regression model predicting housing prices based on square footage. Homoscedasticity requires that the variability in the differences between observed and predicted housing prices remains constant regardless of the square footage. A scatterplot of residuals against predicted values should show a uniform spread of points around zero, without any systematic patterns.

Question 11

Normality of Residuals: Assumption

Answer 11

Assumption: The residuals of the regression model are normally distributed. This means that the distribution of residuals follows a bell-shaped curve.

Example: In a study examining the relationship between age and blood pressure, the normality of residuals assumes that the distribution of errors in predicting blood pressure is approximately normal. A histogram or Q-Q plot of residuals should resemble a bell-shaped curve. Deviations from normality may indicate that the model’s predictions are systematically biased in certain ranges of the predictor variable.