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Jan 9, 2024

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1. Research Question: The research question in this multiple regression analysis appears to be examining the relationship between the variables "HIGHEST YEAR OF SCHOOL COMPLETED" and "AGE OF RESPONDENT" as predictors and the dependent variable "R FEELS DISCRIMINATED BECAUSE OF RACE." The objective is to determine whether these predictor variables significantly influence the feeling of discrimination based on race. 2. Interpretation of Coefficients: a) Constant (Intercept): The intercept represents the estimated mean value of the dependent variable ("R FEELS DISCRIMINATED BECAUSE OF RACE") when all predictor variables are set to zero. In this case, the constant is 1.864. However, since this variable seems binary or categorical (possibly a dummy variable), the interpretation should be cautious and may need to be more straightforward. b) AGE OF RESPONDENT: The coefficient for this variable is 0.000, with a p-value of 0.831, indicating that it is not statistically significant. Therefore, no evidence suggests that the respondent’s age significantly impacts the feeling of discrimination based on race. c) HIGHEST YEAR OF SCHOOL COMPLETED: The coefficient for this variable is 0.006, with a p-value of 0.134. Although it does not reach conventional significance levels (p < 0.05), it is worth noting that the p-value is relatively close to the threshold. This suggests that there might be a weak association between the highest year of school completed and the feeling of discrimination based on race. Still, more data or a larger sample might be required to establish a more robust relationship. 3. Assumptions and Diagnostics: To assess the assumptions of multiple regression, several critical diagnostics need to be checked: a) Linearity: Assumption of a linear relationship between predictors and the dependent variable. You can examine scatterplots of the dependent variable against each predictor and check for any clear non-linear patterns. You can also use partial and residual regression plots to assess linearity further. b) Homoscedasticity: Residuals should have constant variance across all levels of predictors. You can plot the standardized residuals against predicted values and check for any "funnel" shape or patterns. c) Independence of Residuals: The residuals should be independent. The dataset should not exhibit any patterns or autocorrelation in the residuals. d) Normality of Residuals: The residuals should be approximately normally distributed. You can use histograms or Q-Q plots to assess the normality visually. If any of the assumptions are violated, it might impact the validity of the results. Based on the output provided, the assumption of normality of residuals is broken, as the R-squared value is

deficient (0.007), indicating that the model explains very little of the variance in the dependent variable. There might be other unaccounted factors influencing the feeling of discrimination. A possible remedy for the assumption violation could be transforming the dependent variable or one of the predictors to better approximate normality. Alternatively, considering interactions between variables or adding additional relevant predictors may improve the model's fit and address some of the assumptions' violations. However, these remedies should be carefully considered and guided by the study's research question and theoretical underpinnings. Additionally, more data or a larger sample size might be needed to obtain a more reliable model.

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