Use Jasp For This Assignment: Use Average Grade 8 Math Profi

Use Jasp For This Assignmentuse Average Grade 8 Math Proficiency As T

Use JASP for this assignment. Use Average Grade 8 Math Proficiency as the dependent variable. Use Enrollment, Average Grade 8 English Proficiency, and Rigorous Instruction Rating as independent variables. Run a multiple regression test, addressing categorical variable dummy coding, and test for interaction effects between Enrollment and Average Grade 8 English Proficiency by additionally including the interaction term in the analysis. Interpret R, Adjusted R squared, Significance in the ANOVA table, and Significance values in the Coefficient tables. Determine if an interaction effect between Enrollment and Average Grade 8 English Proficiency is detected and explain. Conduct an assumptions check, including all relevant charts and tables, and report the results of each: Independence (Durbin-Watson between 1 and 3), Multicollinearity (VIF less than 10), Linearity (predicted vs residual plot), Homogeneity of variance (residual plot), and Normality (histogram and QQ plot). Based on the evidence, report which assumptions are likely violated or not violated.

Paper For Above instruction

The analysis aims to evaluate the relationship between eighth-grade mathematics proficiency and several explanatory variables, including enrollment, English proficiency, and instructional rigor, using multiple linear regression in JASP. The core objective encompasses assessing the significance and strength of predictors, exploring potential interaction effects, and evaluating the assumptions underlying regression analysis to ensure valid inferences.

Initially, the dependent variable, Average Grade 8 Math Proficiency, is modeled as a function of the three independent variables: Enrollment (a continuous variable), Average Grade 8 English Proficiency (a continuous variable), and Rigorous Instruction Rating (a continuous variable). Given Enrollment is a categorical variable, dummy coding is essential; however, if Enrollment is already in a numerical format, this step may not be necessary. The regression model estimates the extent to which these variables predict math proficiency, with particular interest in the interaction term between Enrollment and English Proficiency, to determine if the relationship between English proficiency and math proficiency varies across levels of Enrollment.

The regression analysis in JASP yields several key statistics. The correlation coefficient (R) indicates the strength of the relationship between the predicted and actual values of math proficiency. An R value closer to 1 suggests a strong model fit, while the Adjusted R squared reflects the proportion of variance in the dependent variable explained by the model, accounting for the number of predictors. The ANOVA table provides the significance of the overall model fit, and the coefficient table reveals the significance of individual predictors, including the interaction term.

The findings reveal whether the interaction between Enrollment and English Proficiency is statistically significant. A significant interaction implies that the effect of English proficiency on math proficiency differs across levels of enrollment, suggesting the relationship is moderated by enrollment status. Visual inspection of scatterplots and interaction plots can help interpret this moderation effect.

To ensure the robustness of the regression model, assumptions are checked meticulously. The independence assumption is examined via the Durbin-Watson statistic; values between 1 and 3 are acceptable, indicating no serious autocorrelation in residuals. Multicollinearity is assessed through Variance Inflation Factors (VIF); values below 10 suggest predictors are not highly correlated, avoiding instability in coefficient estimates. Linearity is checked by plotting predicted values against residuals; the absence of distinct patterns suggests linear relationships hold. Homoscedasticity (constant variance of residuals) is visually inspected through residual plots, looking for a uniform spread. The normality assumption is evaluated via the histogram and QQ plot of residuals; approximate normal distribution signifies no serious violations.

Based on the evidence, if the Durbin-Watson value is within the acceptable range, multicollinearity VIFs are below 10, linearity and homoscedasticity plots show no concerning patterns, and residuals approximate normality, the assumptions are deemed not violated. Conversely, deviations such as a Durbin-Watson near 0 or 4, VIFs exceeding 10, patterns in residual plots, or skewed residual distributions indicate potential violations, warranting further data transformations or alternative modeling approaches.

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