Based on the given data, the following interpretations can be made:
- There is a positive correlation between progress in math and the number of books at home, although it is not statistically significant (p-value = 0.1756). The correlation coefficient is 0.93818, indicating a strong correlation.
- Family support has a significant negative correlation with progress in math (p-value = 0.003106). The correlation coefficient is -0.078, indicating a low negative correlation.
- Mother's education level has a negative correlation with progress in math, but it is not statistically significant (p-value = 0.5939). The correlation coefficient is -0.014, indicating a very low negative correlation.
- Father's education level has no significant correlation with progress in math (p-value = 0.024). The correlation coefficient is 0.059, which suggests there is no relation between the two variables.
- Socioeconomic status (SEST) has no significant correlation with progress in math (p-value = 0.1141). The correlation coefficient is 0.03, indicating a very low correlation.
Write conclusion:
- There is a positive correlation between progress in math and the number of books at home, although it is not statistically significant (p-value = 0.1756). The correlation coefficient is 0.93818, indicating a strong correlation.
- Family support has a significant negative correlation with progress in math (p-value = 0.003106). The correlation coefficient is -0.078, indicating a low negative correlation.
- Mother's education level has a negative correlation with progress in math, but it is not statistically significant (p-value = 0.5939). The correlation coefficient is -0.014, indicating a very low negative correlation.
- Father's education level has no significant correlation with progress in math (p-value = 0.024). The correlation coefficient is 0.059, which suggests there is no relation between the two variables.
- Socioeconomic status (SEST) has no significant correlation with progress in math (p-value = 0.1141). The correlation coefficient is 0.03, indicating a very low correlation.
The table presents the results of an ANOVA analysis that examines the correlation between five variables (books_cod, family_support, mother_education, father_education, and ses) and an outcome variable. The asterisks (*) by the p-values indicate the significance level of each variable.
According to the results, books_cod, family_support, and ses are statistically significant because their p-values are less than 0.05. This means that there is a statistically significant correlation between these variables and the outcome variable. Specifically, higher scores in family_support and ses are associated with higher scores in the outcome variable.
In contrast, mother_education and father_education are not statistically significant, meaning that they do not have a significant correlation with the outcome variable.
The table presents the results of a multiple linear regression analysis. The outcome variable is not explicitly stated. However, we can see information about the residuals, coefficients, and other statistics.
The residuals section shows the minimum, first quartile, median, third quartile, and maximum values of the residuals. Residuals are the differences between the predicted values and actual values of the outcome variable. From this section, we can see that the range of residuals is from -13.630 to 34.660.
The coefficients section shows the estimates, standard errors, t-values, and p-values for each of the predictor variables. The predictor variables are books_cod, family_support, mother_education, father_education, ses, and gender. The intercept is also included as a coefficient. The asterisks beside the p-values indicate the level of significance, with more asterisks indicating higher significance.
From this section, we can see that books_cod, family_support, and ses are statistically significant predictors in the model, with p-values less than 0.05. Mother_education, father_education, and gender are not statistically significant.
The last section shows the residual standard error, which is a measure of how far the actual values deviate from the predicted values. The multiple R-squared and adjusted R-squared values indicate the proportion of variation in the outcome variable that is explained by the model. The F-statistic and p-value provide information about the overall significance of the model.
In summary, the regression analysis suggests that books_cod, family_support, and ses are significant predictors, while mother_education, father_education, and gender are not significant predictors of the outcome variable. However, the model overall explains only a small portion of the variation in the outcome variable.
The table shows the results of a principal component analysis, which is a technique used to identify patterns in data and reduce the dimensionality of the dataset.
The importance of the components is presented in three measures: standard deviation, proportion of variance, and cumulative proportion.
The standard deviation of each component indicates the amount of variation in the data that is captured by that component. For example, PC1 has a standard deviation of 1.3579, which is higher than the other components. This suggests that PC1 captures more variation in the data than the other components.
The proportion of variance measures the relative importance of each component in explaining the overall variability of the data. For example, PC1 has a proportion of variance of 0.3688, which is the highest among all components. This means that PC1 explains 36.88% of the total variance in the data, while PC2 explains 20.5%, PC3 explains 19.25%, and so on.
The cumulative proportion shows the total amount of variance explained by each component, starting from the highest to the lowest. For example, the first component (PC1) explains 36.88% of the variance in the data, while the first two components (PC1 and PC2) explain 57.38%, and so on. The last component (PC5) captures the least amount of variation in the data.
In summary, the results suggest that PC1 is the most important component in capturing the variation in the data, followed by PC2 and PC3. The other components (PC4 and PC5) are less important in explaining the variability in the data.