Final answer:
To assess the results of a prediction using Pearson's r, you need the sample correlation coefficient r, the sample size n, and a scatter plot to confirm the strength and direction of linearity. The regression equation's slope, y-intercept, and the coefficient of determination r² are also essential to evaluate the model's predictive power.
Step-by-step explanation:
In order to assess the results of a prediction using Pearson's r, you would need the sample correlation coefficient r, which estimates the unknown population correlation coefficient. The correlation coefficient r reveals the strength and direction of the linear relationship between the independent variable x and the dependent variable y. Additionally, the sample size n and the scatter plot are crucial for analyzing the data's linear trend.
To evaluate the predictive capability of the correlation coefficient, you would also consider the slope and y-intercept of the regression equation. The coefficient of determination, r², also plays a vital role, as it quantifies the proportion of variability in y that is explained by x through the regression line. If the value of r is significant and the scatter plot displays a linear trend, the regression line can be used for prediction within the domain of observed x values. To assess the results of a prediction using Pearson's r, you would need to consider several key aspects. Firstly, examine the correlation coefficient (r) itself, which quantifies the strength and direction of the linear relationship between two variables. A value close to +1 indicates a strong positive correlation, while a value close to -1 suggests a strong negative correlation. Additionally, assess the p-value associated with the correlation, determining if the observed correlation is statistically significant. Lastly, scrutinize the scatterplot of the data points to visually inspect the fit of the linear model. These components collectively provide insights into the reliability and significance of the predictive relationship.