Final answer:
The correct residual plot should accurately reflect data points and their residuals. An outlier with a large residual can significantly impact the best-fit line, affecting the interpretation of the relationship between the variables. Scatter plots, linear relationships, and statistical significance testing are all important aspects when analyzing data for linear regression.
Step-by-step explanation:
The correct residual plot for the given situation would be the one that shows data points and their residuals relative to a fitted regression line. Residuals are the differences between observed values and predicted values from a regression model. In the mentioned scenario, looking for residuals greater than 32.8 or less than -32.8, we identify an outlier with a residual of 35. This outlier, a student with a grade of 65 on the third exam and 175 on the final exam, can have a significant impact on the best-fit line. Outliers can skew the regression line, potentially affecting the relationship's interpretation between variables.
Effects of Outliers on Linear Regression
When considering whether the X and Y variables in a scatter plot are good candidates for linear regression, it is essential to identify any patterns that suggest a linear relationship. Scatter plots with a random distribution of points indicate weak or no correlation, while a clear trend suggests a potential for linear regression analysis. The slope of the regression line indicates the change in the Y variable given a one-unit change in the X variable, and the y-intercept is the predicted value of Y when X is zero.
Larger residuals indicate points that are further away from the predictive line and can be considered as outliers or influential points. An influential point is an outlier that can change the slope significantly. To assess the fit of a regression model, one would look at the residual plot and other statistical measures like R-squared values.
Furthermore, the presence of a strong linear relationship between variables can often be determined through statistical significance testing, such as a hypothesis test with a significance level (e.g., 0.05).
The complete question is:Which of the following is the correct residual plot for the given situation? is: