Final answer:
A residual plot helps assess the appropriateness of a linear model by showing the dispersion of residuals. The slope and y-intercept provide information about the average change in the dependent variable and its value when the independent variable is zero. Outliers can be identified by residuals that deviate significantly from the rest of the data.
Step-by-step explanation:
A residual plot is a graphical display used to assess whether the assumptions of linearity, equal spread, and normality are met for a linear regression model. If the residuals are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data. This means there is no apparent pattern in the residual plot, indicating that the linear model fits the data well. If there is a pattern in the residuals, this suggests that the model may not be the best fit, and a different model may be needed.
The slope in a regression line represents the average change in the dependent variable (y) for each unit change in the independent variable (x). The y-intercept is the predicted value of y when the independent variable (x) is zero. To determine how well the regression line fits the data, we look for a small number of residuals; the smaller the residuals, the better the fit. Additionally, we can look at the correlation coefficient (r) to judge the strength and direction of the linear relationship.
Regarding outliers and influential points, the point with the largest residual is the one farthest from the regression line. A large residual suggests the point does not fit well with the linear model; if it is also outside the overall pattern of the data, it may be considered an outlier or an influential point.
For the testing of the relationship between variables such as coffee consumption and heart disease death rate, a statistical test such as a t-test for the slope coefficient can be used to determine if there is a significant linear relationship. A p-value less than the significance level (such as 0.05) indicates that there is statistically significant evidence of a linear relationship.