Final answer:
The expected scenario when a regression line is appropriately fitted is a residual plot showing no pattern, which indicates that a linear model is suitable for the data, and an r value close to 1 or -1, showing a strong linear relationship. The slope indicates the rate of change, while the y-intercept represents the value when the independent variable is zero.
Step-by-step explanation:
When a scientist says that fitting a regression line to her research was appropriate, you expect that the residual plot of the regression shows no pattern (option a) because this is an indication that a linear model is suitable for the data. A residual plot with no pattern suggests that the variability of the actual data around the regression line is random, which is a good indication that the linear model is a good fit for the data. Additionally, the value of r for her data set would likely be very close to 1 or -1 (option c), suggesting a strong linear relationship.
The slope of the regression line tells us the rate of change of the dependent variable for every one-unit change in the independent variable. On the other hand, the y-intercept of the regression line is the expected value of the dependent variable when the independent variable is zero. Both give us crucial information about the relationship between the two variables. In terms of how well the regression line fits the data, we look at the coefficient of determination, usually denoted as r2, which tells us the proportion of the variance in the dependent variable that is predictable from the independent variable. A higher r2 value indicates a better fit.