Final answer:
The type of correlation between two variables in a scatterplot is determined by the data patterns and the correlation coefficient (r). Positive correlation is shown when both variables move in the same direction, negative correlation when they move in opposite directions, and zero correlation when no relationship exists between them.
Step-by-step explanation:
To determine the type of correlation shown between two variables in a scatterplot, we look at the pattern of the data points and the sign of the correlation coefficient (r). There are three main types of correlations:
- Positive correlation: indicated by 0 < r < 1, where as one variable increases, the other does as well.
- Negative correlation: indicated by -1 < r < 0, where as one variable increases, the other decreases.
- Zero correlation: indicated by r = 0, where there is no apparent relationship between the variables.
To conclude whether the X and Y variables are good candidates for linear regression, we observe the scatter plot. If the points form a clear linear pattern (either upward or downward), and the correlation coefficient is close to 1 or -1, a linear model is likely appropriate. However, if the scatter plot reveals a different pattern, such as a curve, other models might be more suitable.
An example of positive correlation is illustrated by the duration of steam eruptions from the Old Faithful geyser and the time between these eruptions, depicted by a scatter plot with a blue dotted line representing the upward trend.