1. If Data A has a correlation coefficient of r = -.991, and Data B has a correlation coefficient of r = .991, which interpretation is correct?
a. Data A and Data B have the same strength in linear correlation.
b. Data A has a weaker linear correlation than Data B.
c. Data A has a stronger linear correlation than Data B.
2. A limitation of using trend lines in prediction is that
a. the x values may not be constant.
b. the predictions are not valid for values outside the original domain of x values.
c. the correlation may need to be recalculated.
d. the relationship may be a spurious correlation.
1. a
2. From Internet:
Trendlines have limitations shared by all charting tools in that they have to be readjusted as more price data comes in. A trendline will sometimes last for a long time, but eventually the price action will deviate enough that it needs to be updated.
would #2 be C?
1. To determine which interpretation is correct, you need to understand what the correlation coefficient represents. The correlation coefficient, denoted as "r", measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.
In this case, Data A has a correlation coefficient of r = -0.991, while Data B has a correlation coefficient of r = 0.991. Since they both have values close to -1 and +1 respectively, they are both indicating a strong linear correlation.
However, the sign of the correlation coefficient indicates the direction of the relationship. A negative value indicates a negative relationship, where one variable increases while the other decreases. A positive value indicates a positive relationship, where both variables tend to increase or decrease together.
In this case, since Data A has a negative correlation coefficient, it means that as one variable increases, the other variable tends to decrease. On the other hand, Data B has a positive correlation coefficient, indicating that as one variable increases, so does the other.
Therefore, the correct interpretation is:
b. Data A has a weaker linear correlation than Data B.
2. A limitation of using trend lines in prediction is that b. the predictions are not valid for values outside the original domain of x values.
When you create a trend line to fit a set of data points, it represents the best straight-line approximation of the relationship between the variables. However, it is important to note that the trend line is only valid within the range of x values used to calculate it. Extrapolating the trend line beyond the range of observed data can introduce higher uncertainty and potential errors.
Predicting values outside the original range of x values based on the trend line is less reliable because it assumes that the same linear relationship continues beyond the known data points. In reality, the relationship between variables may change or become less predictable outside the observed range. Therefore, it is crucial to exercise caution when making predictions using trend lines beyond the original domain of x values.