Question
Which of the following statements about correlation are true? Check all that apply. If the correlation between two variables is -1, it indicates a perfect
Which of the following statements about correlation are true?Check all that apply.
If the correlation between two variables is -1, it indicates a perfect negative linear relationship between the two variables.
A positive correlation means that two variables tend to change in opposite directions.
Correlation measures and describes the behavior of a single variable.
Correlation is a numerical value between 1.1 and 2.
The correlation is scaleless; that is, it doesn't change when the measurement units are changed for either or both of the variables.
The sign of the correlation indicates the strength or consistency of the linear relationship between two variables.
The sign of the correlation indicates the direction of the relationship between two variables.
2. Scatter plots and calculating correlation
Suppose you are given the following five pairs of scores:
X | Y |
---|---|
8 | 1 |
7 | 2 |
6 | 3 |
9 | 4 |
0 | 10 |
Based on your scatter diagram, you would expect the correlation to be .
The mean x score is MXX=
, and the mean y score is MYY=
Now, using the values for the means that you just calculated, fill out the following table by calculating the deviations from the means for X and Y, the squares of the deviations, and the products of the deviations.
Scores | Deviations | Squared Deviations | Products | |||
---|---|---|---|---|---|---|
X | Y | X - MXX | Y - MYY | (X - MXX) | (Y - MYY) | (X - MXX)(Y - MYY) |
8 | 1 | |||||
7 | 2 | |||||
6 | 3 | |||||
9 | 4 | |||||
0 | 10 |
The sum of squares for x is SSxx=
. The sum of squares for y is SSyy=
. The sum of products is SP =
Because the sign of the sum of products is ? , the sign of the correlation coefficient ?
The correlation coefficient is r = ?
Look at your scatter diagram again. If you excluded the point (0, 10), you would expect the recalculated correlation coefficient to be ? , because ?
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