With a small sample, a single point can have a large effect on the magnitude of the correlation. To create the following data, we started with the scores from problem 8 and changed the first X value from X = 1 to X = 6.
a. Sketch a scatter plot and estimate the value of the Pearson correlation.
b. Compute the Pearson correlation.
To Construct: A scatter plot.
To determine: The estimated value of the Pearson correlation.
Output using the SPSS software is given below:
The estimated value of the Pearson correlation is around 0.25 to 0.30.
The scores of X and Y.
Step-by-step procedure to obtain the scatter plot using the SPSS software:
The scatter plot shows points clustered around a line sloping up to the right.
Thus, the estimated value of the Pearson correlation, just by looking at the scatter plot, is around 0.25 to 0.30.
To Calculate: The value of Pearson correlation.
The Pearson correlation is 0.277.
The Pearson correlation (r) is calculated as:
Here SP is calculated as:
Squared deviations SSx and SSy are calculated as:
The below table showing the calculations required for calculating correlation:
So the sum of product of deviation (SP) is 5, SSx is 18 and SSy is 18, substitute these values in Pearson correlation formula then:
Thus, the Pearson correlation is 0.277.
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