Find the correlation between the sample means and the contrast coefficients for the cubic trend for these data.

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This problem uses the same data as In particular, n = 10 for each of four groups, with sample means of 10,20, 30, and 40, respectively. We stated in Chapter 4 that alerting is equivalent to the squared correlation between the contrast coefficients and the actual sample means of the groups. Further, the sum of squares for a contrast equals the product of me between-group sum of squares a. Find the correlation between the sample means and the contrast coefficients for the linear trend for these data. What does this tell you about how much of the between-group sum of squares is attributable to the linear trend for these data? b. Find the correlation between the sample means and the contrast coefficients for the quadratic trend for these data. What does this tell you about how much of the between-group sum of squares is attributable to the quadratic trend for these data? c. Find the correlation between the sample means and the contrast coefficients for the cubic trend for these data. What does this tell you about how much of the between-group sum of squares is attributable to the cubic trend for these data?

 

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