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Determining Sample Correlation Coefficients

1. The following statistics were calculated from pairs of observations where X represents the independent variable and Y represents the dependent variable.

Σx = 511 Σy = 314 Σxy = 19,064
Σx^2 = 34,234.5 Σy^2 = 13,036 n = 8

Determine the least squares line.
Determine the sample correlation coefficient between X and Y.
Determine if there is a linear relationship between X and Y at the .10 significance level.
Find a 90% confidence interval for the slope of the regression line.
Find a 90% confidence interval for the mean of Y if X = 60.
Find a 90% prediction interval for Y if X = 60.

Solution Preview

1. The following statistics were calculated from pairs of observations where X represents the independent variable and Y represents the dependent variable.

Σx = 511 Σy = 314 Σxy = 19,064
Σx^2 = 34,234.5 Σy^2 = 13,036 n = 8

a. Determine the least squares line.

Assume the equation of line is y=mx+b

m=(8*19064-511*314)/(8*34234.5-511^2)= -0.62266

b=(314+0.62266*511)/8=79.022
Therefore, the line of equation is: y=-0.62266x+79.022

b. Determine the sample correlation coefficient between X and Y.

R=(8*19064-511*314)/sqrt((8*34234.5-511^2)*(8*13036-314^2))= -0.932

c. Determine if ...

Solution Summary

The expert determines the sample correlation coefficients. The linear relationship between X and Y at the 01 significance level is provided.

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