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    Determining Sample Correlation Coefficients

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    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.

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    https://brainmass.com/statistics/correlation/determining-sample-correlation-coefficients-535715

    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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