# 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.

Î£x = 511 Î£y = 314 Î£xy = 19,064

Î£x^2 = 34,234.5 Î£y^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.

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.

Î£x = 511 Î£y = 314 Î£xy = 19,064

Î£x^2 = 34,234.5 Î£y^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.