# Find the Correlation Coefficient and Slope

A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Find the value of the linear correlation coefficient r. Find the value of the linear correlation coefficient r. Compare the computed linear correlation coefficient r to the critical value of r at the 5% significance level to determine whether there is a linear correlation between the two characteristics. Does the slope of the regression line appear to indicate that an increase in the average time spent in the lab each week may improve the course grade for the computer students?

Number of hours spent in lab Grade (percent)

10 96

11 51

16 62

9 58

7 89

15 81

16 46

10 51

https://brainmass.com/statistics/type-i-and-type-ii-errors/correlation-coefficient-slope-simple-regression-600397

#### Solution Preview

X Y XY X2 Y2

10 96 960 100 9216

11 51 561 121 2601

16 62 992 256 3844

9 58 522 81 3364

7 89 623 49 7921

15 81 1215 225 6561

16 46 736 256 2116

10 51 510 100 2601

So ...

#### Solution Summary

The solution gives detailed steps on finding the correlation coefficient and slope using simple regression and interpret both terms.

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.