Question

A researcher is trying to predict test scores from student’s level of stress. What is the standardized regression equation for the following data taken from 10 students? The average level of stress for students is 9.50 with a standard deviation of 2.76. The average test score for students is 12.50 with a standard deviation of 5.13. The correlation stress and test scores is 0.88.

a) ZY’ = 0.54 (ZX) b) ZY’ = 1.32 (ZX) c) ZY’ = .88 (ZX) d) ZY’ = 1.86 (ZX)

Answer 1

For a given dependent variable Y and an independent variable X, the simple linear regression equation is:

where b0 and b1 are the regression coefficients.

We are interested in standardizing the regression equation if both the variables are measured in different units. In such a case, we standardize the regression coefficients using the formula

where   are the standardized regression coefficients.

sx is the standard deviation of the variable X and

sy is the standard deviation of the variable Y

The standardized regression equation then will be

where ZY' is the predicted standardized value for Y and ZX is the standardized value for X.

Given information:

• Independent variable Y denotes the test scores of students.
• Dependent variable X denotes the student's level of stress.
• Sample size, n=10
• Average level of stress for students,
• Standard deviation of level of stress for students,
• Average test score for students,
• Standard deviation of test score for students, ​​​​​​​
• Correlation between stress and test scores,

​​​​​​​The formula to get the unstandardized regression coefficient is

We are not going to find as in the standardized equation it is equal to 0.

The standardized regression coefficient,

Hence, the standardized regression equation then will be

Note that the standardized regression equation will always be where r is the correlation coefficient between X and Y. I did the whole problem for you to see and understand that the standardized coefficient and are equal to 0.88. In general, r is enough for us.