Question

A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old. The data were analyzed using a simple linear regression model and the statistical results were as following.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49.8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 \ 0.00541

Residual standard error: 5.552 on 9 degrees of freedom

Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505

Based on the correlation coefficient, how do you describe the linear relationship between Age and DBP using the conventional classification?

A. Not enough information to make any statement

B. Positive, strong linear relationship;

C. Negative, strong linear relationship

D. Positive, weak linear relationship

Answer 1

Solution:

Given: A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49.8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 0.00541

Multiple R-squared: 0.5954

Then correlation coefficient is:

r = squar root ( Multiple R-squared)

r = squar root (0.5954 )

r = 0.7716

and slope of the regression is:

b1 = 2.1927 is positive.

Thus there is Positive correlation and since 0.7716 is close to +1, thus there is Positive, strong linear relationship.

Thus correct option is:

B. Positive, strong linear relationship