An experiment was conducted to study the effect of a certain

An experiment was conducted to study the effect of a certain drug in lowering heart rate in adults. The independent variable or covariate is dosage (X) in milligrams of the drug, and the dependent variable is reduction in heart rate (Y) (beats/min). The experiment included 13 subjects. The following is the SAS output for fitting the population regression model: Y = alpha + beta X + epsilon What is the estimated slope of the fitted regression line Make an interpretation of the slope estimate. What is the estimated mean response of reduction in heart rate for dose of 1.00 mg Using the 95% confidence interval for beta, will you reject Ho: beta = 0 versus H_A: beta not equal to 0 at alpha = 0.05 Why or Why not What proportion of the variation in heart rate is explained by the linear relationship of heart rate with drug dose Based on the SAS output, compute the Pearson correlation coefficient between dose and reduction in heart rate.

Solution

The independent variable X is dosage (in milligrams).

The dependent variable Y is reduction in heart rate (beats per minute).

n is number of points = 13

The regression equation is,

y = 7.05495 + 4.08791*x

What is the estimated slope of the fitted regression line? Make an interpretation of the slope estimate.

slope = 4.08791

Interpretation : Unit change in dosage will be result into 4.08791 change in reduction in heart rate.

What is the estimated mean response of reduction in heart rate for dose of 1.00mg?

That is here we have to calculate y when x = 1.00 mg

y = 7.05495 + 4.08791*x

y = 7.05495 + 4.08791*1.00

y = 11.1429

The estimated mean response of reduction in heart rate for dose of 1.00mg is 11.1429.

Usinu the 95% confidence interval for B will you reject H0 : B = 0 Vs Ha : B not=0 at alpha = 0.05?

Here test of the hypothesis is,

H0 : B = 0 Vs Ha : B not=0

where B is population slope.

The test statistic is,

t = b / SEb (test statistic)

where b is slope.

SEb is standard error of the estimate.

t = 10.17

and P-value = 0.0001

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Population slope is differ than 0.

What proportion of the variation in heart rate is explained by the linear relationship of heart rates with drug dose.

This explains by R² .

In the output R² = 0.9039 = 0.9039*100 = 90.39%

The proportion of the variation in heart rate is explained by the linear relationship of heart rates with drug dose is 90.39%.

Based on the SAS output, compute the Pearson correlation coefficient between dose and reduction in heart rate.

Pearson correlation coefficient is simplt the square root of R².

that is r = sqrt(0.9039) = 0.9507

and Pearson correlation coefficient has positive sign because slope has positive sign.