Question

A new drug is being used to relieve the pain of arthritis. However, the drug may reduce a patient’s heartbeat too much. To investigate the drugs effect on a person’s heartbeat, different dosages of the drug were given to six patients, and 30 minutes later, the decrease in each patient’s heartbeat was recorded.

Dosage X = (2.0, 1.5, 3.0, 2.5, 4.0, 3.0) measured in ml.

Decrease Y = (15, 20, 18, 16, 19, 17) measured in beat per minute

Then answer the following questions for exercise 3.11 using SAS output only.

a. Write down the prediction equation.

b. Write down SSE, S2, SSyy and S(std. dev).

c. Predict y when x = 2.5 and then what is the prediction error.

d. Find the 95% confidence interval for 1

. e. Test if the x is significant to the prediction of y.

f. Find the coefficient of determination and interpret.

g. Find the 95% confidence interval for E(Y) when x = 2.5.

h. Find a 95% prediction interval for Y when x = 2.5.

i. Predict Y if x = 3.5 and find the confidence interval for E(y) and the pre

Answer 1

Regression Analysis: Y versus X

The regression equation is
Y = 16.8 + 0.26 X

Predictor Coef SE Coef T P
Constant 16.804 2.952 5.69 0.005
X 0.261 1.060 0.25 0.818

S = 2.07600 R-Sq = 1.5% R-Sq(adj) = 0.0%

Regression Statistics
Multiple R	0.122094
R Square	0.014907
Adjusted R Square	-0.23137
Standard Error	2.076002
Observations	6

Analysis of Variance

Source DF SS MS F P
Regression 1 0.261 0.261 0.06 0.818
Residual Error 4 17.239 4.310
Total 5 17.500

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 17.457 0.866 (15.053, 19.860) (11.211, 23.702)

Values of Predictors for New Observations

New Obs X
1 2.50

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 17.717 1.224 (14.318, 21.117) (11.026, 24.409)

Values of Predictors for New Observations

New Obs X
1 3.50