Question

Exercise 3.11

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

4.            Construct a 95% confidence interval for B1?

4.            Find the coefficient of correlation and interpret its value. ?

5.            Find the coefficient of determination and interpret its value. ?

6.            Find a 95% confidence interval for E(y) when x = 2.5. ?

7.            Find a 95% prediction interval for y when x = 2.5. ?

Answer 1

Regression using Excel.

Step 1) First enter the given data set in excel columns.

Step 2) Then click on Data >>> Data Analysis >>>Regression >>>>OK

Step 3) Input Y Range: Select the data of column "B"

Input X Range: Select the data of column "a"

Click on Lable

then Click on Ouput Range

Look the following Image

Then Click on OK, we get following result.

4. Construct a 95% confidence interval for B1?

From the above output the 95% confidence interval for the slope ( ) is (-2.6831 , 3.2048 )

4.            Find the coefficient of correlation and interpret its value. ?

R = coefficient of correlation = 0.1221

Since it is very close to 0 the correlation between X and Y is very low

5.            Find the coefficient of determination and interpret its value. ?

R² = coefficient of determination = 0.0149

1.49% of variation in Y explained by the variable X.

Let's use minitab for answer the 6. and 7

Step 1) First enter the given data set in minitab columns.

Step 2) Click on Stat>>>Regression>>>General regression...

Response: select Y

Model: select X

Step 3) Click on Prediction

in "New observation for continuous predictors:

put 2.5

Select confidence limits:

and prediction limits

Then click on OK

then click on Option.

Confidence level for all interval: put 95

Types of confidence interval: Two-sided.

then click on OK and again Click on OK

So we get the following minitab output

6.            Find a 95% confidence interval for E(y) when x = 2.5. ?

The 95% confidence interval for E(y) when x = 2.5. is  (15.0528, 19.8602

7.            Find a 95% prediction interval for y when x = 2.5. ?

The  95% prediction interval for y when x = 2.5 is  (11.2115, 23.7016)