Question

Project 2.

Choose a topic of study that will include a simple correlation between 2 variables.

1. Collect 2 variables from at least 8 individuals. (you will have a sample of 8 pair of values)

2. Identify the dependent variable and the independent variable.

3. What is the regression line?

4. Test the significance of the correlation between the variables

5. Choose an independent variables\ to make a prediction of the dependent variable associated with it.

6. What are the coefficient of determination. and non determination?

Answer 1

Example :

The weight of systolic blood pressure of 15 randomly selected males in the age group 25 - 30 are as follows :

2 )  Identify the dependent variable and the independent variable.

Weight = independent variable ( x )

Systolic Bloood Pressure = dependent variable ( y )

3. What is the regression line?

Let's use excel:

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 "C"

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

Click on Lable

then Click on Ouput Range

Look the following Image

Then Click on OK, we get following result.

3. What is the regression line?

From the above output the regression equation is as follows:

4. Test the significance of the correlation between the variables

Level of significance = = 0.05 ( If it is not given then take it as 0.05 )

For n = 15 the critical r by using Pearson correlation table is critical r = 0.514

From the above output the sample correlation coefficient = r = Multiple R = 0.669754

Since r > critical r, so we conclude that the correlation between x and y is significant for 5% level of significance.

5. Choose an independent variables\ to make a prediction of the dependent variable associated with it.

Le's take x = 180

Plug this value in the above regrssion equation, so we get

6. What are the coefficient of determination. and non determination?

coefficient of determination = r² = R Square = 0.448571

coefficient of non determination = 1 - r² = 1 - 0.448571 = 0.551429