Question

The paired data below consist of the number of lifetime surgeries and age of a patient. Number of Surgeries (x) 0 2 3 4 2 5 9 10 Ages (Years) (y) 45 50 65 78 57 86 83 100

1. Plot the data using scatter plot (make sure you have r-square and equation of the line on the graph)
2. Find the value of the linear correlation coefficient r. is it weak or strong
3. Find the equation of the regression line, letting Number of Surgeries be the independent (x) variable.
4. Find the coefficient of determination ( r-square), What this mean in term of the problem?
5. Find the standard error of estimate s_e.

Answer 1

Hence we get r = 0.9100

It is closer to 1 hence there it is strong.

We get linear regression equation:

Y^ = 5.0131 * x + 48.5677 (Rounded to 4 decimal places)

From the given summary we get-

Coefficient of determination R² = 0.8281   (Rounded to 4 decimal places)

That is 82.81 % proportion of variation in Ages (Years) is explained by Number of surgeries.

And we get standard error SE:

We get standard error for intercept = 5.0958 (Rounded to 4 decimal places)

standard error for coefficient of x = 0.9323 (Rounded to 4 decimal places)