Chapter 1. Two-Variable Statistical Calculator

Statistical Applets

Choose a data set on the first tab below, then click the other tabs to view or manipulate the data, see summary statistics including the correlation and equation of the least-squares regression line, or view a scatterplot or residuals plot of the data.

Statisticians are often interested in changes in a variable, or relationships among several variables. This applet describes straight-line relationships between two variables using the methods of correlation and regression.

1.

Choose "User-entered data" as the dataset, then enter the following pairs of values for Column A (x) and Column B (y):

(7, 10)
(27, 35)
(24, 25)
(8, 12)
(10, 19)
(15, 22)

Enter the following statistics for this dataset (accurate to within 2 decimal places):

  • Mean of x:
  • Mean of y:
  • Std. dev. of x:
  • Std. dev. of y:
3
Try again.
Incorrect. See above for the correct answers.
Great job.

2.

Now fill in the following values regarding the correlation and regression line for these two variables:

  • Slope of regression line:
  • Intercept of regression line:
  • Correlation coefficient:
3
Try again.
Incorrect. See above for the correct answers.
Great job.

3.

Examine the scatterplot for the data. Do the two variables appear to be strongly correlated? Do there appear to be any outliers? Justify your answers.
The two variables do appear to be strongly correlated, as evidenced by the fact that the square of the correlation coefficient, r2, indicates that 88% of the variance in y is accounted for by variance in x. Since all 6 points on the scatterplot fall quite close to the regression line, there do not appear to be any outliers in the data.