Chapter 1. Two-Variable Statistical Calculator

Introduction

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.

Click the "Quiz Me" button to complete the activity.

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.

Question 1.1

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: EABNG2fn3flyB0zN
  • Mean of y: 7k9v0q5LX0xt2/l8
  • Std. dev. of x: kuDnLHDRzr0=
  • Std. dev. of y: vcqatSBZW9s=
3
Try again.
Incorrect. See above for the correct answers.
Great job.

Question 1.2

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

  • Slope of regression line: lVex7vblkgI=
  • Intercept of regression line: z1DhTws84hA=
  • Correlation coefficient: +P4mXX9i4Y0=
3
Try again.
Incorrect. See above for the correct answers.
Great job.

Question 1.3

P8p2E3/0eX52rgl566DdKO3HAVtszGGI9jptqOdzLpnhHJwxE9ez1TRybUrfjRL1GArO6PdbHzfPzWGx/F/jgZJCuEphlIoKV1UWw+lzRk97k5EaKvKL6sw2/bXlEAtIZiItlfykg/J+r4dTM2/xADHEZkH6Huxzaee2ClLz34+sxu7RT0deKW42BRIVyCsu2Ax40cJXI7gxW8wS0k9s5To8VjQxHOfB4P+7jn3Tl4PxAde2gmPRs+2sq1w=
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.