Summary Scatter Plots and Regression Lines - Mathematics Grade 12 (IEB)

Scatter plots and regression lines
Univariate data
= single values

Bivariate data
= two variables at the same time for comparison

Graphically the relationship between two variables can be shown by means of a scatterplot.
One variable is placed on the x-axis and on the y-axis.




A linear relationship may exist between two variables.
The straight line that best represents this relationship is called the line of best fit or the least
squares regression line.

y = a + bx (y = c + mx in statistical format)

y - shows that the equation represents a trend that doesn’t give actual y values, but predicted y
, values.
a - y-intercept of the line
b - the gradient

(Average x; average y) is a point that lies on the line of best fit.

Correlation coefficient
=r
Indicates how well the least squares regression line represents the data.
Tells us the type of relationship (positive or negative) as well as the strength of the relationship.
A numerical value, between -1 and 1.
(r is not the slope and therefore is not affected by the flipping of the x and y)