Do you think shoe size affects the number of pairs of shoes owned?
Conjecture: r should be close to 0 LSRL: y=4
Practice makes perfect
Analysis
Before we make any conjecture about the correlation coefficient r, let's think about the variables. On the horizontal axis we have shoe size, and on the vertical axis we have pairs of shoes owned.
Independent variable:& Shoe size
Dependent variable:& Pairs of shows owned
Do you think there is a correlation between these variables? Likely not, right? Why would shoe size affect the number of pairs of shoes owned? Therefore, there should be no correlation, which is what the scatterplot shows.
LSRL
The least square regression line attempts to minimize the sum of the square of the residuals. Visually, this means that our line runs trough the middle of the data. Since we have no observable trend, the least square regression line will have a slope close to 0 and a y-intercept where about half the observations are over the line, and the other half are below the regression line.
