If the standard deviation of matches the standard deviation of , then what is the relationship between the slope in a least squares regression of on and the correlation between and ? Shoppers at a...

If the standard deviation of

matches the standard deviation of
, then what is the relationship between the slope in a least squares regression of

on

and the correlation between

and
?

Shoppers at a local supermarket spend, on average,

during each shopping trip. Imagine the scatterplot that shows the total amount spent each day in the store on the
-axis versus the number of shoppers each day on the
-axis.

(a) Would you expect a linear equation to describe these data?

(b) What would you expect for the intercept of the linear model?

(c) What would you expect for the slope?

(d) Do you expect patterns in the variation around the equation?