A negative slope from a negative correlation

Question

A study links a website's page-load time in milliseconds ( $x$ ) to a satisfaction rating from 1 to 10 ( $y$ ). The summary statistics are

$r = -0.5, \qquad s_x = 10, \qquad s_y = 4.$

What is the slope of the line predicting satisfaction from load time?

Accepted Answer

Apply the slope formula, keeping the sign of the correlation: b = r \cdot \frac{sy}{sx} = -0.5 \cdot \frac{4}{10} = -0.5 	imes 0.4 = -0.2. The negative sign comes straight from the negative correlation: slower load times go with lower satisfaction. The size, -0.2, is small because y (a 1-to-10 rating) is far less spread out than x (load times in milliseconds), so the ratio 4/10 = 0.4 shrinks the effect. Read in units: each extra millisecond of load time is associated with about 0.2 fewer satisfaction points. That per-unit number looks tiny, but slopes must always be read together with a real…

A negative slope from a negative correlation

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