MediumStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Correlation and RegressionNumerical

Six made-up students record their screen time and their sleep on one school night…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Six made-up students record their screen time and their sleep on one school night.

Screen time (hours)	Sleep (hours)
$1$	$8.4$
$2$	$8.1$
$3$	$7.5$
$4$	$7.4$
$5$	$6.8$
$6$	$6.6$

Find the least-squares line that predicts sleep from screen time, with $b = \dfrac{S_{xy}}{S_{xx}}$ . Then predict the sleep of a student with $3.5$ hours of screen time. Give answers to three decimal places.

Need a reminder? The key ideaShow

The least-squares line $\hat{y} = a + bx$ has

\displaystyle b = r\,\dfrac{s_y}{s_x} = \dfrac{S_{xy}}{S_{xx}}, \qquad a = \bar{y} - b\bar{x}.

The slope is the change in $\hat{y}$ for each extra unit of $x$ . Predict inside the range of the data.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← A made-up class records the height of a bean plant every few days for three weeks…A made-up clinic records the mean height of children at ages 2 to 8 years: 86, 95, 102, 109, 115… →

More onStatistics Basics › Correlation and Regression

Discussion (0)

Loading…