8.DS.B.3: Compare the fit of different linear models shown on scatter plots of the same data by describing the overall pattern and the closeness of data points to each line.

Compare the fit of different linear models shown on scatter plots of the same data by describing the overall pattern and the closeness of data points to each line.

Example Problems

All the students at a middle school were asked to identify their favorite academic subject and whether they were in

\text{7th grade}

or

\text{8th grade}

. Here are the results:

Favorite Subject by Grade

Grade	English	History	Math/Science	Other	Totals
7th Grade	38	36	28	14	116
8th Grade	47	45	72	18	182
Totals	85	81	100	32	298

Is there an association between favorite academic subject and grade for students at this school? Support your answer by calculating appropriate

\text{relative frequencies}

using the given data.

A cross country coach wants to look at the relationship between weekly mileage and 5K race times. The data show a linear pattern with the summary statistics shown below:

	mean	standard deviation
x = weekly mileage (miles)	$\bar{x} = 25$	$s_x = 8$
y = 5K race time (minutes)	$\bar{y} = 22$	$s_y = 2.5$
		$r = -0.8$

Find the equation of the least-squares regression line for predicting the 5K race time from the weekly mileage, in the form

\hat{y} = a + bx

.
Round your entries to the nearest hundredth.

A Papa's Pizzeria player wants to look at the relationship between the length of a shift and the tips earned. The data show a linear pattern with the summary statistics shown below:

	mean	standard deviation
$x = \text{shift length (minutes)}$	$\bar{x} = 15$	$s_x = 5$
$y = \text{tips earned (dollars)}$	$\bar{y} = 45$	$s_y = 20$
		$r = 0.95$

Find the equation of the least-squares regression line for predicting the tips earned from the length of the shift, in the form

\hat{y} = a + bx

.
Round your entries to the nearest hundredth.

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