CB.Stats.DAT-1.G: Estimate parameters for the least-squares regression line model.

Estimate parameters for the least-squares regression line model.

Example Problems

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.

Leo is studying the relationship between hours spent playing Minecraft per week and the number of in-game structures a player completes. He surveys a random sample of

20

players. Here is computer output from a least-squares regression analysis on his sample:

Predictor	Coef	SE Coef	T	P
Constant	3.80	1.95	1.95	0.07
Hours played	0.74	0.18	4.11	0.00

S = 2.85 \quad \text{R-sq} = 48.4\%

Assume that all conditions for inference have been met.

Write the expression for a

95\%

confidence interval for the slope of the least-squares regression line.

Ms. Carter is studying the relationship between the number of Blooket review sessions students complete and their final unit test scores (out of 100). She records data for a random sample of 42 students. Here is computer output from a least-squares regression analysis on her sample:

Predictor	Coef	SE Coef	T	P
Constant	68.20	4.10	16.63	0.00
Sessions	2.95	0.71	4.15	0.00

S = 6.80 \qquad \text{R-sq} = 30.0\%

Assume that all conditions for inference have been met.

Write the expression for a

95\%

confidence interval for the slope of the least-squares regression line.

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