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Longer strides In Exercise 43, we summarized the relationship between x =

height of a student (in inches) and y = number of steps required to walk the length of a school hallway, with the regression line y^=113.6鈭0.921x. For this

model, technology gives s = 3.50 and r2 = 0.399.

a. Interpret the value of s.

b. Interpret the value of r2.

Short Answer

Expert verified

Part (a) The predicted number of steps required to walk the length of a school hallway differed on average by 3.50steps from the actual number of steps required to travel the length of a school hallway.

Part (b) The least-square regression line utilizing a student's height as an explanatory variable can explain 39.9% of the variation in the number of steps required to walk the length of a school hallway.

Step by step solution

01

Part (a) Step 1: Given information

The question specifies the link between xa student's height, and y the number of steps required to travel the length of a school corridor.

The regression line is as:

y=113.60.921x

02

Part (a) Step 2: Explanation

And s=3.50 is the value of s. The standard error of the estimations, as we all know, is the average error of forecasts, and thus the average difference between actual and predicted values. Thus, using the equation of least square regression line, the predicted number of steps required to walk the length of a school hallway differed on average by 3.50 steps from the actual number of steps required to travel the length of a school hallway.

03

Part (b) Step 1: Explanation

The regression line is as:

y=113.60.921x

And the value r2is,

r2=0.399=39.9%

The coefficient of determination, as we know, is a measurement of how much variation in the answers y variable is explained by the least square regression model with the explanatory variable. As a result, the least square regression line utilizing a student's height as an explanatory variable can explain39.9% of the variation in the number of steps required to walk the length of a school hallway.

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Most popular questions from this chapter

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