Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables: shoe size – in inches age – in years height – in inches forearm length – in inches Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows: > summary(lm(shoesize ~ age + height + forearm, data = measures)) Coefficients: (Intercept) age height forearm Estimate 10.14882 0.06045 -0.02108 -0.06479 Std. Error 4.49245 0.06838 0.06350 0.06847 t value 2.259 0.884 -0.332 -0.946 Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 Residual standard error: 1.719 on 85 degrees of freedom Multiple R-squared: 0.01983, Adjusted R-squared: 0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 Which of the following is the correct interpretation of the Adjusted R-squared? The probability that our model predicts the correct shoe size of a person using their age, height, and forearm length is 0.01477. 1.477% of the variation in the shoe size of adults ages 18 – 40 can be explained by their age, height, and forearm length. The probability that our model predicts the correct age of a person using their shoe size, height, and forearm length is 0.01477. 0.01477% of the variation in the age, height and forearm length of adults ages 18 - 40 can be explained by their shoe size.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables:

shoe size – in inches

age – in years

height – in inches

forearm length – in inches

Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows:

> summary(lm(shoesize ~ age + height + forearm, data = measures))
Coefficients:
(Intercept) age height forearm	Estimate 10.14882 0.06045 -0.02108 -0.06479	Std. Error 4.49245 0.06838 0.06350 0.06847	t value 2.259 0.884 -0.332 -0.946	Pr(>\|t\|) 0.0264 0.3792 0.7408 0.3467

Residual standard error: 1.719 on 85 degrees of freedom Multiple R-squared: 0.01983, Adjusted R-squared: 0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342

Which of the following is the correct interpretation of the Adjusted R-squared?

The probability that our model predicts the correct shoe size of a person using their age, height, and forearm length is 0.01477.

1.477% of the variation in the shoe size of adults ages 18 – 40 can be explained by their age, height, and forearm length.

The probability that our model predicts the correct age of a person using their shoe size, height, and forearm length is 0.01477.

0.01477% of the variation in the age, height and forearm length of adults ages 18 - 40 can be explained by their shoe size.

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