Question

Asked Sep 27, 2019

20 views

A pediatrician wants to determine the relationship that exists between a

child’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below:

(a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable.

(b) Interpret the slope and y-intercept, if appropriate.

(c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.

(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?

Step 1

**Note: **

Hi there! Thank you for posting the question. As your question has more than 3 parts, we have solved the first 3 for you, according to our policy. If you need help with any other part, please re-post the question and mention the part you need help with.

Step 2

**(a) Equation of the least-squares regression line:**

The equation of the least-squares regression line is *y*-cap = *β*_{0} + *β*_{1}*x*.

From the StatCrunch output, it is observed that the least-squares regression line treating height as the explanatory variable and head circumference as the response variable is,

Step 3

**(b) Interpretation of slope and y-intercept:**

In a regression line equation, *β*0 refers to the *y*-intercept and *β*1 refers to the slope of the line.

Here, the value of *β*0 is 12.49 (approx.) and the value of *β*1 is 0.18 (approx.)

**Slope and y-intercept:**

The value of slope refers that the change in value of *y* for one unit changes in *x*. The *y*-intercept is the value at which line crosses the *y* axis. That is, it is the value when *x* is 0.

**Interpretation of slope:**

The slope v...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Given a set of normally distributed scores with the mean of 20.00 and SD of 5.00, what proportion of...

A: We are givenμ = 20, σ = 5a)We have to find P( 10 < x < 28 )

Q: A researcher was once criticized for falsifying data. Among his data were figures obtained from 44 g...

A: There seems to be printing mistake in a given question.Here 4 groups of rats with 20 individual rats...

Q: Researchers recruited a sample group of older adults and a sample group of younger adults for a stud...

A: Here, denote, x as the age of an old adults.Compute mean, range, variance, and standard deviation fo...

Q: On average, an IRS auditor discovers 4.7 fraudulent income tax returns per day. On a randomly chosen...

A: It is given that; the auditor discovers 4.7 fraudulent income tax returns per day.Thus, the random v...

Q: The website www.nationmaster.com provides data on the amount of money countries have pledged for Ira...

A: Click to see the answer

Q: Assume the IQ scores in a population are normally distributed with a mean value of 100 and a standar...

A: Given DataMean = 100Standard Deviation = 15

Q: 9. (Sec. 3.6) Pokemon are tion of 8 Pokemon/km2 present in tall grass according to a Poisson process...

A: As per the questionAverage concentration of pokeman per square km is 8a)X is the no of Pokémon’sExpe...

Q: What is sample coefficients of variation

A: Measures of variability:The measure of variability or the measures of dispersion can be measured usi...

Q: (1 point) A basketball player makes 200 out of 250 free throws. We would estimate the probability th...

A: It is given that player makes 200 out of 250 throws.Probability:The chance of getting an event can b...