Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: Studenth=19.6+ 0.73x Midparh, R²=0.45, SER=2.0 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. (Following Galton's methodology, both variables were adjusted so that the average female height was equal to the average male height.) For the following questions except (d), type your answers in two decimal places. (a) If we test for the statistical significance of the slope coefficient, the relevant f-statistic is t = (b) Construct a 95% confidence interval for a one inch increase in the average of parental height: ( (c) The prediction for the height of a child whose parents have an average height of 70.06 inches is (d) The model explains percent of the variation in the height of students. Hint: type an integer. inches.
Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: Studenth=19.6+ 0.73x Midparh, R²=0.45, SER=2.0 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. (Following Galton's methodology, both variables were adjusted so that the average female height was equal to the average male height.) For the following questions except (d), type your answers in two decimal places. (a) If we test for the statistical significance of the slope coefficient, the relevant f-statistic is t = (b) Construct a 95% confidence interval for a one inch increase in the average of parental height: ( (c) The prediction for the height of a child whose parents have an average height of 70.06 inches is (d) The model explains percent of the variation in the height of students. Hint: type an integer. inches.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Understanding Regression Analysis in Height Studies**
Sir Francis Galton, a cousin of James Darwin, explored the relationship between the height of children and their parents in the late 19th century, marking the origin of the term "regression." In this study, we update his findings using data from 110 college students to estimate the following relationship:
\[
\text{Student}h = 19.6 + 0.73 \times \text{Midparh}, \quad R^2 = 0.45, \quad SER = 2.0
\]
(7.2) \hspace{1cm} (0.10)
Here, **Studenth** is the height of the student in inches, and **Midparh** is the average of the parental heights. Numbers in parentheses represent heteroskedasticity robust standard errors. (Following Galton's approach, variables were adjusted so the average female height equaled the average male height.)
### Exercises
Except for part (d), provide answers rounded to two decimal places.
(a) **Testing the Slope Coefficient's Significance**
Calculate the \( t \)-statistic for the slope coefficient.
(b) **Confidence Interval for Parental Height's Impact**
Construct a 95% confidence interval for a one-inch increase in the average parental height.
(c) **Predicting a Child’s Height**
Estimate the height of a child whose parents have an average height of 70.06 inches.
(d) **Explaining Variability**
Determine the percentage of variation in the student's height explained by the model. (*Hint: Type an integer.*)
This exercise underscores the application of simple linear regression in understanding inherited characteristics such as height through statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf605b71-789d-48e0-8055-d8207016854b%2F60383fd1-025a-4140-bdf1-23f9fb0a9aaa%2Fy40h8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Regression Analysis in Height Studies**
Sir Francis Galton, a cousin of James Darwin, explored the relationship between the height of children and their parents in the late 19th century, marking the origin of the term "regression." In this study, we update his findings using data from 110 college students to estimate the following relationship:
\[
\text{Student}h = 19.6 + 0.73 \times \text{Midparh}, \quad R^2 = 0.45, \quad SER = 2.0
\]
(7.2) \hspace{1cm} (0.10)
Here, **Studenth** is the height of the student in inches, and **Midparh** is the average of the parental heights. Numbers in parentheses represent heteroskedasticity robust standard errors. (Following Galton's approach, variables were adjusted so the average female height equaled the average male height.)
### Exercises
Except for part (d), provide answers rounded to two decimal places.
(a) **Testing the Slope Coefficient's Significance**
Calculate the \( t \)-statistic for the slope coefficient.
(b) **Confidence Interval for Parental Height's Impact**
Construct a 95% confidence interval for a one-inch increase in the average parental height.
(c) **Predicting a Child’s Height**
Estimate the height of a child whose parents have an average height of 70.06 inches.
(d) **Explaining Variability**
Determine the percentage of variation in the student's height explained by the model. (*Hint: Type an integer.*)
This exercise underscores the application of simple linear regression in understanding inherited characteristics such as height through statistical analysis.
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