Below is some output from a bivariate regression with respondents’ systolic blood pressure readings (measured in millimeters of mercury) as the dependent variable and weight (in kilograms) as the independent variable. Please use whatever information you think is necessary to explain the relationship between systolic blood pressure and weight that we should expect to see in the U.S. adult population. Be sure to address any statistical and substantive significance you may see, as well as how well the model “fits" the data (that is, how accurate our predictions appear to be). Your answer should be in paragraph form. Remember, the "residual standard error" reported below is the same thing as the "root MSE" in your slides.

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
icon
Related questions
icon
Concept explainers
Topic Video
Question

Help with the problem

Below is an output from a bivariate regression analysis where the dependent variable is the respondent's systolic blood pressure (measured in millimeters of mercury), and the independent variable is weight (measured in kilograms). 

The regression output provides insight into how systolic blood pressure is expected to vary with weight in the U.S. adult population. It's important to note both the statistical and substantive significance of this relationship, as well as to assess the model's fit—how accurately it predicts blood pressure based on weight. The "residual standard error" is synonymous with the "root MSE."

**Coefficients:**

- **Intercept:**
  - Estimate: 99.64576
  - Standard Error: 1.05350
  - t value: 94.58
  - p-value: < 2e-16
  - Significance: ***

- **Weight:**
  - Estimate: 0.43444
  - Standard Error: 0.01433
  - t value: 30.32
  - p-value: < 2e-16
  - Significance: ***

**Keys:**
- Significance codes: 0 '***', 0.001 '**', 0.01 '*', 0.05 '.', 0.1 ' ', 1

**Model Fit:**
- Residual Standard Error: 22.37 on 10,335 degrees of freedom
- Multiple R-squared: 0.08168
- Adjusted R-squared: 0.08159
- F-statistic: 919.2 on 1 and 10,335 DF
- p-value: < 2.2e-16

This analysis indicates that there is a statistically significant positive relationship between weight and systolic blood pressure, as shown by the low p-value and high t value for the weight coefficient. Each kilogram increase in weight is associated with an approximate 0.43444 mmHg increase in systolic blood pressure. The model explains about 8.168% of the variability in blood pressure, which, while statistically significant, suggests that other factors also play substantial roles in determining blood pressure. The residual standard error indicates the typical error in millimeters of mercury by which blood pressure varies from values predicted by the model.
Transcribed Image Text:Below is an output from a bivariate regression analysis where the dependent variable is the respondent's systolic blood pressure (measured in millimeters of mercury), and the independent variable is weight (measured in kilograms). The regression output provides insight into how systolic blood pressure is expected to vary with weight in the U.S. adult population. It's important to note both the statistical and substantive significance of this relationship, as well as to assess the model's fit—how accurately it predicts blood pressure based on weight. The "residual standard error" is synonymous with the "root MSE." **Coefficients:** - **Intercept:** - Estimate: 99.64576 - Standard Error: 1.05350 - t value: 94.58 - p-value: < 2e-16 - Significance: *** - **Weight:** - Estimate: 0.43444 - Standard Error: 0.01433 - t value: 30.32 - p-value: < 2e-16 - Significance: *** **Keys:** - Significance codes: 0 '***', 0.001 '**', 0.01 '*', 0.05 '.', 0.1 ' ', 1 **Model Fit:** - Residual Standard Error: 22.37 on 10,335 degrees of freedom - Multiple R-squared: 0.08168 - Adjusted R-squared: 0.08159 - F-statistic: 919.2 on 1 and 10,335 DF - p-value: < 2.2e-16 This analysis indicates that there is a statistically significant positive relationship between weight and systolic blood pressure, as shown by the low p-value and high t value for the weight coefficient. Each kilogram increase in weight is associated with an approximate 0.43444 mmHg increase in systolic blood pressure. The model explains about 8.168% of the variability in blood pressure, which, while statistically significant, suggests that other factors also play substantial roles in determining blood pressure. The residual standard error indicates the typical error in millimeters of mercury by which blood pressure varies from values predicted by the model.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning