Why is the equation of the regression line for this scatter plot ? ### Simple Linear Regression Results**Dependent Variable:** - Height (in.)**Independent Variable:** - Shoe Size (in.)**Regression Equation:** - Height (in.) = 52.293743 + 1.3679745 * Shoe Size (in.)**Sample Size:** - 16**Statistics:** - R (correlation coefficient) = 0.72170907- R-sq = 0.52086398- Estimate of error standard deviation: 2.6920127---### Parameter Estimates| Parameter | Estimate | Std. Err. | Alternative DF | T-Stat | P-value ||-----------|-----------|------------|----------------|---------|---------|| Intercept | 52.293743 | 3.4200195 | ≠ 0 | 14 | 5.290481 | <0.0001 || Slope | 1.3679745 | 0.35065598 | ≠ 0 | 14 | 3.901187 | 0.0016 |---### Analysis of Variance Table for Regression Model| Source | DF | SS | MS | F-stat | P-value ||--------|----|----------|--------|--------|---------|| Model | 1 | 110.29295| 110.29295 | 15.21926 | 0.0016 || Error | 14 | 101.45705| 7.2469323 | | || Total | 15 | 211.75 | | | |---### Graphical Representation- **Graph Description:** A scatter plot shows the relationship between shoe size (x-axis) and height (y-axis). Each point represents an observation within the dataset. A fitted line is drawn through the data points, indicating the trend predicted by the regression model. The line slopes upwards, suggesting a positive correlation between shoe size and height. The datapoints are dispersed around this line, indicating variability in the data.

The regression equation is, y=a+bx In the formula a is the intercept value, and x is the slope…

Answered: Why is the equation of the regression…

Math

Statistics

Why is the equation of the regression line for this scatter plot ?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: If the slope of the fitted regression line is -0.91, then describe the relationship between two…

A: It is given that the slope of the fitted regression line is –0.91. The variable y represents the…

Q: Beltrami Company used multiple regression on 10 months of data on materials handling cost (in U.S.…

A: From the above given data the following solution is provided below: Given data, Intercept = 500…

Q: The given paired data lists the heights (in inches) of various males who were measured on their…

A: Given that ; X Y X \cdot YX⋅Y X^2X2 Y^2Y2 52 69 3588 2704 4761 50 66 3300 2500 4356…

Q: Why should we include more than one variable in our regression?

A: If a variable to be studied depends upon a single variable then this can be studied by simple…

Q: Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of…

A: Introduction:Here, the response variable, y, is the range of ankle motion while wearing typical…

Q: We expect a car's highway gas mileage to be related to its city gas mileage. Data for all 1198…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: A study of the mail survey response rate patterns of people aged 60-90 found a prediction equation…

A: According to the provided information, The linear equation is: Y=90.2 - 0.6 X Where, 90.2 is the…

Q: Use data on tab “printers data.” --Run a regression with “Cartridges” as the dependent variable and…

A: Using Excel, we can perform regression analysis as follows, Enter the data in Excel spreadsheet. Go…

Q: Use the time/tip data from the table below, which includes data from New York City taxi rides. (The…

A: x is the predictor variable (time) y is the response variable (tip) Time(x) Tips(y) 27.00 0.00…

Q: Interpret the slope of the regression line in terms of the problem. Predict the weight of trash in…

Q: Smokers don’t live as long (on average) as nonsmokers, and heavy smokers don’t live as long as light…

A: More smoking less survival time.

Q: The same researcher wants to know if perception of stress (X) predicts a person's frustration level…

A: Regression is a statistical method used in finance, investing, and other disciplines that attempts…

Q: What is meant by the slope of the regression

A: In a linear regression model, We have one dependent variable and one independent variable.

Q: It appears that over the past 50 years, the number of farms in the United States declined while the…

A: From Given data X Y 5.61 215 4.68 256 3.95 298 3.41 342 2.94 369 2.55 421 2.41 426…

Q: RaceJA started manufacturing race cars four years ago. The company wants to know the relationship…

Q: The equation used to predict college GPA (range 0-4.0) is y=0.18+0.53x1+0.002x2, where x1 is high…

A: Given, The equation used to predict college GPA is y=0.18+0.53x1+0.002x2, where x1 is high school…

Q: Use the time/tip data from the table below, which includes data from New York City taxi rides. (The…

A: It is required to predict the tip (dollars) for a ride, using the time taken to complete that trip…

Q: This regression is on 1744 individuals and the relationship between their weekly earnings (EARN, in…

Q: A researcher found that the linear regression equation has a slope of 3 and an intercept of -6. What…

A: The objective of this question is to find the predicted value of Y for a given value of X using the…

Q: The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross…

Q: The relationship between the cost of a concert ticket and a ranking of the performer's popularity…

A: Given, The relationship between the cost of a concert ticket and a ranking of the performer’s…

Q: A sports statistician was interested in the relationship between game attendance (in thousands) and…

A: Given Information: Regression equation: y = 4.9x + 15.2

Q: A sports statistician was interested in the relationship between game attendance (in thousands) and…

A: The relationship between game attendance (in thousands) and the number of wins for baseball teams is…

Q: if an estimated regression line has a y-intercept of 10 and a slope of -4, then when x=2, what is…

A: It is given that, An estimated regression line has y-intercept ,a= 10 Slope,b=-4 Thus,The estimated…

Q: The US government is interested in understanding what predicts death rates. They have a set of data…

A: Identify the correct option for which of the variables has negative correlation with the deaths. The…

Q: make a regression analysis about any healthcare issue

A: Let's perform a simple regression analysis on a healthcare issue. We'll analyze the relationship…

Q: What is the slope and intercept for the regression equation given this data? X = 72, 81, 54, 50, -3…

A: Given that X Y 72 69 81 97 54 73 50 22 -3 -10

Q: Suppose that a simple linear regression model is appropriate for describing the relationship between…

A: Given data in the problem isthe true regression line is y = 22500 + 43x σ = 5000We have to…

Q: Suppose Isabella has developed the following estimated regression equation for the price of an…

A: a) If someone wants to purchase an Edmonton condo with a size of 1010 square feet, how much should…

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

Why is the equation of the regression line for this scatter plot ?

### Simple Linear Regression Results

**Dependent Variable:**
- Height (in.)

**Independent Variable:**
- Shoe Size (in.)

**Regression Equation:**
- Height (in.) = 52.293743 + 1.3679745 * Shoe Size (in.)

**Sample Size:**
- 16

**Statistics:**
- R (correlation coefficient) = 0.72170907
- R-sq = 0.52086398
- Estimate of error standard deviation: 2.6920127

---

### Parameter Estimates

| Parameter | Estimate | Std. Err. | Alternative DF | T-Stat | P-value |
|-----------|-----------|------------|----------------|---------|---------|
| Intercept | 52.293743 | 3.4200195 | ≠ 0 | 14 | 5.290481 | <0.0001 |
| Slope | 1.3679745 | 0.35065598 | ≠ 0 | 14 | 3.901187 | 0.0016 |

---

### Analysis of Variance Table for Regression Model

| Source | DF | SS | MS | F-stat | P-value |
|--------|----|----------|--------|--------|---------|
| Model | 1 | 110.29295| 110.29295 | 15.21926 | 0.0016 |
| Error | 14 | 101.45705| 7.2469323 | | |
| Total | 15 | 211.75 | | | |

---

### Graphical Representation

- **Graph Description:** A scatter plot shows the relationship between shoe size (x-axis) and height (y-axis). Each point represents an observation within the dataset. A fitted line is drawn through the data points, indicating the trend predicted by the regression model. The line slopes upwards, suggesting a positive correlation between shoe size and height. The datapoints are dispersed around this line, indicating variability in the data.

Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Correlation, Regression, and Association$

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

How can you find the amount of intercept in the regression involving standardized variables
Isla Esme, Inc., sells tea products to various customers. In recent years, profits have been declining. The CFO of the business investigated the reasons for the profit decline and performed regression analysis for sales and costs. He determined that sales depend on product price, delivery speed, customer services, and marketing expenses. He also determined that total costs consist of variable costs of $25 per unit and fixed costs of $56,000. Marketing expenses have a coefficient of determination of 75% related sales.Question: Define the coefficient of determination and explain what it means in this scenario.
A real estate company wants to study the relationship between house sales prices and some important predictors of sales prices. Based on data from recently sold homes in the space, the following variables are used in a multiple regression model. y = sales price (in thousands of dollars) x₁ = total floor area (in square feet) x₂ = number of bedrooms x3 distance to nearest high school (in miles) = The estimated model is as follows. =76+0.098x₁ +16x₂ - 8x3 Answer the questions below for the interpretation of the coefficient of X₂ in this model. (a) Holding the other variables fixed, what is the average change in sales price for each additional bedroom in a house? dollars (b) Is this change an increase or a decrease? O increase O decrease X
Explain the curvilinear regression analysis?
A study was conducted to determine if a linear relationship exists between Calculus II (Y) grades and Calculus I (X). The researcher found out that the values of the slope and the y-intercept of the regression line is equal to 1.0134 and – 5.239, respectively. What is the predicted Calculus II grade when the Calculus I grade is equal to 85?
The following table gives the data for the grades on the midterm exam and the grades on the final exam. Determine the equation of the regression line, yˆ=b0+b1xy^=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Grades on Midterm and Final Exams Grades on Midterm 78 63 85 92 82 89 69 89 83 61 Grades on Final 77 75 88 92 86 86 80 85 77 63
Draw the regression line for the following equation: Y = -3 + (1) X Show your calculation for a low and high value on the predictor value.
write the regression equation that will predict the number of manatees killed given thenumber of powerboat registrations (in 1000's). Show all work usingformulas for slope, b1, and y-intercept, b0, calculations roundingto 4-decimal places, if necessary. Show all the calculations and math of slope, b1, and y-intercept, b0, calculations roundingto 4-decimal places, if necessary. SHOW ALL WORK! DO NOT USE EXCEL! I need to be able to see every single part and how you got it. attached is the question
What needs to change in an overall problem if one wants to use linear regression?
Would I use the regression line to predict Y from X ? And what is the pattern of the scatterplot?
A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled " The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes and depth D is in meters. The report then says, " The regression equation for this bird is: DD = 2.3 + 0.0021 D. %3D (a) What is the slope of the regression line?. ANSWER minutes per meter. (b) According to the regression line, how long does a typical dive to a depth of 400 meters last? ANSWER minutes.
The applet displays a scatterplot with the following points: (7,10),(27,35),(24,25),(8,12),(10,19),(15,22). Identify the slope of the regression line, intercept of the regression line, and correlation coefficient. Report your answers accurate to within two decimal places.