### Analyzing Scatter Diagrams and Regression Lines**A data set is given below:**#### Steps to Analyze and Graph Data1. **Drawing a Scatter Diagram:** - **Instruction:** Draw a scatter diagram. Comment on the type of relation that appears to exist between \( x \) and \( y \). - **Information Given:** \[ \begin{array}{c|c|c|c|c|c} x & 1 & 2 & 4 & 6 & 6 \\ \hline y & 5.2 & 5.8 & 4.5 & 3.6 & 2.0 \\ \end{array} \] 2. **Determining the Least-Squares Regression Line:** - **Formula:** \[ \hat{y} = b_0 + b_1 x \] - **Given Parameters:** \[ \bar{x} = 3.8333, \quad s_x = 2.0412, \quad \bar{y} = 3.8833, \quad s_y = 1.5651, \quad r = -0.9338 \] - **Calculation Steps:** - Slope (\( b_1 \)): \[ b_1 = r \left(\frac{s_y}{s_x}\right) \] - Intercept (\( b_0 \)): \[ b_0 = \bar{y} - b_1 \bar{x} \]3. **Graphing the Least-Squares Regression Line:** - **Instruction:** Graph the regression line on the scatter diagram drawn in part (a).#### Analyzing the Scatter Diagrams and Choosing the Correct One- **Scatter Diagrams (a):** You are provided with four different scatter diagrams (A, B, C, D). The correct scatter diagram that matches the given data points is B.- **Comment on Relationship:** There appears to be a **linear, negative** relationship between \( x \) and \( y \).#### Formulating the Regression Equation- **Given Equation:** \[ \hat{y} = b_0 + b_1 x \]- **Finding the Values:

Procedure to obtain scatterplot using excel:Enter the data of x and y in an excel sheet.Select data…

Answered: A data set is given below. (a) Draw a…

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

Similar questions

A study of fuel economy for various automobiles plotted the fuel consumption vs. speed. A LSRL was fit to the data. Here is the residual plot from this least-squares fit. What does the pattern of the residuals tell you about the linear model? 3. 2
Give a plausible example of a three-variable research problem in which partial correlation would be a useful analysis. Define X1, X2, and Y. Make sure that you indicate which of your three variables is the "controlled for" variable ( X2). What results might you expect to obtain for this partial correlation, and how would you interpret your results (e.g., spurious correlation, mediation, moderation, and so on)?
Consider the set of points (0,9),(1,5),(6,3) and (9,2). In this set of points, the age of a dolphin is the first part of each ordered pair and the second part is the number of tricks that the dolphin learned in a month. So, the 6 year-old dolphin learned 3 tricks in the month. Write the least squares regression line for this data. Use the line to estimate how many tricks a 4 year-old dolphin could learn. Then find r and r2. Explain what r2 means.
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y=nothingx+(nothing) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. A weightless car will get nothing miles per gallon, on average. It is not appropriate to interpret the slope. B. For every pound added to the weight of the car, gas mileage in the city will decrease by nothing mile(s) per gallon, on…
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year Using technology, what is the slope of the least-squares regression line and what is its interpretation? period. The results are given in the table. The slope is 1.98, which means for each additional 35 inch in height, the child's weight will increase by 1.98 Weight (x) 8. 12 18 24 30 32 37 40 30 32 33 36 38 pounds. Helght (v) 22 23 26 35 The slope is 1.98, which means for each additional inch in height, the child's weight is predicted to increase by 1.98 pounds. The slope is 0.50, which means for each additional pound in weight, the child's height will increase by 0.5 inches. The slope is 0.50, which means for each additional pound in weight, the child's height is predicted to increase by 0.5 inches.
For the data given in the table below, find the linear correlation coefficient r and the least-squares regression line x y ------- 1 18 3 13 3 9 6 6 7 4 -------
The accompanying data represent the number of days absent, x, and the final exam score, y, for a sample of college students in a general education course at a large state university. Complete parts (a) through (e) below. Click the icon to view the absence count and final exam score data Click the icon to view a table of critical values for the correlation coefficient. ..... he final exar (a) Find the least-squares Reference Absences and final exam scores (Round to three decimal Critical Values for Correlation Coefficient answer box (b) Interpret the slope an (Round to three decimal No. of 9. absences, x 0 1 2 3 4 5 6 7 3 0.997 t appropriate O A. For every addition 0.950 Final 86.7 83.6 80.2 78.3 73.5 64.7 72.2 65.9 65.9 O B. For every addition erage final e exam score, y 88.4 5 0.878 O C. The average final 0.811 terpret the sl 0.754 O D. It is not appropria 8 0.707 Print Done (c) Predict the final exam 6. 0.666 y =(Round to two de 10 0.632 11 0.602 Compute the residual. 12 0.576 (Round…
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. Click here to view the weight and gas mileage data. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. x + (Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as needed.) Car Weight and MPG Miles per Weight (pounds), x Gallon, y 3728 16 3911 15 2637 26 3617 20 3407 21 2905 24 3822 17 2579 25 Print Done Enter your answer in the edit fields and then click
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.6667, sy =2.3381, y = 3.9167, s, = 1.8563, and r= - (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 0.9570, determine the least-squares regression line. 1 1 y 5.1 6.4 5.1 2.8 1.9 2.2 (a) Choose the correct graph below. O A. В. Ay 7- Ay 7- Ay 7- X X 6 6 6. There appears to be a linear, negative relationship. (b) y =x+ (O (Round to three decimal places as needed.)
3. In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. Price = -6677 + 175 × Horsepower
Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.883 and the least squares regression line is y = 0.134x + 13.693. Complete parts (a) and (b) below. Height, x Head Circumference, y 17.4 27.75 25.25 26 25.25 27.25 26.75 26 27.25 27 27.25 26.75 17.1 17.3 17.0 17.4 17.2 17.2 17.3 17.3 17.4 17.3 ..... (a) Compute the coefficient of determination, R?. R? % (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately % of the variation in is explained by the least-squares gression model. (Round to one decimal place as needed.)
(b)

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS