Answered: The below data on the production volume… | bartleby

MATLAB: An Introduction with Applications

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

Question

This educational content covers the analysis of production volume versus total cost for a manufacturing operation using regression analysis.

### Data Table:
The table below shows the relationship between production volume (in units) and total cost (in dollars).

| Production Volume (units) | Total Cost ($) |
|---------------------------|----------------|
| 400 | 3,900 |
| 450 | 4,900 |
| 550 | 5,300 |
| 600 | 6,000 |
| 700 | 6,500 |
| 750 | 6,900 |

### Regression Equation:
Using the provided data, the estimated regression equation is formulated as:

\[ \hat{y} = 1,029.33 + 7.92x \]

Where:
- \( \hat{y} \) is the estimated total cost.
- \( x \) is the production volume.

### Problem Analysis:
(a) **Point Estimate of Total Cost:**
The company's production schedule indicates that 500 units will be produced next month. Calculate the point estimate of the total cost for this volume. The answer should be rounded to the nearest cent.

(b) **Prediction Interval:**
Determine a 99% prediction interval for the total cost for next month and round the answers to the nearest cent.

(c) **Managerial Concerns:**
If the actual production cost next month is $5,900, assess if this value falls within the prediction interval. Discuss whether managers should be concerned about this cost by selecting the appropriate options: "inside" or "outside" the prediction interval.

This resource helps in understanding how to apply regression analysis in cost estimation and decision-making processes within a manufacturing context.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y = 1.405x – 12.307. Complete parts (a) and (b) below. Average Weekly Wages (state), x Average Weekly Wages (federal), y 751 760 791 817 835 881 924 951 1002 1047 1115 1149 1195 1250 1269 1300 (a) Find the coefficient of determination and interpret the result. 12 =O
Fit a linear regression model for the following data.
Personal wealth tends to increase with age as older individuals have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and records their total wealth (Y) and their current age (X). Data provided in the image. a. State the estimated regression line and interpret the slope coefficient.b. What is the estimated total personal wealth when a person is 50 years old?c. What is the value of the coefficient of determination? Interpret it. d. Test whether there is a significant relationship between wealth and age at the 10%significance level. Perform the test using the following six steps. Step 1. Statement of the hypothesesStep 2. Standardised test statisticStep 3. Level of significanceStep 4. Decision. Step 5. Calculation of test statistic. Step 6. Conclusion Please solve the d) part only.
1.
A statistical program is recommended. The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Television Gross Newspaper Advertising Advertising ($1,000s) ($1,000s) Revenue ($1,000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 1 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) y = 88.64 + 1.60x1 X (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of…
9 students were surveyed to see what their age is and what their income level is. Find the equation of the line using linear regression. We want to predict their age using their income. age 18 24 38 22 19 35 28 19 27 income 456 786 835 855 645 244 587 1400 975 Just a side note, the 19 year old is making 1400, would be considered an outlier since they are making way more than everyone else. (y=-.0061x+34.9874 4 decimals) y=30.3709-.0064
The City of Bellmore’s police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 What is the IV? What is the DV? If the mileage increases by one mile, what is the predicted increase in maintenance costs? If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?
The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 95% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $895. The equation of the regression line is y = 1.454x- 36.984. Wages (state), x Wages (federal), y 712 778 789 801 843 878 927 937 939 958 1,014 1,054 1,116 1,146 1,191 1,248 1,270 1,302 1,335 1,401 Construct and interpret a 95% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $895. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) O A. We can be 95% confident that when the average weekly wages of state government employees is $895, the average weekly wages of federal government employees will be between $ and…
The police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?
The following table shows the approximate amount of trash produced in an industrialized country from 1980 to 2000. Let x represent the year after 1980 (1980 is year 0) and y represent the amount of trash (millions of tons). Year Million Tons 1980 150 1990 202 2000 220 (a) Draw the graph for this data. (b) Find the equation of the regression line for the data. (Round your answers to one decimal place.)y = x + (c) Use the equation to predict the amount of trash y that will be produced in 2010 and 2015. (Round your answers to one decimal place.) 2010: _______million tons 2015: _______ million tons
A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is ý = 81 + 4x. Years of Annual Sales Salesperson Experience ($1,000s) 80 3 97 3 102 4 4 102 103 6. 8 101 10 119 8 10 123 9. 11 127 10 13 136 (a) Compute SST, SSR, and SSE. SST = SSR = SSE = (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line did…

Recommended textbooks for you

MATLAB: An Introduction with Applications

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

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 for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

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 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…

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

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

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