(a) Use least-squares regression to fit a linear polynomial to the data given in the table below:2461012141618411.41 412.54 413.29 414.25 414.17 415.39 415.71 416.80 416.68Calculate the standard deviation for the regression line. Then, use the fitted linear formula toestimate the y-value at x 14.6. Round all your computations to 6 decimal points.(b) Repeat part (a) but with using the general least-squares estimation approach (i.e., the oneimplementing the matrix-vector form). Comment on the vector of residuals.Hint: You do not need to develop a program for this problem. Solve it manually and submit.

Given information: x y 2 411.41 4 412.54 6 413.29 8 414.25 10 414.17 12 415.39 14…

Answered: (a) Use least-squares regression to fit…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 33EQ

See similar textbooks

Similar questions

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
A manufacturer of widgets has developed the following table showing the monthly profit P, in dollars, at a monthly production level of N widgets. Number N Profit P 200 1000 250 1475 300 1900 350 2275 400 2600 (a) Judging on the basis of the table, should the profit P be modeled by a linear function or by a quadratic function of N? linearquadratic Find the appropriate regression model for P. (Round your coefficients to two decimal places.)P(N) =
Compute the least-squares regression equation for the given data set. Round the slope and y-intercept to at least four decimal places. 2 4 7 6 6 5 3 3 4 2
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number of social science doctorates for each additional education doctorate. The slope tells us the increase in the number of social science doctorates for each additional education doctorate.…
Consider the following table containing unemployment rates for a 10-year period. Unemployment Rates Year Unemployment Rate (%) 1 5.85.8 2 3.23.2 3 5.55.5 4 8.68.6 5 6.16.1 6 6.86.8 7 7.57.5 8 5.25.2 9 11.111.1 10 7.47.4 Step 1 of 2 : Given the model Estimated Unemployment Rate=β0+β1(Year)+εi,Estimated Unemployment Rate=�0+�1(Year)+��, write the estimated regression equation using the least squares estimates for β0�0 and β1�1. Round your answers to two decimal places.
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) =
The results of a sample of 7 data points are presented below in terms of the Average Daily Temperature (oF) and the Average Monthly Precipitation (inches): Average Daily temperature x 86 81 83 89 80 74 64 Average Monthly Precipitation y 3.4 1.8 3.5 3.6 3.7 1.5 0.2 d- Determine the regression line equation e- Plot the regression line on the scatter plot (on same graph) f- Calculate the standard error of estimate g- Find the 95% prediction interval for the 95oF average daily temperature
The overall purpose of regression analysis is: a) to lessen our error in making predictions b) to make perfect predictions, since all data points mustfall on the regression line c) to exploit the correlation between Y and X and use it to help make better predictions of Y d) two of the above e) three of the above f) none of the above
A manufacturer of widgets has developed the following table showing the monthly profit P, in dollars, at a monthly production level of N widgets. Numer N Profit P 200 700 250 1225 300 1700 350 2125 400 2500 a)Judging on the basis of the table, should the profit P be modeled by a linear function or by a quadratic function on N? b) Find the appropriate regression model for P. (Round your coefficients to two decimal places.) P(N)=
A sample of the number of sales per hour at Store X and the number of sales at Store Y at the same times is as indicated below. Find the Y-value of the regression line where X = 5. X Y 0 1 0 2 1 2 3 4 4 6
Suppose that a multiple linear regression model was fit to data and that the following output resulted: Coefficients: (Intercept)stop distancempgweight Estimate8.63315-0.06078 -0.037930.17295 Std. Error5.916410.073680.086610.08165 t value1.459-0.825 -0.438 2.118 Pr(>|t|)0.14820.41170.66260.0371 True or False? It is likely that at least one explanatory variable would be left in our model if a backwards selection process were performed. (Our significance level is 0.05 for all testing purposes.) True False

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Functions and Change: A Modeling Approach to Coll…

Algebra

ISBN:

9781337111348

Author:

Bruce Crauder, Benny Evans, Alan Noell

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS