Answered: 4. Given the following data, do a… | bartleby

Linear Algebra: A Modern Introduction

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 31EQ

See similar textbooks

Related questions

Question

4. Given the following data, do a quadratic least squares polynomial fit using
P2(r) = ao + a1r + azx?.
Yi
Yi
Yi
-1.0
7.904
-0.3
0.335
0.4
-0.711
0.224
0.689
-0.9
7.452
-0.2 -0.271
0.5
-0.8
5.827
-0.1
-0.963
0.6
0.7
-0.7
4.400
-0.847
0.861
-0.6
2.908
0.1
-1.278
0.8
1.358
-0.5
2.144
0.2
-1.335
0.9
2.613
-0.4
0.581
0.3
-0.656
1.0
4.599

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

10. For the following data, compute the least squares regression line for predicting gpagiven SAT.SAT: 500 530 590 660 610 700 570 640gpa: 2.3 3.1 2.6 3.0 2.4 3.3 2.6 3.5
Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?̂ is the predicted value of ?, the size of the male crab in cm. ?̂=8.2052+0.5693? What is the value of ?̂ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal place
Table 14.17 The Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05? Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01? Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model? Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval. Calculate the 99 percent confidence interval for…
In Galton’s height data (Figure 7.1, in Section 7.1), the least-squares line for predictingforearm length (y) from height (x) is y = −0.2967 + 0.2738x.a) Predict the forearm length of a man whose height is 70 in.b) How tall must a man be so that we would predict his forearm length to be 19 in.?c) All the men in a certain group have heights greater than the height computed in part(b). Can you conclude that all their forearms will be at least 19 in. long? Explain.
Find the least-squares equation for the following pairs of data: x = earthquake magnitude 2.9 4.2 3.3 4.5 2.6 3.2 3.4 y = depth of earthquake (in km) 5 10 11.2 10 7.9 3.9 5.5 A. y = 2.16 + 0.221x B. y = 0.221 + 2.16x C. y = 2.16 + 0.312x D. y = 0.221 + 2.82x
Suppose the least squares regression line for predicting weight (in pounds) from height (in inches) is given by Weight= -110+3.5*(height) Which of the following statements is correct? l. A person who is 61 inches tall will weigh 103.5 pounds ll. For each additional inch of height, weight will decrease on average by 3.5 pounds. lll. There is a negative linear relationship between height and weight. a) l and lll only b) l and ll only c) ll only d) l only e) ll and lll only
Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?ˆ is the predicted value of ?, the size of the male crab in cm. ?ˆ=8.1312+0.5226? What is the value of ?ˆ when a male crab is 23.0736 months old? Provide your answer with precision to two decimal places. ?ˆ = Interpret the value of ?. The value of ?ˆis the predicted size of a crab when it is 23.0736 months old. the predicted incremental increase in size for every increase in age by 23.0736 months. the predicted number of crabs out of the 1,000 crabs collected that will be 23.0736 months old. the probability that a crab will be 23.0736 months old.
#3. What is the least squares regression line for the following set of data? y-hat = 2.18x + 27.74 y-hat = 2.14x + 27.44 y-hat = 1.94x + 26.24 y-hat =1.86x + 26.28
Based on the data presented in the table below, please calculate the values of b0 and b1 using OLS (ordinary least squares) and for the equation: q1 = β0 + β1pi + ui. qi pi 1 2 2 3 3 5
What is the least squares regression line for the following scatter plot? y-hat = 0.89x + 1.36 y-hat = 0.31x + 1.95 y-hat = 0.67x + 0.87 y-hat = 1.05x + 1.37
11/15 find the least squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable. Round to three decimal places as needed.
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS