Table 5 Student Enrollment at UIUCFall semesterNumber of students201242,883201343,398201443,603201544,087(a) Find the least-squares line for these data.(b) The university will build more student housing oncampus once enrollment exceeds 46,000. Based on yourmodel in part (a), in what year should the universitybuild more student housing?

Let fall semester be x and number of students be y. Then, x y x-x y-y (x-x)(y-y) (x-x)2 (y-y)2…

Answered: Table 5 Student Enrollment at UIUC Fall…

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

Similar questions

The datafile Gestation06 lists the average gestation period (in days) and longevity (in years) for a sample of animals, as reported in The World Almanac and Book of Facts 2006.Use the least squares line to calculate the fitted value and residual for a polar bear. [Hint: First, find the polar bear's longevity and gestation period in the datafile.]
A chemical company, seeking to study the effect of extraction time on the efficiency of an extraction operation, obtained the data from a table: Fit a straight line to the data given with the least squares method and use it to predict the extraction efficiency that would be expected when the extraction time is 35 minutes. x = Extraction time (minutes)y = Extraction efficiency (%)
The following table shows the percent of water and the number of calories in various canned soups to which 100 g of water are added. (show all the necessary solution) Percent Water in Soups % Water Calories 83.3 28 92.3 26 91.9 39 89.4 57 89.5 57 90.5 36 91.9 32 91.7 32 a. Find the equation of the least squares line for the data. b. Use the equation in part a to find the expected number of calories in a soup that is 87% water. c. Determine the correlation coefficient of the data.
The article “Characterization of Highway Runoff in Austin, Texas, Area” (J. of Envir. Engr., 1998: 131–137) gave a scatterplot, along with the least squares line, of x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot. x <‐ c(5, 12, 14, 17, 23, 30, 40, 47, 55, 67, 72, 81, 96, 112, 127) y <‐ c(4, 10, 13, 15, 15, 25, 27, 46, 38, 46, 53, 70, 82, 99, 100) Test at level 0.05 whether there is a useful linear relationship between rainfall and runoff,and then calculate a 95% confidence interval for the true average change in runoff volumeassociated with one unit (one m3) increase in rainfall volume.
Consider the following table of points in the plane: Fit a straight line to the data in the above table by the least squares method ( Work with two decimal digits)
How many indicator variables would be included in the model in order to prevent the least squares estimation from failing?
Define the concept of Weighted Least Squares?
Apply the linear least-squares method to each set of data to obtain a mathematical model showing the relationships between variables.
Ex[lain the Two Stage Least Squares Estimator?
Based on the least-squares criterion, the line that best fits a set of data points is the one with the _____ possible sum of squared errors.
Find the least-squares line for the given data(2,1),(3,2),(4,3),(5,2)
The shape of the mean-variance frontier that results from the combination of a riskless and arisky asset is…..:a. Is U-shaped, tilted 90 degrees clockwise.b. Is a straight line passing from the mean-variance points of the two assets.c. Is a hyperbola.d. Consists of two straight lines, each connecting one of the two assets to a risk-freeportfolio

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS