Consider the linear regression model Y; = Bo + BịX; + U; for each i = 1, ..., n with n = 1,000. X; represents the annual income ofindividual i (measured in $10,000) and Y; represents the home size (measured in square feet). We run an OLS regression and get:B1,n= 43.2, SE(B1,n) = 10.2,Bon0,n = 700, SE(Bon) == 7.4.Suppose that we want to test Ho : B1 = 0 against Hị : B1 > 0 at 5% significance level. Assuming that the sample size is large enough, whichcritical value z should we use?O a.z = 1.64O b.z = -1.64z = -1.96C.Od.z = 1.96

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Answered: Consider the linear regression model Y;…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section4.3: Fitting Linear Models To Data

Problem 34SE: For the following exercises, consider this scenario: The profit of a company decreased steadily...

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.
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?
For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span.The following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded years: (3,600,2000);(4,000,2001);(4,700,2003);(6,000,2006) 42. Use linear regression to determine a function y,where the year depends on the population, to threedecimal places of accuracy.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2 Day Date Weekday Daily Demand Weekend 1 4/25/2016 Mon 297 0 2 4/26/2016 Tue 293 0 3 4/27/2016 Wed 327 0 4 4/28/2016 Thu 315 0 5 4/29/2016 Fri 348 0 6 4/30/2016 Sat 447 1 7 5/1/2016 Sun 431 1 8 5/2/2016 Mon 283 0 9 5/3/2016 Tue 326 0 10 5/4/2016 Wed 317 0 11 5/5/2016 Thu 345 0 12 5/6/2016 Fri 355 0 13 5/7/2016 Sat 428 1 14 5/8/2016 Sun 454 1 15 5/9/2016 Mon 305 0 16 5/10/2016 Tue 310 0 17 5/11/2016 Wed 350 0 18 5/12/2016 Thu 308 0 19 5/13/2016 Fri 366 0 20 5/14/2016 Sat 460 1 21 5/15/2016 Sun 427 1 22 5/16/2016 Mon 291 0 23 5/17/2016 Tue 325 0 24 5/18/2016 Wed 354 0 25 5/19/2016 Thu 322 0 26 5/20/2016 Fri 405 0 27 5/21/2016 Sat 442 1 28 5/22/2016 Sun 454 1 29 5/23/2016 Mon 318 0 30 5/24/2016 Tue 298 0 31 5/25/2016 Wed 355 0 32 5/26/2016 Thu 355 0 33 5/27/2016 Fri 374 0 34 5/28/2016 Sat 447 1 35 5/29/2016…
The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old male individual is _____. a. $46,800 b. $49,800 c. $13.80 d. $13,800
The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown below. Find the regression equation. y = 34.661 + 0.433x y = 0.777 + 12.0623x y = 12.0623 + 0.777x y = 34.661 - 0.433x
in the regression specification y =α+βx +δz +ε, the parameter α is called
The managing director of a company wants to find whether there is a relationship between units of a product produced and the profits in a period of 12 months. Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Units produced (X)‘000 2 3 5 8 11 10 12 15 17 18 20 24 Profits (Y) ‘000 3 5 8 11 13 14 16 20 22 24 26 30 i. Calculate the regression equation of the form Y = a + bX and hence estimate the value of the profits when 25,000 units are produced. ii. Calculate the regression equation of the form X = a + bY and hence estimate the value of the units produced when 27,000 in profits is made. iii. Calculate and both the Pearson correlation coefficient and coefficient of determination, interpret both and justify in this case why it would be prudent to rely on the coefficient of determination rather than Pearson in decision…

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