Consider the linear regression model Y; = Bo + B1X; +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:B1n = 43.2, SE(B1m)= 10.2,Ban0,m = 700, SE(B0,n) = 7.4.Assuming that the sample size is large enough, which one of the following is true about the 99% confidence interval for B1?a. The 99% confidence interval for Bị is [43.2 – V10.2 * 2.57, 43.2 + V10.2 * 2.57]O b. The 99% confidence interval for B1 is [43.2 – 10.2 * 1.96, 43.2+ 10.2 * 1.96]The 99% confidence interval for B1 is 43.2 – 10.2 * 2.57, 43.2 +10.2 * 2.57O d. None of the answers

The independent variable is annual income of individual. The dependent variable is home size. This…

Answered: Consider the linear regression model Y;…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

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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?
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 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
A surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: y-hat = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Yvette worked 10 hours and slept 8 hours. What is Yvette’s residual? 0.1 1 6 7
in the regression specification y =α+βx +δz +ε, the parameter α is called
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 female individual is _____.
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…
Based on the table below, compute the regression line that predicts Y from X. MX MY sX sY r10 12 2.5 3.0 -0.6
Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.6x2 – 7.8x3 + 1.8x4 (c) If x2 = 10, x3 = 7, and x4 = 7, what is the predicted value for x1? (Use 1 decimal place.) answer: -4.5 Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? answer:3.6 Suppose x2 increased by 2 units. What would be the expected change in x1? answer: 7.2 Suppose x2 decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 13 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.461. Construct a 95% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t 7.81 t critical ±
According to the summary result of linear regression model between A and B obtained from R given below, we can fit a regression line. Assume thatA has any value. If we decrease the value of A by 3, how would Y be affected?a) 58.8945 decreaseb) 58.8945 increasec) 29.8827 increased) 49.5142 decreasee) 29.8827 decrease
The following are data on the average weekly profits(in $1,000) of five restaurants, their seating capacities, andthe average daily traffic (in thousands of cars) that passestheir locations: Seating Traffic Weekly netcapacity count profitx1 x2 y120 19 23.8200 8 24.2150 12 22.0180 15 26.2240 16 33.5 (a) Assuming that the regression is linear, estimate β0, β1,and β2.(b) Use the results of part (a) to predict the averageweekly net profit of a restaurant with a seating capacityof 210 at a location where the daily traffic count averages14,000 cars.
What is the general formular for simple linear regression? * a) y = ßo + ß1x b) y = ß1 + ß0x c) none of the above d) both A and B

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