Given the following quantities for a simple linear regression model results from a sample of sizen-8 observations: Σx-47.7,Σy = 315, Σ x ? 304.59, Σν2- 13527.0, Σxy = 1735.3 %3D %3D %3D a) Use the above information to calculate SSxy, SSyy, and SSxx- b) Use the quantities in a) above to calculate B, c) Calculate SSE and use it to calculate the estimated standard error of B1, s. d) Test Ho: B1 = 0 O against Ha:B, # 0 at a = 0.05 level of significance. %3D %3D
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- 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…A forecaster used the regression equation Qt = a + bt + c1D1 + c2D2 + c3D3 and quarterly sales data for 2004I–2021IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2 and D3 are dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 64 0.8768 107.982 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.80 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.00 3.33 0.0015 D2 25.0 7.20 3.47 0.0010 D3 40.0 15.80 2.53 0.0140 What is the estimated intercept of the trend line in the second quarter?A forecaster used the regression equation Qt = a + bt + c1D1 + c2D2 + c3D3 and quarterly sales data for 2004I–2021IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2 andD3 are dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 64 0.8768 107.982 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.80 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.00 3.33 0.0015 D2 25.0 7.20 3.47 0.0010 D3 40.0 15.80 2.53 0.0140 Using the estimation results given above, the predicted level of sales in 2022II is _______ units.
- Consider the following two a.m. peak work trip generation models, estimated by household linear regression: T = 0.62 + 3.1 X1 + 1.4 X2 R2= 0.590 (2.3) (7.1) (5.9) T = 0.01 + 2.4 X1 + 1.2 Z1 + 4.0 Z2 R2= 0.598 (0.8) (4.2) (1.7) (3.1) X1 = number of workers in the household X2 = number of cars in the household, Z1 is a dummy variable which takes the value 1 if the household has one car, Z2 is a dummy variable which takes the value 1 if the household has two or more cars. Compare the two models and choose the best. If a zone has 1000 households, of which 50% have no car, 35% have one car, and the rest have exactly two cars, estimate the total number of trips generated by this zone. Use the preferred trip generation model and assume that each household has an average of two workersin the regression specification y =α+βx +δz +ε, the parameter α is calledRefer to the following nonlinear model which relates W to P, Q, and R: W = aPbQcRd The computer output form the regression analysis is: DEPENDENT VARIABLE: LNW R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 2.50 0.45 5.56 0.0001 LNP -5.10 1.75 -2.91 0.0113 LNQ 12.40 3.20 3.88 0.0017 LNR -6.00 1.50 -4.00 0.0010 Based on the information in the table, the nonlinear relation can be transformed into the following linear regression model:
- Consider the following data for two variables, x and y x 9 32 18 15 26 y 9 20 22 17 23 A. Develop an estimated regression equation for the data of the form ŷ = b0 + b1x. (Round b0 to two decimal places and b1 to three decimal places.) B. Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to two decimal places and b1 to three decimal places and b2 to four decimal places.) C. Use the model from part (b) to predict the value of y when x = 20. (Round your answer to two decimal places.) Please be as detailed as possible in the solution so i may follow along. Thank you for the help!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.Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 4 11 14 Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y): Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 2.
- A random sample of twelve students were chosen, and their midterm test score (y), as- signment score (x1), and missed classes (x2) were recorded as follows: Midterm Score, y Assignment Score, x1 Classes Missed, x2 85 74 76 90 85 87 94 98 81 91 76 74 65 50 55 65 55 70 65 70 55 70 50 55 5 7 5 2 6 3 2 5 4 3 1 4 (i) What is the fitted multiple linear regression equation of the form yˆ = b0 + b1x1 + b2x2? (ii) From part (i) above, estimate the midterm test score grade for a student who has an assignment score of 60 and missed 4 classes.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 40 120 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) = Graph the associated points and regression line. (b) 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 education doctorates for each additional social science doctorate. The slope tells us the increase in the number…The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 40 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) = (b) Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =