linear model
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![Given the estimated linear model shown below, complete the following computations.
y = 13 + 5x, + 3x2 + 4X3
a. Compute y when x4
16, x2 = 14, and x3 = 11.
b. Compute y when x, = 27, x2 = 18, and x3 = 14.
c. Compute y when x, = 31, xX, = 27, and x3 = 22.
d. Compute y when x, = 11, x2 = 25, and
X3
= 31.
а.
a. y = 179
b. ý =]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53000c28-491d-41be-848a-14fc4791e71d%2Fda9fc578-1df3-4dfc-bb52-c24f68ae264a%2F5w9f1qq_processed.png&w=3840&q=75)
the equation is
a )
b)
c)
d)
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- Given the “data” determined by y = x^3 + (x-1)^2 with x = 0.1, 1.2, 2.3, and 2.9, calculate SSTO, SSR, and R^2. Then recalculate these using x = 0.3, 1, 2.45, and 2.8. Does where you collect your data (i.e., which values of x) appear to impact your interpretation of how good the linear model fits?.Given the estimated linear model shown below, complete the following computations.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.9 8.6 7.1 3.8 2.3 2.3 2.2 0.3 y 14.3 11 9.9 7.3 5.7 5.7 5.6 4.1 x = thousands of automatic weaponsy = murders per 100,000 residentsThis data can be modeled by the equation y=0.87x+3.75. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 5 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 10.5 thousand automatic weapons?Answer = Round to 3 decimal places.
- Given the following estimated linear modelŷ = 10 + 2x1 + 12x2 + 8x3a. What is the change in ŷ when x1 increases by 4?b. What is the change in ŷ when x3 increases by 1?c. What is the change in ŷ when x2 increases by 2?Find a linear model for the following data.x 4.0 4.5 4.6 4.9y 9.0 8.5 6.3 6.0 a) 3.5 x - 23.2 b) y = 2x + 3c) y = -3.5x+23.2d) y = –2x +15The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.5 8.5 6.7 3.8 2.6 2.5 2.3 0.4 y 13.9 11.4 9.5 7.1 6.3 6.2 6.1 4.2 x = thousands of automatic weaponsy = murders per 100,000 residents This data can be modeled by the equation y=0.86x+3.96. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. A) How many murders per 100,000 residents can be expected in a state with 1.8 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 9.7 thousand automatic weapons? Answer = Round to 3 decimal places.
- Find an equation of the form y=abx+csin(π2x)y=abx+csin(π2x) that fits the data belowBased on the data shown below, a statistician calculates a linear model y=2.41x+2.76y=2.41x+2.76. x y 4 12.5 5 14.35 6 16.9 7 20.65 8 22.1 9 23.95 Use the model to estimate the yy-value when x=9x=9y=y=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 population of a city in 2001 was 177,536 people. By 2010, the population of the city had grown to 189,793. (a) Assuming the population grows linearly, find the linear model, y=mx+b, representing the population x year since 2000. (round m and b to 3 decimal places) (b) Using the linear model from part (a), estimate the population in 2025. (round to the nearest whole number)Consider the following data set x: 1 2 3 4 5 y: 4 4.4 5.2 6.4 8 Fit it to a linear model and a quadratic model. Which model is better, and how do you know?1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.