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- EXER 5.1: Given the observations (1,1), (2,3), (4,5), find the least squares estimates for m and b for the best fit line y=mx+b.3. Fit a least squares quadratic curve to the following data and estimate Y at X = 2.4 fig. 03 2 3. 4. గోలిగౌజి రర్ Y 1.7 1.8 2.3 2.3 A. The required least squares quadratic curve(parabola) and the estimated value of Y at X=2.4? * 大 O Y= 2- 0.5X + 0.2X^2; Y = 1.952 Y= 2-0.6X+ 0.2X^2; Y = 1.712 O Y= 2.1 - 0.5X + 0.2X^2;Y = 2.052 Y= 2- 0.5X + 0.4X^2; Y = 3.104Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.
- The data in the accompanying table are from a national vital statistics report. Entries in the tables are the birth rates (births per 1,000 of population) for a certain year. State Births State Births Alabama 14.0 Missouri 13.6 Alaska 16.4 Montana 13.0 Arizona 16.4 Nebraska 15.4 Arkansas 14.7 Nevada 16.3 California 15.5 New Hampshire 10.8 Colorado 14.7 New Jersey 13.1 Connecticut 11.6 New Mexico 15.5 Delaware 14.3 New York 13.3 District of Columbia 15.3 North Carolina 14.5 Florida 13.3 North Dakota 13.8 Georgia 15.6 Ohio 13.4 Hawaii 14.6 Oklahoma 15.4 Idaho 16.9 Oregon 13.4 Illinois 14.3 Pennsylvania 12.3 Indiana 14.4 Rhode Island 11.9 Iowa 13.9 South Carolina 14.2 Kansas 15.3 South Dakota 15.1 Kentucky 14.0 Tennessee 14.3 Louisiana 15.1 Texas 17.3 Maine 10.9 Utah 20.8 Maryland 13.6 Vermont 10.5 Massachusetts 12.3 Virginia 14.3 Michigan 12.1 Washington 13.8 Minnesota 14.4 West Virginia 12.3 Mississippi 15.6 Wisconsin 13.0 Wyoming 15.3Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isLet x, be the 1 × (k + 1) vector of explanatory variables for observation t. Show that the OLS estima- tor ß can be written as Dividing each summation by n shows that ß is a function of sample averages.
- ExeR. 2. PrOve That opTimaL Variance V = と」 Di bouND Saris Fies THe uppeR V < min AiIf the slope of a regression line (b1) is 1.5, then a) for every unit of change in x, there is a change of 1.5 units in y b) for every unit of change in y, there is a change of 1.5 in x. c) the score of each case is 1.5 times higher on yt han on x d)y causes Xwww.sd206.orx ← → CO QUESTIONS sd206.org bookmarks. E. Parallel Lines and Transversals-11/10/2022 07:45 ● Item 4 O Item 5 O Item 6 O Item 7 O Item 8 0 0 O Item 9 O Item 10 O Item 11 O Item 12 o O Item 13 O Item 14 O Item 15 O Item 16 O Item 17 O Item 18 Ingrid Lyons-FX E Edulastic: Form X E- Edulastic X M [EXTERNAL EN X b Answered: 5 TIX SIS Grades and At x app.edulastic.com/student/practice/636d007b09ab160008d204f9/class/62f3b538951d49af6e3cfbda/uta/636d0ffb13b2c800085ad878/itemld... Q BOOKMARK ✓ CHECK ANSWER X Q 4 + * 19 ☐ 5 LEFT + X :
- 3. An economist used the least squares procedure to fit a regression model of the form y₁ = B₁ + B₁x₁, +B₂x2, +,, where y is quantity demanded of a good (in million units), x, is price of the good (in cedis), x₂ is household income (in thousand cedis), and E, ~ N (0,0¹). Tabulated below are sums obtained 8 sets of observations Σ.y=483 2y =30567 Ex₁y=3068 Σχ =53 Σχ = 365 Σx₂y=3795 Calculations have produced the following matrix (x'x)' = 50.68462 -4.03077 0.33846 Ex=60 Σ.x = 472 Σxx, = 382 -3.18077] 0.23846 0.21346 a. Form the matrices: XX and X'Y. b. Use (X'X) and X'Y to compute the OLS estimates for B₁, i = 0,1,2. c. Write the fitted regression model and interpret the partial regression coefficients.Definea. rejection regionb. non rejection regionc. critical value(s) Please please answer thatassroom.google.com/u/1/c/MTQYOTAOOTY3NDA1/a/M]94MZYXNDUONJEX/details 5. Classify each of the following tables of values as linear or non-linear. (а) (b) (c) (d) y 3 -3 15 8. 15 6. 4 -4 13 6. 5 20 4 9. 2 -5 11 7. 25 12 4 -6 9. 8 -1 30 16 15 6. -7 7 -4 35 32 mm
