3. [3] Consider a simple linear regression model for (y, X),Yi = Bo + xiß1+ €;,where the e;'s are iid N(0, o²). Show that T2 = F, whereT =VMSres/SaaandMSRMSresare used to test the hypothesis Ho : B1 = 0 (in simple and multip

Answered: Image /qna-images/answer/c4fbee71-8238-4757-9fbd-c33c2d3cf46c.jpg

Answered: 3. [3] Consider a simple linear…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

See similar textbooks

Similar questions

The least squares regression line for a set of data is calculated to be y = 24.8 + 3.41x. (a) One of the points in the data set is (4, 37). Calculate the predicted value. (b) For the point in part (a), calculate the residual.
Which pair of data points are always on the regression line: Y = a + bx? (0, 0) (0, b) (X, Y) (a,0)
c) Give the expression of R˜^2 in terms of R^2 , and justify your answer.
A Perodua dealer has hired you to analyze automobile demand in 30 regional markets for MyVi Model. A regression analysis was conducted using the following model. Q, = a + b, P, + b, Y +b, P + b, A Where, Q, = quantity demanded per year of MyVi automobiles. P,= average price of MyVi automobiles in thousands, (RM40) Y = household income in thousands, (RM24) P= average price of Kia Rio automobiles in thousands, (RM45) A = advertising expenditures per year in thousands, (RM400) The results of the computer analysis based on data collected in 30 regional markets are shown below: Variable Coefficient Std Error t-statistics Intercept 2,000 1000 2.00 Pp -10 2.5 -4.00 Y 0.025 0.02 1.25 PM 1.5 3.33 А 0.0825 0.025 3.3 Coefficient of determination, R = 0.96 %3D Standard error of estimate, SEE = 5.0 c) Based on 95% confidence level, identify the independent variables which can significantly influence demand for MyVi (t 2s. a s005 = 2.06). d) Calculate the price elasticity of demand. Would a…
29. Below is the result of running linear regression in R. The least-squares regression equation is Call: Lm(formula = variable_C ~ variable_W) Coefficients: (Intercept) -5.5162 variable_W 0.2666 A. variable_W -5.5162 + 0.2666 * variable C B. variable C = -5.5162 + 0.2666 * variable W C. variable W = 0.2666 – 5.5162 * variable C D. variable_C = 0.2666 – 5.5162 * variable_W B. bO. None of the above. MacBook Air DD 80 888 000 F3 F4 F6 F7 F8 F9 F5 # $ & 8
O Suppose amultiple Regression Model 9 = B. + R, X1 +. . +RXk+ E ory=xB+E @EStiMate BS . O show that Bis unbiaS.
The number of murders and robberies per 100,000 population for a random selection of states are shown. Find the equation of the regression line y'=ax+b, and predict the number of robberies when x=4.5 murders murders,x: 2.4,2.7,5.6,2.6,2.1,3.3,6.6,5.7 robberies,y : 25.3,14.3,151.6,91.1,80,49,17.3,45.8
Use the general equation for the least square regression line to show that this line always passes through the point (x,y) * bars above the x and y.That is, set x=x(with a bar above the x) and show that the line predicts that y=y (with a bar above the y).
Some non-linear regressions can also be estimated using a linear regression model (using "linearization'). Assume that the data below show the selling prices y (in dollars) of a certain equipment against its age x (in years). We'd like to fit a non-linear regression in the form y= cd to estimate parameters c and d from the data by linearizing the model through In y= In c+ (In d)x = bo + b,x. y y 1 6312 5387 5697 4973 5734 4892 (Click the button to copy or download the data.) Using Excel ot other software, the non-linear regression model y = cdX can be estimated as: (Round c and d to four decimal places, inlcuding any zeros.)
Suppose that based on a sample of high schools, a researcher estimates via OLS the regression model Yi = 30,1 + 2,0,2 + x3,130,3 + x4,iß0,4 + Ui where y, denotes the percentage of students passing the grade 10 math test in high school i, x2, denotes average annual teacher compensation in high school i, 3, denotes 1000 * (staff to student ratio) in high school i and 4,i denotes student enrollment in high school i. Part of the Stata output is given on the following page. Using this output, test whether the data are consistent with the belief that an increase in the staff to student ratio leads to an increase in the percentage of students that pass the grade 10 math test. Be sure to justify your conclusion clearly. Stata output for Question 2(c): Source I Total I SS Model | 2422.93434 3 Residual | 42394.2462 404 y I df 44817.1805 407 Coef. x_2 I . 0004586 x_31 .0479199 -.0001976 x_4 | _cons | 2.274021 807.644779 104.936253 MS 110.115923 Std. Err. .0001004 .039814 .0002152 6.113794 t P>|t|…
2. We will show a link between regression and the T-test. Suppose we have data of written of the form (Yij, xj), equal to, (Y11, 1), (12, 1), (Yin, 1) (Y21, 1), (22,-1),..., (2n-1) And assume the model, Yij = Bo+B₁xj + Eij, where Eij id N(0.02) (a) Show that Bo Y. : = == +Y=-12. 2n (b) Show for the fitted values, Y₁₁ = Y₁., and Y2j = Y2. for 1jn (c) Show that ²= 82 for the pooled variance t-test (d) Show that the test statistic for the hypothesis test Ho₁ = 0, HA: B00 can be written as, Y₁. - Y2. T And therefore the pooled variance T-test can be written via the SLR equation
A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e

SEE MORE QUESTIONS

Recommended textbooks for you

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt