![Consider the model yi = β나! +Axi2 + ei, eis i.i.d. N(0.c2). There are 15 observations and the sum of the squared observations is YY 3.03. Use the normal equations given below a) Give 98% confidence intervals for A and A- b) Perform an α = 0.05 test for H0 : = 0.5. The normal equations are 15.00 374.50 | |β| 74.50 9482.75] [A158.25 6.03](http://img.homeworklib.com/questions/31bb9980-f00d-11eb-94a9-755b790e65bc.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
Consider the model yi = β나! +Axi2 + ei, eis i.i.d. N(0.c2). There are 15 observations...
Consider the zero intercept model given by Yi = B1Xi + ei (i=1,…,n) with the ei...
Consider the zero intercept model given by Yi = B1Xi + ei (i=1,…,n) with the ei normal, independent, with variance sigma^2. For this mode (i) find the sum of (Yi –Yi-hat). (ii) find the sum of (Yi – Yi-hat)Xi. (iii) find the estimator of the error variance, sigma^2. (iv) is the estimator of the error variance biased?
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,......
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,... ,n. Let b1 = s^y/8r and bo = Y - b1 t be the least squared estimators of B1 and Bo, respectively. We showed in class, that N(B; 02/) Y~N(BoB1 T;o2/n) and bi ~ are uncorrelated, i.e. o{Y;b} We also showed in class that bi and Y 0. = (a) Show that bo is...
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ)...
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ), β-(A ,A, β), and σ2 are unknown parameters, zı, known constants with x1 +... + Xm-Tm+1 + +xn0 , zn are 1, write the model in vector form as Y = Xß+ε describing the entries in the matrix X. 2, Determine the least squares estimator β of β.
Exercise5 Consider a linear model with n -2m in which...
1) Consider n data points with 3 covariates and observations {xil, Гіг, xī,3, yi); i-1,.,n, and y...
1) Consider n data points with 3 covariates and observations {xil, Гіг, xī,3, yi); i-1,.,n, and you fit the following model, y Bo+B+B32+Br+e that is yi-An + ßiXiut Ali,2 + Asri,3 + Ei where є,'s are independent normal distribution with mean zero and variance ơ2 For a observed covariate vector-(1, ri, ^2, r3) (with the intercept and three regressor variables) and observed yg at that point a) write the expression for estimated variance for the fit zs at z. (Let...
linear stat modeling & regression 1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari...
linear stat modeling & regression
1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares ...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
1. Consider the simple linear regression model: Ү, — Во + B а; + Ei, where 1, . . , En are i.i.d. N(0,02), for i1,2,... ,n. Let b1 = s^y/8r and bo = Y - b1 t be the least squared estimators of B1 and Bo, respectively. We showed in class, that N(B; 02/) Y~N(BoB1 T;o2/n) and bi ~ are uncorrelated, i.e. o{Y;b} We also showed in class that bi and Y 0. = (a) Show that bo is...
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ), β-(A ,A, β), and σ2 are unknown parameters, zı, known constants with x1 +... + Xm-Tm+1 + +xn0 , zn are 1, write the model in vector form as Y = Xß+ε describing the entries in the matrix X. 2, Determine the least squares estimator β of β.
Exercise5 Consider a linear model with n -2m in which...
1) Consider n data points with 3 covariates and observations {xil, Гіг, xī,3, yi); i-1,.,n, and you fit the following model, y Bo+B+B32+Br+e that is yi-An + ßiXiut Ali,2 + Asri,3 + Ei where є,'s are independent normal distribution with mean zero and variance ơ2 For a observed covariate vector-(1, ri, ^2, r3) (with the intercept and three regressor variables) and observed yg at that point a) write the expression for estimated variance for the fit zs at z. (Let...
linear stat modeling & regression
1) Consider n data points with 3 covariates and observations {xn, ^i2, xi3,yid; i,,n, and you fit the following model, y Bi+Br2+Br+e that is yi A) +Ari,1 +Ari,2 +Buri,3 + єї where є,'s are independent normal distribution with mean zero and variance ơ2 . H the vectors of (Y1, . . . ,Yn). Assume the covariates are centered: Σίχί,,-0, k = 1,2,3. ere, n = 50, Let L are Assume, X'X is a diagonal matrix...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
Most questions answered within 3 hours.
-
Tip Calculator App
For this project, you will create a tip calculator Android
app. The user...
asked 4 minutes ago -
A first order chemical reaction has an energy of activation of
90.0 kJ/mol and a rate...
asked 1 hour ago -
Which statement is not correct?
Mutations change the sequence of nucleotides in DNA.
Mutations can be...
asked 3 hours ago -
An organization is not required to accommodate an employee's
disability when the accommodation would cause "undue...
asked 3 hours ago -
Mojo Mining has a bond outstanding that sells for $2,165 and
matures in 17 years. The...
asked 3 hours ago -
Olympic weightlifter Zoe Smith holds a 58 kg barbell over her
head, 2.1 meters above the...
asked 3 hours ago -
For sample average = 28 and a μ = 17 and a s = 4 and...
asked 3 hours ago -
A
short forward contract that was negotiated some time ago will
expire in three months and...
asked 3 hours ago -
If R = R1L2/L3, what is the measurement error dR based on the
rules of error...
asked 4 hours ago -
At equilibrium, the concentrations of N2(g),
O2 (g) and NO (g) in a sealed reaction vessel...
asked 4 hours ago -
Find P(X-bar > 15.5)
n=81, Mean=15, SD=1
asked 4 hours ago -
3. What percentage of search engine users don’t go to the next
page of search results?...
asked 4 hours ago